SGN: Shifted Window-Based Hierarchical Variable Grouping for Multivariate Time Series Classification
Authors: Zenan Ying
Zhi Zheng
huijun hou
Tong Xu
Qi Liu
Jinke wang
Wei Chen
Venue: NeurIPS 2025 poster ()
Keywords: Deep Learning
Multivariate Time Series Classification
Primary area: deep_learning

Abstract: Multivariate time series (MTS) classification has attracted increasing attention across various domains. Existing methods either decompose MTS into separate univariate series, ignoring inter-variable dependencies, or jointly model all variables, which may lead to over-smoothing and loss of semantic structure. These limitations become particularly pronounced when dealing with complex and heterogeneous variable types.
To address these challenges, we propose SwinGroupNet (SGN), which explores a novel perspective for constructing variable interaction and temporal dependency.
Specifically, SGN processes multi-scale time series using (1)
Variable Group Embedding (VGE), which partitions variables into groups and performs independent group-wise embedding; (2) Multi-Scale Group Window Mixing (MGWM), which reconstructs variable interactions by modeling both intra-group and inter-group dependencies while extracting multi-scale temporal features; and (3) Periodic Window Shifting and Merging (PWSM), which exploits inherent periodic patterns to enable hierarchical temporal interaction and feature aggregation. Extensive experiments on diverse benchmark datasets from multiple domains demonstrate that SGN consistently achieves state-of-the-art performance, with an average improvement of 4.2% over existing methods. We release the source code at https://anonymous.4open.science/r/SGN.

SGN: Shifted Window-Based Hierarchical Variable Grouping for Multivariate Time Series Classification
Zenan Ying', Jinke Wang', Zhi Zheng'; Tong Xu',
Wei Chen', Qi Liu', Huijun Hou
State Key Laboratory of Cognitive Intelligence, University of Science and Technology of China NNo
(znying, wjk1008, chenweicw, liuqilq] @mail. ustc.edu. {tongxu, zhengzhi977 (rengzhhi7)@ustee @ustc. edu. cn huijun.houtnich wwwwhoh.ucccco.o.
Abstract
Multivariate time series (MTS) classification has attracted increasing attention across various domains, Existing methods either decompose MTS into separate univariate series, ignoring inter-variable dependencies, or jointly model all vari- ables, which may lead to over-smoothing and loss of semantic structure. These limitations become particularly pronounced when dealing with complex and hetero- geneous variable types. To address these challenges, propose SwinGroupNet (SGN), which explores a novel perspective for constructing variable interaction and temporal dependency. Specifically, SGN processes multi-scale time series using (1) Variable Group Embedding (VGE), which partitions variables into groups and performs independent group wise embedding: (2) Multi-Scale Group Win- dow Mixing (MGWM), which reconstructs variable interactions by modeling both intra-group and inter-group dependencies while extracting multi-scale temporal features; and (3) Periodic Window Shifting and Merging (PWSM), which exploits inherent periodie patterns enable hierarchical temporal interaction and feature aggregation. Extensive experiments on diverse benchmark datasets from multiple domains demonstrate that SGN consistently achieves state-of-the-ar performance, with an average improvement of 4.2% over existing methods. We release the source code at buttps://githhn com hate///olssoossS
Introduction
Multivariate time series (MTS) consist of multiple temporal variables, each representing distinct dynamic patterns over time. MTS classification, which aims to analyze and model these temporal signals jointly extract meaningful patterns for decision-making has demonstrated significant
importance across a wide range of application domains, including meteorology [ 2], healthcare
34, industrial monitoring 7), and human activity recognition [8, 99. In recent years, many
models have been developed specifically for temporal data analysis 100 11
12
13
[4
15 [6],
achieving impressive performance across diverse applications. Among these, Convolutional Neural Networks (CNNs) have demonstrated continual development the time series domain [8] 19 20) due to their strong ability extract local features along the temporal dimension and have been shown to strike an effective balance between performance and computational efficiency [2
In multivariate time series processing, in addition modeling along the temporal dimension, cap- turing the dependencies among variables is equally critical. However, the complex and intertwined
Corresponding author.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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dependencies among variables pose significant challenge for effective modeling. Existing works have mainly adopted two strategies for modeling variable relationships, namely independent modeling and mixed modeling. Specifically,
shown in Figure a.). independent modeling-bant based methods
treat multivariate data as collection univariate series and process each variable separately, thereby neglecting the inter-van variibla interdependencies. In contrast, shown in Figure [b)) mixed modeling-basee methods [24] [5] jointly model all variables by mixing them together. However, when dealing with complex and heterogeneous variable types, this strategy blurs the semantic distinc- tions between variables [26], leading to excessive smoothing and making difficult for the model to capture meaningful relationships [27].
22 23
Varity Series
Group Series
farity Series
Soft Assignment
Training
(a) Varity Independent
Update
Testing
Hard Assignment
Varity Series
(b) Varity Dependent
(c) Group Varity Interaction
Figure 1: Illustration for Variety Interaction. (a) Variety Independent. (b) Variety Dependent. (c) Our Group Variety Interaction.
To address these challenges, in this paper, introduce novel perspective for modeling variable dependencies by transforming global variable interactions into structured intra-group and inter- inter-group group relationships. Specifically, design the Variable Group Embedding (VGE) module, which partitions variables into groups based on an assignment matrix derived from their intrinsic similarity and performs independent group-wise embedding. As illustrated in Figure [c), the module employs soft assignments during training to allow flexible learning, and switches to hard assignments during inference ensure stable group structures. This design particularly effective when dealing with heterogeneous multivariate time series, as it enhances the model's capacity to capture diverse variable characteristics and their interactions.
Moreover, we segment the input sequence into small periodic windows and propose the Multi-Scale Group Window Mixing (MGWM) module, which reconstructs variable interactions by modeling both intra-group and inter-group dependencies while extracting temporal features at multiple scales. To further enhance the modeling of temporal dynamics, introduce the Periodic Window Shifting and Merging (PWSM) module, which leverages inherent periodic patterns to enable hierarchical temporal interaction and feature aggregation. By integrating both variable and temporal perspectives, we present the SwinGroupNet (SGN) architecture, which performs structured variable grouping and interaction modeling in the variable dimension, and efficient multi-scale feature extraction in the temporal dimension. Meanwhile, SGN effectively balances performance and computational efficiency while capturing long-range dependencies and complex temporal patterns in multivariate time series. Extensive experiments on diverse datasets from various domains demonstrate that SGN consistently achieves state-of- the-art results. Our main contributions are summarized as follows:
We propose novel variable interaction strategy that transforms variable relationships into intra-group and inter-group dependencies based on variable grouping, unveiling underlying patterns and enhancing the interpretability of variable relationships.

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Extensive experiments demonstrate that SGN consistently outperforms existing state-of- art methods, with an average accuracy gain 4.2% and achieves near-perfect performance several benchmarks, with accuracy approaching 100%.
We exploit the inherent periodic characteristics of time series to enable hierarchical temporal feature extraction, allowing CNN-based models capture long-term dependencies while maintaining high efficiency.
2 Related Work
2.1
Convolution in Time Series Analysis
In recent years, convolutional methods have seen increasing adoption in time series analysis. CNN- based models typically focus on local patterns, with convolutional kernels adept at capturing localized features from the input. To expand the receptive field and capture long-range temporal dependencies, employ dilated convolutions. MICN [17 integrates both local and global features through multi-scale extraction, enabling the modeling of complex temporal patterns. TimesNet
TCNs
28
29
18 transforms univariate time series into two-dimensional format via periodic decomposition and applies 2D convolutions to capture intra-period and inter-period patterns. ModernTCN [9] further extends the receptive field by utilizing large convolutional kernels. TVNet [20] reshapes ID sequences into 3D representations to extract hierarchical information across temporal dimensions. Despite these advancements, existing convolutional models often overlook the intricate dependencies between local and global contexts as well as heterogeneous variable interactions. Therefore, there
remains considerable room for improvement in developing models that comprehensively capture the complexity of multivariate time series.
2.2 Variable Modeling Strategies in Multivariate Time Series
In multivariate time series analysis, variable modeling strategies aim to capture the dependencies among multiple variables. Given the inherently complex inter-variable relationships in such data, explicitly modeling these dependencies is crucial for learning comprehensive representations and enhancing model performance. Existing approaches can be broadly categorized into two strategies. Methods such as PatchTST [22]. RLinear [16] treat each variable independently. enabling the model to specialize per variable. In contrast, models like TTransformer [24). Crossformer [25] mix all variables to learn cross- variable correlations, while CrossGNN 30 leverages graph structures to enhance the representation and understanding of variable interactions. These approaches have collectively
advanced the field of multivariate time series analysis. Prior studies [31 32
33 34 suggest that
duriable-indpennde models often offer greater model capacity. whereas variable-mixing strategies tend to exhibit improved robustness. However, striking balance between these strategies remains challenge. Recent work [35] 36
37 38 has explored the utility of variable clustering, yet in the time series domain, remains unclear how best to translate variable-to-cluster relationships into meaningful interactions and how clustering can be leveraged to enhance inter- variable modeling. This remains an open and promising direction for further research.
3 Method
As shown in Figure 2 we propose SwinGroupNet (SGN), model for multivariate time series classification that captures structured interactions among variable groups. Specifically, we design a Variable Group Embedding (VGE) module that segments the input sequence into short periodic windows and embeds variables into groups based on their similarity. Next, the Multi-Scale Group Window Mixing (MGWM) module extracts features along both the temporal and variable dimensions. Furthermore, the Periodic Window Shifting and Merging (PWSM) module exploits inherent periodic patterns to enable hierarchical interaction and aggregation of temporal features. Finally, a projection layer produces the classification output. The following sections provide detailed descriptions of each component.
3

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Time
Small Period
Period Merging
Period Shifting
Output Projection
Partitioning
Series Input
Multi-Scale Group Window
Multi--caale
Group Window
Variety Group
Mixing
Miking
embedding
Assignment Matrix
Group embedding
Depth Conv
Group intra Point Conv
Group Graup-inter inter Point Conv
28c
Variety
Depth
Similar Discover
Depth Conv
Figure 2: An illustration of the SwinGroupNet architecture.
3.1 Variable Group Embedding
In this module, we first group the different variables of each sample and perform interactions within and across groups capture the relationships among variables. For heterogeneous multivariate data, directly mixing all variables, including those with large differences, can cause over- wer-smoothing and confuse the semantic meanings between variables. On the other hand, modeling each variable independently would neglect the dependencies among them. By clustering variables into groups, our method strikes balance between these two extremes: it preserves the distinct properties of each variable while simultaneously mitigating interference among variables.
Specifically, for the input time series X CCLL where L represents the time length and C' denotes the number of variables, the feature channels C' are dynamically assigned to predefined groups G using the Gumbel-Softmax allocation mechanism [39] [40). Given categorical distribution, to avoid the collapse problem, instead of using randomly initialized unnormalized class logits, we compute the Brownian Distance Covariance (BDC) 41 between all variables. The specific formula is follows:
(C,
1
Σ $J=1
A
12
Here, A'y and Byy denote the elements of the centered distance matrices for X, and X2, respectively, which are derived from the Euclidean distances between observations in X2 and X2. Given the number of groups G, the similarity is then computed based the BDC distance, and K-means clustering is applied to obtain class logits vectors II = [Ti ................................ Ta], where each vector n, C For more details, refer Appendix And the Gumbel-Softmax sampling is defined as:
exp ((logme Tej + ET)/T)
Mss D exp (log Thj + (4)/T))
1= 1,1, G.
Here, 6 ~~ G00bel(0. 1) denotes noise sampled from a standard Gumbel distribution, used to enhance the exploration during assignment. The parameter 0 is the temperature that controls the smoothness of the resulting distribution. gradually annealed following an exponential decay schedule during training.
The input tensor X is grouped according to the assignment matrix M E RCG where Mjs denotes the soft assignment probability of variable to group i. We use Softmax-based soft assignment

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during training and one-hot hard assignment during evaluation. To avoid inconsistent assignments and unstable optimization, we introduce variable similarity regularization term guide the Gumbel- based assignment towards more reasonable groupings. During the training process, the cosine similarity S,y is dynamically computed with Variety X; and X, after normalizing the variables to obtain the similarity matrix S RCCC while incorporating the assignment matrix into the loss function. The specific regularization loss formula is as follows:
Simm ΣES,) S.y. 1I Mjl1? 1.j
Therefore, the final loss is given by L Liss BL and 3 is regularization parameter for balancing classification accuracy and cluster quality. Meanwhile, to facilitate effective intra-group and inter-group interactions after variable grouping, perform independent embeddings for each variable group.
3.2 Multi-Scale Group Window Mixing
Small Periodic Window Partitioning. Specifically, periodic patterns in time series often rely on information in the frequency domain. To capture this, first apply the Fast Fourier Transform (FFT) to the input data X and compute the mean of the amplitude spectrum [8].
A Avg(Amp(FFT((X)).
To achieve a better trade-off between performance and efficiency, instead of selecting the top-K periods with the highest amplitudes, we choose the smallest period among the top-K candidates as the cycle window.
(L]
Ss E argTopk (A), i == 1,2,.... K .K]. J
P = min
(5)
Each & corresponds the i-th dominant frequency component. Given the selected period window P. divide the time series into N [ segments, where zero-padding is applied the end if L is not divisible by P, obtain the output sequence X CxNxP Considering the extensibility of periodic patterns, we further incorporate multiple scales by merging additional period windows corresponding the remaining Top-K dominant frequencies. This approach allows extract multi-scale periodic information and enhance computational efficiency.
J,
Multi-Scale Group Window Extracting. Given multivariate time series X R CxXXxP to better extract temporal and variable features, We follow the design proposed by Liu 42 43 adopting a combination of depthwise convolution and pointwise convolution to separate temporal and variable information. Along the temporal dimension, we apply multiple convolution kernels of different receptive fields within each period window to perform multi-scale feature extraction like [18 44 45)
The extracted features from different scales are then aggregated through average pooling to enhance the robustness of the output representations. The detailed formulation is given as follows:
K-1
((k) (X), Y Σ (X),
= Vi (0, 1......... K 1},
(6)
where c(lk)()) denotes a grouped convolution operation applied at a specific scale parameterized by the kernel size k; Across the variable dimension, we decouple the full variable interactions into untra-group and inter-group interactions, effectively mitigating the oversmoothing issue commonly observed in deep architectures. Specifically, we apply separate pointwise convolutions within each group and across different groups, respectively, to jointly learn fine-grained dependencies among variables within group and higher-order relationships among different groups. The detailed structure of the Multi Swin Window block is illustrated in Figure]
5

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3.3 Periodic Window Shifting and Merging
Periodic Window Shifting. Although the above procedure successfully extracts features from small periodic windows, it lacks connections across different windows, which limits interactions across periodic segments. Inspired by the Swin Transformer [46], we leverage the phase shift property of periodic signals to enable efficient cross-window communication. Specifically, we first perform cyclic left shift of the input time series X by P/2 units, where is the periodic window length. We then redivide the shifted sequence into windows and extract the features accordingly. The process can be formulated as follows:
X Sshifeed = T_ (Reshape(X (C,NN.)))
where T_ denotes cyclic left shift operation by P/2 units. After feature extraction, we apply a cyclic right shift to restore the original temporal order. This operation introduces cross-window interactions while maintaining computational efficiency. By alternating between standard window partitioning and shifted partitioning, the model captures both intra-window and inter-window depen- dencies within the same periodic scale. Specifically, as shown in Figure this approach effectively enhances the model's 's ability to capture complex temporal patterns.
Original Time series
Shifted Time series
Perted
period
shift
period
Figure 3: Illustration Periodic Window Shifting Block.
Periodic Window Merging, Based on the extensibility periodic patterns, we further merge adjacent periodic windows to capture features over extended cycles. Specifically, two neighboring periodic segments are combined to generate representations corresponding 2 P-lengthh cycles. Notably, such extended periods often correspond to dominant frequencies among the top-k spectral components. To enhance computational efficiency, we employ an adaptive merging strategy based on the number of detected periodic windows. When the number of periods exceeds four, adopt exponentially decaying merging scheme, in which non-overlapping adjacent windows are progressively merged. In contrast, when fewer than four periods are present, switch to a linearly decaying merging strategy that allows overlapping windows, thereby enabling more effective feature extraction from larger periodic structures.
Experiments
Dataset. To evaluate the effectiveness of the proposed SwinGroupNet model, conduct extensive experiments on a diverse set multivariate time series datasets. The detailed main dataset information provided in Table [ Furthermore, comprehensively assess the generalization ability of model, we additionalTy select 10 multivariate datasets from the UEA Time Series Classification Archive, which was introduced by Bagnall [47]. For additional details on data characteristies and preprocessing, please refer to Appendix B
Baseline. We include 10 state-of-the-art time series methods baselines to comprehensively evaluate the performance of our proposed method. These methods include six Transformer-base models: Reformer [48], i'Trnsffrmer (24), Crossformer (25). FEDformer [14), PatchTST (22). Medformer
49
One MLP-based model: DLinear [[5] And three CNN-based models: MICN 177, TimesNet
18
TCN 19]
Implementation. In the main datasets, we adopt six evaluation metrics: Accuracy, Precision, Recall, Fl Score, AUROC, and AUPRC. The training process is conducted using five different random seeds

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Table Summary of the four benchmark datasets used in our experiments. The table lists the number
of samples, classes, channels, length, sampling rate and modality.
Datasets
Samples
Timestamps
Channel
Class
Sampling Rate
Modality
FileSize
TDBRAIN
6,240
256
33
256 Hz
EEG
57IMB
PTB-XL
191,400
250
12
5
250
ECG
4,28GB
FLAAP
13,123
100
6
HAR
60MB
UCI-HAR
10,299
128
9
50Hz
HAR
91MB
(41-45) on fixed training, validation, and test splits to compute the mean and standard deviation of the results. For the 10 multivariate datasets from the UEA Time Series Classification Archive, we follow the standard preprocessing protocol established by Wu [18]. See Appendix C. for more implementation details.
Table Performance comparison on Main Datasets from different domains. Bold values represent the best performance, and underlined values indicate the second-ber best scores.
Dataset
Model
Accuracy
Precision
Recall
F1 Score
AUROC
AUPRC
Reformer
87 +02:272 2.01
88.64
1.40
87.92
2.01
$7.85 2.08
96.30 +: 0.54
96.40 + 0.45
Crossforeer
81.56
81.97
2.25
81.56
81.50
2.20
91.20
91.51
FEDiomer
78.13 1: 1.98
78.52
1.91
78.13
1.98
78.04
2.01
1.86 86.56
86.48 1: 1.99
ITrunsfommrr
71.67
1.06
1.06
83.73
PacchTT
79.25 1 3.79
79.60
1.00-44.000 4.09
79.25
3.79
3.77 79.20
87.95
4.96
86.36 1: 6.67
TDBRAIN
Medformer
89.62
0.81
96.51
Dlincar
54.73 2.11
54.79 2:48
54.73
2.14
54.62 2.13
55.83 + 2.36
54.73 + 1.98
Timesnet
05.08
95.08
95.08 0.56
98.92
98.95
MICN
90.92 2.22
01.37
1.82
90.92
2.44
90.80
2.46
07.58
07.58.+111 1.84
97.62 + 1.93
ModemTTCN
87.00
88 $8.10= 1.38
2.03 87.60
87.51 2.13
95.72
95.87 0.91
SGN (Ours)
99.90 0.10
99.89
0.11
99.90
0.10
99.90 0.10
100.00
0.00
100.00 1: 0.00
Reformer
71.72 0.413
63.12 2 1.02
59.20
0.75
60.69 = 0.18
85 80 0.221
61.72 + 0.47
Crussoomer
73.30
0.35
0.33
67
FEDiormer
57.20 4 9.47
52.38 + 6.09
49.04 + 7.26
47.89 8.44
82. 4.17
52.31 + 7.03
TTranffomner
09.28 0.22
59.59 0.45
54.62 0.18
0.19
86.71 +
60.27
PatchTST
73.23 0.22
65.70
0.64
60.82 0.76
62.61 0.34
89.74 + 0.19
67.32 + 0.22
PTB-XL
Medformer
72.87
64.14
60.60
62.02 0.37
89.66 0.13
66.39 0.22
Dlincar
45.49 0.03
20.25 2.99 9.92
20.10 0.09
12.78 0.26
00.63:10.0
20.75 = 0.13
Timesnet
71.80 0.53
62.73 0.88
59.53 0.99
B0.72 0.49
88.27 0.65
63.53 1.07
MICN
67.33 4 0.36
56.98
0.93
51,90
0.81
53.29
0.52
85.63
0.29
57.70 0.49
ModemiTCN
72.85 0.19
63.68
0.43
60.20
0.82
61.33
0.64
89.54
66.00 1: 0.46
SGN (Ours)
73.80
0.34
65.88
0.47
62.17
0.61
63.43 0.49
0.17 90.25
67.76 0.58
Reforner
70.88 1 0.88
71.47
0.77
70.22
1.13
1.02 76.14
70.19
95.27 1 0.28
74.64 1. 1.24
Crossfomer
76.33
76.25
0.93
0.84
0.13
80.25
FEDfomeer
68.30 2.06
09 10018-40 0.96
67.60
+ 2.12
06.80
2.96
94.15 0.76
70.85 + 3.12
Tansformer
75.53 11
75.70 0.65
75.82
0.56
75.37 0.53
96.70 0.14
80.32 : 0.64
PachTTT
56.23 1. 0.22
56.21 0.69
55.45
0.24
55.37 0.35
88.92 0.09
38,40 0.28
FLAAP
Medformer
74.00 2.37
71.53 2.48
73.84
2.61
13.37 2.55
96.58 0.60
78.91 2.90
Dlincar
30.26 1. 1.46
27.46 1.06
28.20
0.99
25.71 0.49
70.76
26.70 0.23
Timesnet
73.79 0.94
73.55
0.78
0.92 73.57
72,82 0.96
95.70 05.70+-0.12
77.30 0.84
MICN
62.63 0.59
51.74
0.76
51.45
$1.45=0.00
50.84
0.56
85.35 0.332
48.81 0.45
ModemTCN
71.66 1.69
1.45 72.23
1.66 71.55
71.37 = 1.46
95.01 0.30
73.47 = 1.99
SGN (Ours)
80.81 0.41
80.
0.50 80.35
80.35
97.42 0.10
85.73 0.37
Reformer
90.00 +: 0.63
90.10
0.71 90.83
90.14 0.75
89.92 0.63
98.97
0.08
95.86 +: 0.29
Crossforeer
90.06
90.69
1.02
90.68 1.04
99.14 0.15
96.08 0.61
FEDfommer
86,90 +: 3.46
88.57 1: 0.99
87.58 3.15
87.71 2:21
97.66 1.08
92.87 1.61
Transformer
93.47 0.15
93.59
0.23
93.49
0.14
93.46 0.16
99.53 0.02
97.91 0.01
PutcTTST
86.83 + 0.68
87.59
0.68
87.15
+ 0.78
$7.17 0.77
98.43 0.12
93.57 0.50
UCI-HAR
Medformer
90.17 0.55
90.36
0.66
90.30
0.68
90.27 0.66
99. 90.10
95.81 + 0.75
Dlinear
61.28 1.26
60.59
1.34
59.37
1.36
58.83 1.00
84.70+-0.0
59.29 0.41
Timesnet
92.71 -
0.16 92.78
92.86 0.53
92.75 0.51
99.25 25.5
96.87 + 0.21
1:
ModemTTCN
92.75 1. 2.00
2.31 95.79
92.96
2.16 95.61
92.88
02.80 2.18
99.35 0.19
96.98 1 0.91
(Ours)
95.62
0.72
98.96 0.39
4.1 Result of Main Datasets
Setups. In our main experimental setup, the training, validation, and testing sets are partitioned either by subject or according to a fixed ratio, depending on the dataset characteristics. Samples from each subject are assigned to the respective sets following a fixed allocation ratio. Importantly, samples
7

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from the same subject are restricted to single subset to avoid any data leakage. This design ensures the independence and objectivity of model training and evaluation.
Results, As shown in Table 2 SGN consistently outperforms ten strong baseline models across four benchmark datasets of different types, achieving the best performance all evaluation metries. On average, in terms of accuracy, our method surpasses the second-bed best approach 4.2% Specifically, SGN yields significant improvements on TDBRAIN, FLAPP, and UCI-HAR, outperforming the second-best models by 4.8 %. 4.5 %. and 2.2% %. highlighting the advantage of modeling variable dependencies through variable grouping. Notably, on the TDBRAIN dataset, SGN achieves an impressive approaching 100 % accuracy. However, the performance gain on the PTB-XL dataset is relatively marginal. This can attributed the inherent variable similarity structure: TDBRAIN exhibits clear boundaries among variable clusters, enabling effective group-base basdd modeling, while PTB-XI. presents high similarity across variables with blurred boundaries, causing most variables to be grouped together. As result, group interactions degenerate into conventional mixed-varian approach. The variable similarity visualizations for each dataset are provided in Appendix [B.6]
Dataset
W++MUSE M.-FCN
TapNet ShapeNet
TodyNet
SVPT
ShapeHormer
MPTSNet
(Ours)
Articulary NecdReconntionn
99.0
97.3
98.7
98.7
98.7
99.3
99.0
97.7
Abrialiibiilation
33.3
26.7
33.3
40.0
46.7
40.0
53.3
53.3
66.7
BasicMotions
100.0
95.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
Cricket
100.0
91.7
95.8
98.6
100.0
100.0
94.4
94.4
DuckDuckGeese
57.5
67.5
57.5
72.5
58.0
70.0
64.0
68.0
64.0
Epilepsy
100.0
76.1
97.1
98.7
97.1
98.6
98.6
97.1
97.8
EthanolConcentraiee
13.3
37.3
32.3
31.2
35.0
33.1
41.1
43.3
44.5
ERing
43.0
13.3
13.3
13.3
91.5
93.7
87.4
94.4
95,9
FaceDetection
54.5
54.5
55.6
60.2
62.7
51.2
65.8
69.8
70.3
FingerMoverentss
58.0
$3.0
58.9
60.0
55.0
HandMovement Direction
36.5
36.5
37.8
33.8
64.9
39.2
41.9
63.5
75.7
Handwriting
60.5
28.6
35.7
45.1
43.6
43.3
30.2
34.4
50.4
Heurbeatt
72.7
66.3
75.1
75.6
75.6
79.0
81.5
75.6
77.1
L.bras
87.8
85.6
K5.0
85.6
85.0
88.3
95.5
87.2
83.9
LSST
59.0
37.3
56.8
$9.0
61.5
66.6
63.8
60.4
63.7
MotorImagery
50.0
51.0
59.0
61.0
64.0
65.0
N/A
NATOPS
87.0
88.9
93.9
88.3
97.2
90.6
96.1
94.4
98.3
PenDigits
94.8
97.8
98.0
97.7
98.7
98.3
99.1
98.9
99.1
PEMS-SF
N/A
69.9
75.1
75.1
78.0
86.7
N/A
94.2
PhonemeSpectra
19.0
11.0
17.5
29.8
30.9
17.6
29.3
14.4
23.1
RacketSports
93.4
80.3
86.8
88.2
80.3
84.2
88.8
87.5
93.4
SelfRegulationS(CP11
71.0
65.2
78.2
89.8
Se SelfRegulationSSC2
46.0
47.2
$5.0
$7.8
55.0
60.0
56.1
$7.2
60.6
StandWalkJJmp
33.3
6.7
40.0
$3.3
46.7
46.7
66.7
$3.3
53.3
UWaveGestureLibrray
91.6
89,4
90.6
90.0
Average Rank Number of Top-1
6.04
7.60
6.68
5,14
4.64
3.94
3.70
4,20
2.56
Wins Draws Loses
17
23
23
19
20
15
13
15
3
3
Table 3: Performance comparison with the recent advanced MTSSC-dedicated models on 25 UEA datasets. the table, 'N/A' indicates that the results for the corresponding method could not be obtained due to memory computational limitations
4.2 Result of UEA Multivariate Datasets
Setups. We selected multivariate time series datasets from the UEA Multivariate Time Series Classification Archive. All datasets have been preprocessed and standardized using established preprocessing techniques. To ensure comprehensive comparison, incorporated several state- of-the-art baseline methods into our evaluation framework like LSTNet [50), LightTS [51]. Rocket
[52] LSSL (53), Flowformer [54). MTSMixer [55). TVNet 20 TimeMixer++ (56) the UEA-10
datasets. Meanwhile, we incorporated WEASEL+MUSE 57].
MLSTM-FCN (58). TapNet [59],
ShapeNet (60), TodyNet (61, SVPT (62) ShapeFormer 66 and MPTSNet [64 the UEA-25
datasets, under the same experimental settings.
Results of UEA-10. As illustrated in Figure we present the average classification accuracy across ten UEA datasets. be observed that SGN surpasses the current best-performing model, TimeMixer++, and consistently outperforms other categories of models. Notably, MLP-base models

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exhibit subpar performance on classification tasks, which can be attributed to their lack of explicit modeling of dependencies among variables. In contrast, CNN-based models perform better due to their strong local feature extraction capabilities and ability to capture variable interactions. Complete results are provided in Appendix
Results of UEA-25. Our proposed SGN model consistently demonstrates superior performance across the 25 UEA multivariate time series classification datasets compared with eight state-of-the-a baseline models, as shown in Table 3 It achieves the best average rank of 2.56, the highest number of first-place results (14 datasets), and an overall best win-loss record against all competitors. Notably, SGN outperforms all other models in more than half of the datasets, while maintaining competitive performance in the remaining ones. Furthermore, it exhibits strong generalization ability across diverse domains, including human activity recognition, healthcare, and speech recognition tasks.
4.3 Ablation Studies
Ablation on Variable Grouping. To evaluate the effectiveness our pro- posed variable grouping strategy, we conduct ablation studies on the main datasets by removing specific compo- nents (w/o). The results, as shown Ta- ble demonstrate that performing both intra-group and inter-group interactions outperforms the strategy of directly mix- ing all variables. This confirms the ne-
RNN-based
Convolution-based MLP-based
Average Accuracy (80
Transformer-based
75.3
Ours
74.6
74.6
73.2
72.5
72.5
71.8
72.1
70.9
70.4
70.9
70.7
cessity and effectiveness of our struc- tured variable interaction design. Fur- thermore, we observe that inter-group interaction yields better performance than intra-grovd interaction alone, indi- cating that the model benefits more from capturing diverse dependencies across groups than from modeling redundant information among similar variables.
67.5
LSTNel
LEGL
DLimer
LighTss
MrS-Mbar
Rocket
TimesHet
TVNtet
ModternTCH
Timemizerr
informer
Fgotormet
Croastormer
PatchTST
Flowforner
SoN(uur))
Figure 4: UEA Classification Result of UEA-10 datasets.
Table 4: Ablation Study on Variable Grouping Module across Main Datasets.
Dataset
TDBrain
PTB-XL
FLAAP
UCI-HAR
Metric
Accuracy
Accuracy
F1
Accuracy
Accuracy
F1
Variable Group Embedding & Group Interaction
99.90
99.90
73.80
63.43
80.81
80.35
95.62
95.64
wio Variable Grouping Embeddiig
92.16
91.64
73.05
62.46
76.85
76.35
93.58
93.58
w/o Group-intra Interaction
99.81
99.81
72.19
61.02
73.82
73.63
91.62
91.69
w/o Group-inter Interaction
99.83
99.83
71.70
00.06
70.00
70.21
88.20
88.15
Ablation on Periodic Window Shifting and Merging, This module is designed to validate the effectiveness of extracting features using small periodic windows by leveraging periodic properties. We conduct experiments on the main datasets used in the previous sections, and the detailed results are presented Table As observed, the impact of periodic fusion is particularly significant, confirming its ability to effectively capture global patterns through multi- aggregation. Additional ablation studies on hyperparameter sensitivity and efficiency analysis are provided in Appendix [ and Appendix E respectively.
Table 5: Ablation Study on Periodic Window Module across Main Datasets.
Datuset
TDBruin
FTB-XL
FLAAP
UCI-HAR
Metric
Accuracy
Accurncy
F1
Accuracy
F1
Accuracy
Periodic Window Shifting & Merging
99.90
99.90
73.80
63.43
80.81
80.35
95.62
95.64 64.64
w/o Periodic Window Shifting
99.79
99.79
73.32
62.50
78.05
77.66
87.05
87.22
w/o Periodic Window Merging
99.58
99.58
72.81
62.31
69.68
68.77
77.79
77.83

---

4.4 Model Analysis.
Analysis of Variable Clustering. As illustrated Figure 5(a), the initial similarity matrix of variables in the TDBRAIN dataset computed using the BDC distance reveals distinct block structures. These structures indicate inherent similarity among subsets of variables even before model training. Figure 5 b) presents the Pearson correlation matrix computed from the model outputs under the best- best-performing setting without variable grouping. The results reveal highly diverse and complex relationships among variables, indicating that dependencies exist but are not explicitly structured.
In contrast, Figure (jc) shows the transformed correlation structure under the variable group- ing strategy. where correlations are aggregated both intra-group and inter-group levels. Af- ter training, the intra-group correlations are significantly stronger, suggesting tight depen- dency within groups, while inter-group cor- relations are considerably weaker, indicating minimal redundancy across groups. These re- sults demonstrate that variety grouping not only alleviates complex inter-variable depen- dencies and potential redundancies, but also enhances interpretability and performance in modeling multivariate relationships.
102
Group
RDC Stalariy
1.0
3.00
8.5
5.6
525
800
Analysis of Periodic Shifting and Merging, Figure 0 shows the temporal correlation across SGN layers on the UCI-HAR dataset using learned periodic windows. As observed, in the first layer, the temporal dependencies are pri- marily concentrated around local neighboring time points.
015
Nariety mtiking F'mmlatiin
SKN CorvaaCotriation
Figure 5: Visualization of TDBRAIN Variety mixing and Variety Grouping matrices.
In contrast, in the last layer, each time point exhibits high correlation with almost all points within the periodic window, demon- strating that SGN effectively integrates hier- archical periodic information. This enables the model to extend the local feature extrac- tion strength of convolutional networks to global temporal context, enhancing its ca- pacity for comprehensive temporal under- standing. Additional visualization results of other main datasets and experimental anal- yses are provided in Appendix [F for further reference.
1.
09
03
Time Stpp
04
0.7
Fayer
Last Layer
Figure 6: Visualization of time correlation under UCI- HAR dataset.
Conclusion
In this paper, we propose SwinGroupNet, a novel and effective framework for multivariate time series (MTS) classification. By leveraging the Variable Group Embedding strategy, we convert variable-level interactions into structured group-based representations. The Multi-Scale Group Window Mixing mechanism further enhances interaction modeling by capturing both intra-group and inter-group dependencies, while simultaneously extracting multi-scale temporal features to enrich temporal representations. Furthermore, the Periodic Window Shifting and Merging approach integrates hierarchical periodic information, enabling the model to better capture dynamic temporal patterns. SGN achieves state-of-the-ar performance across diverse datasets spanning multiple domains. Limitations and potential directions for future research are discussed in Appendix G
10

---

Acknowledgments and Disclosure of Funding
This work was supported in part by the grants from National Natural Science Foundation of China NNo.6222211,, U22B2059), in part by the Postdoctoral Fellowship Program and China Postdoctoral Science Foundation under Grant Number BX20250387. This work was also supported by USTC-NIO Smart Electric Vehicle Joint Lab.
References
[1] Rafal A. Angryk, Petrus C. Martens, Berkay Aydin, Dustin J. Kempton, Sushant S. Mahajan, Sunitha Basodi, Azim Ahmadzadeh, Xumin Cai, Soukaina Filali Boubrahimi, Shah Muhammad Hamdi, Michael A. Schuh, and Manolis K. Georgoulis. Multivariate time series dataset for space weather data analyties. Scientific Data, 2020.
[2] Markus Reichstein, Gustau Camps-Vall Bjom Stevens, Martin Jung, Joachim Denzler, Nuno Carvalhais, and Prabhat. Deep learning and process understanding for data-driven earth system science. Nat., 566(7733):195 2044, 2019.
[3] Yihe Wang, Yu Han, Haishuai Wang, and Xiang Zhang. Contrast everything: A hierarchical contrastive framework for medical time-series. Advances in Neural Information Processing Systems, 36, 2024.
[4] Dominik Klepl, Fei Hc, Min Wu, Daniel J. Blackburn, and Ptolemaios G. Sarrigiannis. Adaptive gated graph convolutional network for explainable diagnosis of alzheimer's discase using EEG data. CoRR, 05522344405874, 2023.
[5] Dani Kiyasseh, Tingting Zhu, and David A. Clifton. CLOCS: contrastive learning of cardiac signals across space, time, and patients. In Marina Meila and Tong Zhang, editors, Proceedings of the 38th International Conference on Machine Learning, ICMI. 2021, 18-24 July 2021, Virtual Event, volume 139 of Proceedings of Machine Learning Research, pages 5606-5615 PMLR, 2021.
[6] Pavel Filonov, Andrey Lavrentyev, and Artem Vorontsov. Multivariate industrial time series with cyber-attack simulation: Fault detection using an lstm-based predictive data model. CoRR. abs/16 1.2.66667, 2016.
[7] Mohammad Ali Nemer, Joseph Azar, Jacques Demerjian, Abdallah Makhoul, and Julien Bourgeois. A review of research on industrial time series classification for machinery based on deep learning. In 4th IEEE Middle East and North Africa COMMunications Conference, MENACOMM 2022, Amman, Jordan, December 6-8, 2022, pages 89-94. IEFE, 2022.
[8] Jaeho Kim, Hyewon Kang, Jaewan Yang. Haneul Jung, Seulki Lee, and Junghye Lee. Multi-task deep learning for human activity, speed, and body weight estimation using commercial smart insoles. IEEE Internet of Things Journal, 2023.
[9] Junru Chen, Tianyu Cao, Jing Xu, Jiahe Li, Zhilong Chen, Tao Xiao, and Yang Yang. Con4m: Context-aware consistency learning framework for segmented time series classification. In Amir Globersons, Lester Mackey, Danielle Belgrave, Angela Fan, Ulrich Paquet, Jakub M. Tomezak, and Cheng Zhang, editors, Advances Neural Information Processing Systems 38: Anmual Conference on Neural Information Processing Systems 2024, NewrlPS 2024, Vancouver, BC, Canada, December 10 15, 2024, 2024.
[10] Zheng Zhao, Weihai Chen, Xingming Wu, Peter CY Chen, and Jingmeng Liu. LSTM network: a deep learning approach for short-term traffic forecast. IET Intelligent Transport Systems, 11(2):68-75. 2017.
[11] Haixu Wu, Jiehui Xu, Jianmin Wang, and Mingsheng Long, Autoformer: Decomposition trans- formers with auto-correlation for long-term series forecasting. In Mare' Aurelio Ranzato, Alina Beygelzimer, Yann Dauphin, Percy Liang, and Jennifer Wortman Vaughan, editors, Advances in Neural Information Processing Systems 34: Annual Conference on Neural Information Processing Systems 202 I, NeurIPS 2021, December 14, 2021, virtual, pages 22419-22430, 2021.
11

---

[12] Haoyi Zhou, Shanghang Zhang, Jieqi Peng, Shuai Zhang, Jianxin Li, Hui Xiong, and Wancai Zhang. Informer: Beyond efficient transformer for long sequence time-series forecasting. In Thirty-Fifth AAAI Conference on Artificial Intelligence, AAAI 2021, Thirty-Thine Conference on Innovative Applications of Artificial Intelligence, IAAI 2021, The Eleventh Symposium on Educational Advances in Artificial Intelligence, EAAI 2021, Virtual Event, February 2-9, 2021, pages 11106-11115, AAAI Press, 2021.
[13] Yong Liu, Haixu Wu, Jianmin Wang, and Mingsheng Long. Non-stationary transformers: Exploring the stationarity in time series forecasting. In Sanmi Koyejo, S. Mohamed, A. Agarwal, Danielle Belgrave, K. Cho, and A. Oh, editors, Advances in Neural Information Processing Neural Information Processing Systems 2022, NeurIPS 2022, New Orleans, LA, USA, November 28- December 9, 2022, 2022.
Systems 35: Annual Conference
[14] Tian Zhou, Ziqing Ma, Qingsong Wen, Xue Wang. Liang Sun, and Rong Jin. Fedformer: Frequency enhanced decomposed transformer for long-term series forecasting. In Kamalika Chaudhuri, Stefanie Jegelka, Le Song, Csaba Szepesvári, Gang Niu, and Sivan Sabato, editors, International Conference on Machine Learning, ICML 2022, 17-23 July 2022, Baltimore, Maryland, USA, volume 162 of Proceedings of Machine Learning Research, pages 27268- 27286. PMLR, 2022.
[15] Ailing Zeng, Muxi Chen, Lei Zhang, and Qiang Xu. Are transformers effective for time series forecasting? In Brian Williams, Yiling Chen, and Jennifer Neville, editors, Thirty-Seventh AAAI Conference on Artificial Intelligence, AAAI 2023, Thirty-Fifth Conference Innovative Applications of Artificial Intelligence, IAAI 2023, Thirteenth Symposium on Educational Ad- vances in Artificial Intelligence, FAAI 2023, Washington, DC, USA, February 7-14, 2023, pages 11121-11128. AAAI Press, 2023.
[16] Zhe Li, Shiyi Qi, Yiduo Li, and Zenglin Xu. Revisiting long-term time series forecasting: investigation on linear mapping. CoRR, abs/2305. 10721, 2023.
[17] Huiqiang Wang, Jian Peng, Feihu Huang, Jince Wang, Junhui Chen, and Yifei Xiao. MICN: multi-scale local and global context modeling for long-term series forecasting. In The Eleventh International Conference on Learning Representations, ICLR 2023, Kigali, Rwanda, May 1-5, 2023. OpenReview.net, 2023.
[18) Haixu Wu, Tengge Hu, Yong Liu, Hang Zhou, Jianmin Wang, and Mingsheng Long. Timesnet: Temporal 2d-variation modeling for general time series analysis. In The Eleventh Interna- tional Conference on Learning Representations, ICLR 2023, Kigali, Rwanda, May 1-5, 2023. OpenReview.net 2023.
[19] Donghao Luo and Xue Wang. Modernten: A modern pure convolution structure for general time series analysis. In The Twelfth International Conference on Learning Representations, ICLR 2024, Vienna, Austria, May 7-11, 2024. OpenReview.net, 2024.
[20] Chenghan Li, Mingehen Li, and Ruisheng Diao. TVNet: A novel time series analysis method based on dynamic convolution and 3d-variation. In The Thirfeenth International Conference on Learning Representations, 2025.
[21] Ao Wang, Hui Chen, Zijia Lin, Hengjun Pu, and Guiguang Ding. Repvit: Revisiting mobile CNN from vit perspective. CoRR. fos/2307.09288. 2023.
[22] Yuqi Nie, Nam H. Nguyen, Phanwadee Sinthong, and Jayant Kalagnanam. A time series is worth 64 words: Long-term forecasting with transformers. The Eleventh International Conference on Learning Representations, ICLR 2023, Kigali, Rwanda, May 1-5, 2023. OpenReview.net, 2023.
[23] Jaeho Kim, Seok-Ju Hahn, Yoontae Hwang, Junghye Lee, and Seulki Lee. CAFO: feature- centric explanation on time series classification. In Ricardo Baeza- Yates and Francesco Bonchi, editors, Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, KDD 2024, Barcelona, Spain, August 25-29, 2024, pages 1372-1388 ACM, 2024.
12

---

[24] Yong Liu, Tengge Hu, Haoran Zhang, Haixu Wu, Shiyu Wang, Lintao Ma, and Mingsheng Long. itransformer. Inverted transformers are effective for time series forecasting. In The Twelfth International Conference on Learning Representations, ICLR 2024, Vienna, Austria, May 7-11, 2024. OpenReview.net, 2024.
[25] Yunhao Zhang and Junchi Yan. Crossformer: Transformer utilizing cross dros-dimmnnsoon dependency for multivariate time series forecasting. In The Eleventh International Conference on Learning Representations, ICLR 2023, Kigali, Rwanda, May 1-5, 2023. OpenReview.net, 2023.
[26] Shoaib Ahmed Siddiqui, Dominique Mercier, Mohsin Munir, Andreas Dengel, and Sheraz Ahmed. Tsviz: Demystification of deep learning models for time-series analysis. IEFE Access, 7:67027-67040, 2019.
[27] Jialin Chen, Jan Eric Lenssen, Aosong Feng, Weihua Hu, Matthias Fey, Leandros Tassiulas, Jure Leskovec, and Rex Ying. From similarity to superiority: Channel clustering for time series forecasting. In Amir Globersons, Lester Mackey, Danielle Belgrave, Angela Fan, UIrich Paquet, Jakub M. Tomezak, and Cheng Zhang, editors, Advances in Neural Information Processing Systems 38: Annual Conference on Neural Information Processing Systems 2024, NeurIPS 2024, Vancouver, BC, Canada, December 10 15, 2024, 2024.
[28] Shaojie Bai, J. Zico Kolter, and Vladlen Koltun. An empirical evaluation of generic convolu- tional and recurrent networks for sequence modeling. CoRR, abs/ 0ess/8803.0177., 2018.
[29] Rajat Sen, Hsiang-Fu Yu, and Inderjit S. Dhillon. Think globally, act locally: A deep neural network approach to high-dimensional time series forecasting. In Hanna M. Wallach, Hugo Larochelle, Alina Beygelzimer, Florence d' Alché-Buc, Emily B. Fox, and Roman Garnett, editors, Advances in Neural Information Processing Systems 32: Annual Conference on Neural Information Processing Systems 2019, NeurlPS 2019, December 8-14, 2019, Vancouver, BC, Canada, pages 4838 4847, 2019.
[30]
Qihe Huang, Lei Shen, Ruixin Zhang, Shouhong Ding, Binwu Wang, Zhengyang Zhou, and Yang Wang. Crossgnn: Confronting noisy multivariate time series via cross interaction refine- ment. In Alice Oh, Tristan Naumann, Amir Globerson, Kate Saenko, Moritz Hardt, and Sergey Levine, editors, Advances in Neural Information Processing Systems 36: Annual Conference on Neural Information Processing Systems 2023, NeurlPS 2023, New Orleans, LA, USA, December 10 16, 2023, 2023.
[31] Peiwen Yuan and Changsheng Zhu. Is channel independent strategy optimal for time series forecasting? CoRR, abs/2310.17658, 2023.
[32] Lu Han. Han-Jia Ye, and De-Chuan Zhan. The capacity and robustness trade-off: Revisiting the channel independent strategy for multivariate time series forecasting. IFFE Trans. Knowl. Data Eng., 1129-7274 2024.
[33] Pablo Montero-Manss and Rob J. Hyndman. Principles and algorithms for forecasting groups of time series: Locality and globality. CoRR, abs/2008.00444 2020.
[34] Xue Wang, Tian Zhou, Qingsong Wen, Jinyang Gao, Bolin Ding, and Rong Jin. CARD: channel aligned robust blend transformer for time series forecasting. In The Twelfth Interna- tional Conference on Learning Representations, ICLR 2024, Vienna, Austria, May 7-11, 2024. OpenReview.net, 2024.
[35] Jung- Yi Jiang, Ren-Jia Liou, and Shie-Jue Lee. A fuzzy self-constructing feature clustering algorithm for text classification. IEFE Trans. Knowl. Data Eng., 23(3):335-349, 201
[36] Dmitrii Marin, Jen-Hao Rick Chang, Anurag Ranjan, Anish Prabhu, Mohammad Rastegari, and Oncel Tuzel. Token pooling in vision transformers for image classification. In IEEE/CVF Winter Conference on Applications of Computer Vision, WACV 2023, Waikoloa, HI, USA, January 2-7, 2023, pages 12-21. IEEE, 2023,
[37] Hao Li, Alin Achim, and David R. Bull. Unsupervised video anomaly detection using feature clustering. IET Signal Process., 6(5):521-533, 2012.
13

---

[38] Lijimol George and P Sumathy. An integrated clustering and bert framework for improved topic modeling. International Journal of Information Technology, pages 1-9, 2023.
[39] Eric Jang, Shixiang Gu, and Ben Poole. Categorical reparameterization with gumbel-softmax In 5th International Conference on Leurning Representations, ICLR 2017, Toulon, France, April
24-26, 2017, Conference Truck Proceedings. OpenReview.net, 2017.
[40] Chris Maddison, Andriy Mnih, and Yee Whye Teh. The concrete distribution: A contin- uous relaxation of discrete random variables. In 5th International Conference on Learning Representations, ICLR 2017, Toulon, France, April 24-26, 2017, Conference Track Proceedings. OpenReview.net, 2017.
[41] Gâbor J Székely, Maria L Rizzo, and Nail K Bakirov. Measuring and testing dependence by correlation of distances. The Annals of Statistics, 35(6):2799-2794, 2007.
[42] Zhuang Liu, Hanzi Mao, Chao-Yuan Wu, Christoph Feichtenhofer, Trevor Darrell, and Saining Xie. A convnet for the 2020s. In Proceedings of the IEEE/CVE Conference on Computer Vision and Pattern Recognition (CVPR), pages 11976-11986, 2022.
[43] Yazan Abu Farha and Jürgen Gall. MS-TCN: multi-stage temporal convolutional network for action segmentation. In IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2019, Long Beach, CA, USA, June 16-20, 2019, pages 3575-3584, Computer Vision Foundation / IEEE, 2019.
[44] Liu Che, Tong Xu, Qi Liu, Zhi Zheng, Jingyu Peng, and Enhong Chen. MERGE: multi-view relationship graph network for event-driven stock movement prediction. In Wenjie Zhang, Anthony K. H. Tung, Zhonglong Zheng, Zhengyi Yang. Xiaoyang Wang, and Hongjie Guo, editors, Web and Big Data 8th International Joint Conference, APWeb- WAIM 2024, Jinhua, China, August 30- September 1, 2024, Proceedings, Part III, volume 14963 of Lecture Notes in Computer Science, pages 239-239. Springer, 2024.
[45]
Qi Liu, Jingqing Ruan, Hao Li, Haodong Zhao, Desheng Wang, Jiansong Chen, Wan Guanglu, Xunliang Cai, Zhi Zheng, and Tong Xu. AMoPO: Adaptive multi-objective preference optimiza- tion without reward models and reference models. In Wanxiang Che, Joyce Nabende, Ekaterina Shutova, and Mohammad Taher Pilehvar, editors, Findings of the Association for Computa- tional Linguistics: ACL 2025, pages 8832-8866 Vienna, Austria, July 2025, Association for Computational Linguistics.
[46] Ze Liu, Yutong Lin, Yue Cao, Han Hu, Yixuan Wei, Zheng Zhang, Stephen Lin, and Baining Guo. Swin transformer: Hierarchical vision transformer using shifted windows. In 2021 IEEE/CVF International Conference on Computer Vision ICCV 2021, Montreal, QC, Canada, October 10-17, 2021, pages 9992-10002. IEEE, 2021.
[47] Anthony J. Bagnall, Hoang Anh Dau, Jason Lines, Michael Flynn, James Large, Aaron Bostrom, Paul Southam, and Eamonn J. Keogh. The UEA multivariate time series classification archive, 2018. CORR, abs/ 881 100075, 2018.
[48] Nikita Kitaev, Lukasz Kaiser, and Anselm Levskaya. Reformer: The efficient transformer. In 8th International Conference on Learning Representations, ICLR 2020, Addis Ababa, Ethiopia, April 26-30, 2020. OpenReview.net, 2020.
[49] Yihe Wang, Nan Huang, Taida Li, Yujun Yan, and Xiang Zhang. Medformer: multi- granularity patching transformer for medical time-series classification. In Amir Globersons, Lester Mackey, Danielle Belgrave, Angela Fan, Ulrich Paquet, Jakub M. Tomezak, and Cheng Zhang, editors, Advances in Neural Information Processing Systems 38: Annual Conference on Neural Information Processing Systems 2024. NeurIPS 2024, Vancouver. BC, Canada, December 10- 15, 2024, 2024.
[50] Guokun Lai, Wei-Cheng Chang, Yiming Yang, and Hanxiao Liu. Modeling long- and short- term temporal patterns with deep neural networks. In Kevyn Collins-Thompson. Qiaozhu Mei, Brian D. Davison, Yiqun Liu, and Emine Yilmaz, editors, The 41st International ACM SIGIR Conference on Research Development Information Retrieval, SIGIR 2018, Ann Arbor, MI, USA, July 08- 12, 2018, pages 95- 104. ACM, 2018
14

---

[51] Tianping Zhang, Yizhuo Zhang, Wei Cao, Jiang Bian, Xiaohan Yi, Shun Zheng, and Jian Li. Less is more: Fast multivariate time series forecasting with light sumpling-orient oriented MLP structures. CoRR, abs/2207 .11 186, 2022.
[52] Angus Dempster, François Petitjean, and Geoffrey I. Webb. ROCKET: exceptionally fast and accurate time series classification using random convolutional kernels. Data Min. Knowl. Discov. 34(5):1454-1495 2020.
[53] Albert Gu, Karan Goel, and Christopher Ré. Efficiently modeling long sequences with structured state spaces. In The Tenth International Conference Learning Representations. ICLR 2022, Virtual Event, April 25-29, 2022. OpenReview.net, 2022.
[54] Haixu Wu, Jialong Wu, Jiehui Xu, Jianmin Wang, and Mingsheng Long. Flowformer: Lineariz- ing transformers with conservation flows. Kamalika Chaudhuri, Stefanie Jegelka, Le Song, Csaba Szepesvári, Gang Niu, and Sivan Sabato, editors, International Conference on Machine Learning, 2022, 17-23 July 2022, Baltimore, Maryland, USA, volume 162 of Proceedings of Machine Learning Research, pages 24226-24244 PMLR, 2022.
[55] Zhe Li. Zhongwen Rao, Lujia Pan, and Zenglin Xu. Mts-mixers Multivariate time series forecasting via factorized temporal and channel mixing. CoRR, abs/2302.00401,, 2023.
[56) Shiyu Wang, Jiawei LI, Xiaoming Shi, Zhou Ye, Baichuan Mo, Wenze Lin, Ju Shengtong, Zhixuan Chu, and Ming Jin. Timemixer++: A general time series pattern machine for universal predictive analysis. In The Thirteenth International Conference on Learning Representations, 2025.
[57] Patrick Schäfer and Ulf Leser. Multivariate time series classification with WEASEL+MUSE. CoRR, abs/1711..1144 2017.
[58] Fazle Karim, Somshubra Majumdar, Houshang Darabi, and Samuel Harford. Multivariate Istm-fens for time series classification. Neurul Networks, 116:237-245, 2019.
[59] Xuchao Zhang, Yifeng Gao, Jessica Lin, and Chang-Tien Lu. Tapnet: Multivariate time series classification with attentional prototypical network. In The Thirty-Fourth AAAI Conference on Artificial Intelligence, AAA! 2020, The Thirty-Second Innovative Applications of Artificial Intelligence Conference, IAAI 2020, The Tenth AAAI Symposium on Educational Advances in Artificial Intelligence, EAAI 2020, New York, NY, USA, February 7-12, 2020, pages 6845-6852. AAAI Press, 2020.
[60]
Guozhong Li, Byron Choi, Jianliang Xu, Sourav S. Bhowmick, Kwok-Pan Chun, and Grace Lai- Hung Wong. Shapenet: A shapelet-neural network approach for multivariate time series classification. In Thirty-Fifth AAAI Conference on Artificial Intelligence, AAAI 2021, Thirty- Third Conference on Innovative Applications of Artificial Intelligence, IAAI 2021, The Eleventh Symposium on Educational Advances in Artificial Intelligence, EAAI 2021, Virtual Event, February 2-9, 2021, pages 8375-8383 AAAI Press, 2021.
[61] Huaiyuan Liu, Donghua Yang. Xianzhang Liu, Xinglei Chen, Zhiyu Liang, Hongzhi Wang, Yong Cui, and Jun Gu. Todynet: Temporal dynamic graph neural network for multivariate time series classification. Inf. Sci., 677:120914, 2024.
[62] Rundong Zuo, Guozhong Li. Byron Choi, Sourav S. Bhowmick, Daphne Ngar-yin Mah, and Grace Lai-Hung Wong. SVP-T: A shape-level pariable-position transformer for multivariate time series classification. In Brian Williams, Yiling Chen, and Jennifer Neville, editors, Thirty-Seventh AAAI Conference on Artificial Intelligence, AAAI 2023, Thirty-Fifih Conference on Innovative Applications of Artificial Intelligence, IAAI 2023. Thirteenth Symposium Educational Advances in Artificial Intelligence, EAAI 2023, Washington, DC, USA, February 7-14, 2023, pages 1 11497-11551 11505. AAAI Press, 2023.
[63] Muan-May Le, Ling Luo, Uwe Aickelin, and Minh-Tuan Tran. Shapeformer: Shapelet trans- former for multivariate time series classification. In Ricardo Baeza- and Francesco Bonchi, editors, Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, KDD 2024, Barcelona, Spain, August 25-29, 2024, pages 1484-1494 ACM, 2024.
15

---

[64] Yang Mu, Muhammad Shahzad, and Xiao Xiang Zhu. Mptsnet: Integrating multiscale periodic local patterns and global dependencies for multivariate time series classification. In Toby Walsh, Julie Shah, and Zico Kolter, editors, AAAI-25, Sponsored by the Association for the Advancement of Artificial Intelligence, February 25- March 4, 2025, Philadelphia, PA, USA, pages 19572-19580. AAAI Press, 2025.
[65] Stuart P. Lloyd. Least squares quantization in PCM. IEEE Trans. Inf. Theory, 28(2): 1982.
[66] Hanneke van Dijk, Guido van Wingen, Damiaan Denys, Sebastian Olbrich, Rosalinde van Ruth, and Martijn Arns. The two decades brainclinics research archive for insights in neurophysiology (tdbrain) database. Scientific Data, 9()):333, 2022.
[67] Patrick Wagner, Nils Strodthoff, Ralf-Dieter Bousseljot, Dieter Kreiseler, Fatima I Lunze, Wojeiech Samek, and Tobias Schaeffter. Ptb-xl: large publicly available electrocardiography dataset. Scientific Data, 7(1):1-15, 2020.
[68] Prabhat Kumar and S Suresh. Flaap: An open human activity recognition (har) dataset for learning and finding the associated activity patterns. Procedia Computer Science, 212:64-73, 2022.
[69] Davide Anguita, Alessandro Ghio, Luca Oneto, Xavier Parra, Jorge Luis Reyes-Ortiz, al. public domain dataset for human activity recognition using smartphones. In European Symposium Artificial Neural Networks (ESANN), volume 3, page 3, 2013.
[70] Diederik P. Kingma and Jimmy Ba. Adam: A method for stochastic optimization. Yoshua Bengio and Yann LeCun, editors, 3rd International Conference on Learning Representations, ICLR 2015, San Diego CA, USA, May 7-9, 2015, Conference Track Proceedings, 2015.
[71] Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, Alban Desmaison, Andreas Köpf, Edward Yang. Zachary Vito Martin Raison, Alykhan Tejani, Sasank Chilamkurthy, Benoit Steiner, Lu Fang. Junjie Bai, and Soumith Chintala. Pytorch: An imperative style, high-performance deep learning library. In Hanna M. Wallach, Hugo Larochelle, Alina Beygelz- imer, Florence d' Alché-Buu Buc, Emily B. Fox, and Roman Garnett, editors, Advances in Neural Information Processing Systems 32: Anmual Conference on Neural Information Processing Systems 2019, NeurlPS 2019, December 8- 14, 2019, Vancouver, BC, Canada, pages 8024-800 8035, 2019.
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A Variety Assign Logits
Previous studies commonly adopt the Pearson correlation coefficient to measure dependencies between variables, which is effective for capturing linear relationships. The Pearson correlation between two variables x, E I= is defined as:
Σ Li (Ii 3) {) 9)
x(x,)) EE= (2; x)² Ei=1 (V: 5)²
(8)
where E and y denote the sample means of x and y, respectively. While this approach performs well under linear assumptions, fails capture complex nonlinear dependencies- an issue particularly prominent in multivariate time series, where variable interactions can be intricate and highly nonlinear.
To address this limitation, adopt the Brownian Distance Covariance (BDC) Unlike Pearson correlation, BDC is nonparametric statistical measure that can detect both linear and nonlinear dependencies without assuming any specific distribution. It provides more general and powerful tool for modeling complex interactions in multivariate time series. The empirical BDC between x and y is defined as:
alternative.
V) (x,)))) (x Vy
Here, (x, y) quantifies the strength of dependence between and y, with value of implying statistical independence. This quantity is computed based on the following formulation:
B. (xx = n2 ==1==1
(10)
where Ai and Big double-centered distance matrices derived from and y, respectively. Then double-centered using the following formula:
1 Σ
A. ||, xyl
10 x
xyll
aay xy (11)
n²
where denotes the Euclidean norm. The same procedure applies to matrix B to obtain the centered version B:y. Finally, the normalized BDC value lies within the interval [0, 1). where 1 indicates perfect dependence and 0 indicates independence. Importantly, the BDC measure is strictly zero if and only if the variables are independent in the population. Therefore, it serves as robust and comprehensive dependency metric, particularly valuable for analyzing complex, nonlinear relationships in multivariate time series.
After computing the Brownian Distance Covariance (BDC) matrix, apply the K-means clustering algorithm on the rows of the BDC matrix to construct a pre- arr-nnssigmmet matrix. Each row corresponds to variable's 's dependency pattern across all other variables. Let R [0, 1] denote the BDC correlation matrix among C' variables. We treat each row R4 E RCC as feature vector representing variable and perform K-means clustering (65 to partition the variables into G clusters:
KMeans (R. G);
(12)
where π E (1,...,G]C C is the cluster assignment vector. Based on these assignments, we construct a pre-assignment matrix (0, cx where each row indicates the cluster membership of the corresponding variable using one-hot encoding. This pre-assignment matrix serves as an initial grouping prior for subsequent model components, such as channel interaction modules hierarchical aggregation mechanisms.

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B Datasets
B.1 TDBRAIN Dataset
The TDBrain dataset, referenced in (66], is large-scale EEG time series dataset containing recordings from 1,274 subjects using 33 channels. Each subject participated in two trials: one with eyes open and another with eyes closed. The dataset includes total of 60 diagnostic labels, allowing for multi-label classification as each subject may be associated with multiple conditions. In this paper, we utilize a subset of the dataset comprising 25 subjects diagnosed with Parkinson's disease and 25 healthy controls, all under the eyes-closed condition. Each eyes-closed trial is segmented into non-overiapping I-second windows, each containing 256 time points. Segments shorter than I second are discarded. This preprocessing results in a total of 6,240 samples. Each sample is tagged with a subject ID to indicate its origin.
B.2 PTB-XL Datuset
The PTB-XL dataset [6]] is a large-scale public ECG time series dataset collected from 18,869 subjects, each with 12-channel recordings and annotated with or more of five labels, including four heart disease categories and one healthy control. Since each subject may have multiple trials, we remove subjects whose diagnoses vary across trials to ensure label consistency, resulting in 17,596 subjects retained. Each trial is a 10-second ECG segment, available in both 100 Hz and 500 Hz sampling rates. In our study, we use the 500 Hz version, downsampled to 250 Hz and normalized using a standard scaler. We then segment each trial into non-overlapping I-second samples (250 time steps per sample), discarding any segment shorter than second. This preprocessing yields split, allocating 60%,
total of 191, 4,0 samples. For model training, we adopt a 20% and 20% of subjects (and their corresponding samples) the training, validation, and test sets, respectively.
B.3 FLAAP Dataset
The FLAAP dataset [68] is human activity recognition (HAR) dataset collected using smartphone- based inertial sensors, specifically accelerometers and gyroscopes placed at the waist of subjects. records ten distinct daily activities performed by eight subjects, with data continuously captured between February 1tt and May 31st, 2022, at sampling rate of 100 Hz. Unlike many existing HAR datasets that focus primarily on activity classification, FLAAP emphasizes discovering associated patterns within activities, aiming to better reflect the structure of Activities of Daily Living (ADL). Each activity is segmented into fixed-length windows, producing a total of 13, samples with sensor channels and 100 time steps per sample. In experiments, the dataset is divided into 60% for training, 20% for validation, and 20% for testing. The dataset serves as a valuable benchmark for studying representation learning, pre-processing effects, domain transfer, and activity association mining in multivariate time series.
B.4 UCI-HAR Dataset
The UCI-HAR dataset 69 is widely used benchmark for human activity recognition (HAR), collected using smartphone-basel inertial sensors. It contains recordings from 30 subjects performing six different daily activities (walking, walking upstairs, walking downstairs, sitting, standing, and lying) while carrying smartphone equipped with a tri-axial accelerometer and gyroscope. Data were collected at sampling rate of 50 Hz and then preprocessed by applying noise filters and segmenting the continuous signal into fixed-length windows of 2.56 seconds (128 time steps) with a 50% overlap. Each segment is labeled with the corresponding activity. In our study, we use the processed version with 9 selected channels and 128 timestamps per sample, resulting in a total of 10,299 labeled samples. The dataset is split into training and test sets based on a certain ratio.
B.5
UEA Classification Dataset
The UEA dataset 47 is comprehensive collection of multivariate time series samples spanning wide range of application domains, primarily designed for classification tasks. includes diverse recognition scenarios such as facial, gesture, and action recognition, as well as audio classification.
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Beyond these, it serves practical purposes in areas like industrial monitoring, health surveillance, and medical diagnosties, with particular attention to cardiac data analysis. Typically, the dataset is structured into 10 distinct classes. Table 6 provides detailed classification statistics, highlighting the dataset's versatility and broad applicability across multiple domains.
Table 6: Datasets and mapping details of UEA dataset.
Dataset
Sample Numbers (train, test)
Variable Number
Series Length
EthanolConncentrationn
(261, 263)
1751
FaceDetection
(5890, 3524)
144
62
Handwriting
(150, 850)
152
Heartbeat
(204, 205)
61
405
Japanese Vowels
(270, 370)
29
PEMS SF
(267, 173)
963
144
SellRegulattonSSCPI
(268, 293)
896
SellRegulationSCP2
(200, 180)
1152
SpokenArabicDigits
(6599, 2199)
93
UWaveGestureLLibray
(120, 320)
315
B.6 Datasets BDC Similarity Visualization
Figure 7 displays the similarity matrices computed using Brownian Distance Covariance (BDC) across different datasets. The x-axis and y-axis represent the variable (channel) indices.
Figure 7: BDC Similarity Visualization of Main and UEA Datasets.
10
1.0
08
Variety Index
0.4
02
Variety
Variety Index
TDBRAIN Similarity Matrix
PTB-XL Similarity Matrix
1.0
1.0
0.9
0.8
0.8
Varicty Index
varlety Index
0.5
0.6
0.5
0.2
0.2
Variety Index
Variety Index
UCI-IAR Similarity Matris
FLAAP Similarity Matris
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1.0
0.8
Variety Index
Variety Index
0.6
0.2
Variety Index
0.0
Variety Index
0.0
EthanolConeenttaatton Similarity Matrix
FaceDetection Similarity Matris
Variety Index
Variety Index
0.6
0.4
0.4
0.2
0.2
Variety
Variety
Handwriting Similarity Matrix
Hcartbeat Similarity Matrix
1.0
1.0
0.8
Variety Index
Variety
0.4
0.4
0.2
0.2
Variety Index
0.0
Variety
Japanese Vowels Similarity Matrix
PEMS-SE Similarity Matrix
1.0
1.0
Variety Index
Varlety Index
0.6
0.6
0.4
0.4
0.2
0.2
Variety Index
0.0
Variety
SelfRegulationSCCI Similarity Matrix
SelfRegulationSCPP Similarity Matrix
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1.0
Variety Index
Variety Index
0.6
0.4
0.4
0.2
0.2
Variety Index
Variely
DiokenArrabiciigits Similurity Matrix
UWaveGesstureLBbrary Similarity Matrix
Experiments Details
C.1 Main Datasets Implement Details
Implementation Details. All methods are implemented within a unified framework to ensure fair comparison. Specifically, we re-implement each approach using a consistent training strategy. We compare our model against a variety of state-of-the-arr time series models, including six Transformer- based models, one MLP-based model, and three CNN-based models as baselines. For baseline implementations, we adopt the official code and follow the recommended best configurations, The learning rate is fixed at 0.0001, and the Adam [70] optimizer employed for all experiments. The batch sizes are set according to the dataset: (32, 256, 32, 32) for TDBrain, PTB-XL, UCI-HAR. and FLAAP, respectively. In the data preprocessing stage, we adopt the processing pipeline from Wang 49 to ensure consistency and comparability across datasets. All models are trained for 100 epochs using five different random seeds (41 45), and we report the average results along with the standard deviations. To prevent overfitting, we adopt an early stopping strategy based on the F1 score on the validation set. All experiments are conducted using four NVIDIA RTX 4090 GPUs (24GB memory) with the PyTorch framework [71).
SwinGroupNet (Our Method). We perform clustering on multivariate time series based on the similarity matrix derived from BDC, generating an initial assignment matrix (see Appendix A for details). Different similarity thresholds result different numbers of groups We then apply Gumbel- Softmax sampling to obtain differentiable assignment matrix, followed by independent embedding each group. our proposed Multi-Swin Periodic Window, multi-scale feature extraction is conducted on the input, and information from different layers is fused to produce the final output. The learning rate is set to 0.001, and an early stopping strategy adopted. The experimental configurations the main datasets, including the number of variable groups, the regularization parameter 3, embedding dimension, model depth, number kernels depthwise convolution, period window size, and channel expansion ratio, summarized in Table 7
Table Experiment configuration of SGN.
Dataset
# Groups
#3
# Embedding Dim
Layers
Kernels
# Period Window
#Channel Ratio
TDBRAIN
0.1
32
7
26
2
PTB-XL
0.1
64
7
25
2
UCI-HAR
0.1
64
7
32
2
FLAAP
0.1
64
7
50
2
C.2 Baselines Details
To evaluate the effectiveness of our proposed method, we selected set of strong baseline models that cover a wide range of architectural paradigms. Specifically, for the main benchmark datasets, we include convolution-hased models such as MICN [7]. ModernTCN [19), and TimesNet [18]:
(Tranin Transformer-bast based models including iTransformer 24
Reformer (48), FedFormer [14, Crossformer
28

---

25 PatchTST [22], and MedFormer 49;; and MLP-based models like DLinear [15]. These models have demonstrated strong capabilities in temporal modeling and provide a solid foundation for comparative analysis. To further validate our method, we also conducted experiments the UEA datasets by including additional baselines such as CNN-based models (TVNet [20], TimeMixer++ [56. Rocket () RNN- models (LSTNet [50]. LSSL [53), and MLP-based models (LightT'S
50
MTX-Mixer (55))
C,3 Full result of UEA Datasets
Implementation Details. Our method is trained using the cross-entropy loss, with classification accuracy (%) adopted the evaluation metric. The model is initialized with learning rate of 10 and an early stopping strategy is applied to prevent overfitting. The symbol "*" in Transformer-basse models indicates the specific model name (e.g.. *former may refer Informer, Crossformer, etc.). Detailed results are presented in Table 8 As shown in the table, MLP-based models exhibit relatively poor performance. In contrast, CNN-based models demonstrate superior results by effectively extracting local features and incorporating various strategies to capture global patterns.
Table &: Performance comparison of various models on different datasets with accuracy metrics for classification.
Dutusets/ Model
RNN-based
Consolation-aae braed ModeniTUN
MLPP-hased
Trunsformer- based
SGN (Ouns)
LSTNet LSSL.
Rocket 3030
TimeiNet
TVast
Tineniserr 122
DLinear NG1
LighTS
MTS Mixer
In.
PaxcITIST
Cioss.
Flow.
FED
2005
1022
1051
1831
503
3223
2005
PaceDetection
07.6
25.8
13.8
Hasebea
15.4
76.6
Japanss Nowces
08.1
98.4
94.3
PLMSS
M6.7
M6.1
3900
390
91.0
88.7
90.1
81.5
8922
860
50.9
$4.0
90.8
908
9188
91.7
981
90.7
92.0
95.3
90.1
92.1
90.3
58.7
91.
SedResuulaiioSCP
52.8
52.2
53.3
$4.7
56.3
60.5
65.6
50.5
$1.1
55.5
53.3
56.1
56.0
56.1
$4,4
60.6
1000
100.0
71.2
99.0
9911
99.4
99.8
91.4
100.0
99.5
100.0
99.1
99.6
98.8
100
99.7
t U'BosClotrrd limrr
67.8
85.9
94.4
$8.3
56.7
96.6
98.2
82.1
80.3
82.3
85.6
85.8
85.6
66.6
55.3
02.2
Average Accurncy
71.8
70.9
72.5
73.6
14.2
74.6
15.3
67.5
70.4
70.9
72.1
72.5
732
73.0
70.7
77.6
D Hyperparamter Sensitivity
In this section, we conduct a sensitivity analysis on four key hyperparameters in the SGNet model to evaluate its robustness. Specifically, we investigate the effects of (1) the number of variable groups, (2) the number of convolution kernels, (3) the selection of periodic window sizes, and (4) the embedding dimension within each group. We present a detailed evaluation of how these hyperparameters impact model performance. The corresponding experimental results are summarized below.
Group Numbers of Varieties. Figure presents the ablation study on variable grouping. According the number of variables in each dataset, we partition them into {1, 2, 3, 4, 5, 6) groups Here, a group number of indicates that no grouping strategy is applied and all variables are treated jointly. We observe that as the number of groups increases, performance metrics such as accuracy initially decrease and then gradually improve. Notably, the TDBRAIN dataset exhibits significant performance gain when variable grouping is employed, highlighting the effectiveness of our method in capturing complex inter-variable variable relationships.
Figure 8: Analysis of hyperparameter sensitivity concerning the group numbers on main datasets.
200
Precidin
Meeris
Metrics
Group Numbers
Group Numbers
Group Mumbars
UCH-HAR
TDBRAIN
FLAAP
29

---

Table and Table I0 present the performance of our model under different embedding dimensions Dm [16, 32, 64, 128. 256} and convolution kernel sizes Tig E {3. 5, 7, 9. 11), respectively. Note that the effective receptive field of each convolutional layer is 2n + We evaluate these configurations on the main datasets.
Embedding Dimensions and Number of kernels.
As shown in Table 9 the TDBRAIN dataset exhibits minimal sensitivity to changes in embedding dimension, with accuracy consistently remaining above 99%. contrast, for the other three datasets, accuracy gradually improves as the embedding dimension increases from 16 to 64. However, further increasing the dimension beyond 64 leads noticeable performance drop, particularly from 128 to 256. Therefore, considering both performance and computational efficiency, embedding dimensions of 32 or 64 identified as optimal choices. And the Table [O]sows that the number convolution kernels increases, leading to a larger effective receptive field, the classification accuracy improves gradually. This indicates that the model is capable of extracting temporal features effectively even with smaller kernels, demonstrating its strong robustness and reduced reliance on extensive kernel coverage.
Table 9: Analysis of hyperparameter sensitivity concerning the dataembedding on main datasets.
Dataset
TDBrain
PTB-XL
FLAAP
UCI-HAR
Metric
Accuracy
F1
Aceuracy
F1
Accuracy
F1
Accuracy
Dm 16
99.75
99.75
73.58
62.56
78.28
77.87
94.96
94.53
Dm 32
99.90
99.90
73.65
62.92
79.64
79.25
94.62
94.67
Dm 64
99.56
99.56
73.80
63.43
80.81
80.35
95.62
95.64
Dm 128
99.46
99.46
73.56
62.67
79.66
79.40
93.52
93.56
Dm 256
99.54
99.54
73.54
62.43
78.34
77.98
87.86
88.06
Table 10: Analysis of hyperparameter sensitivity concerning the kernel numbers on main datasets.
Dataset
TDBrain
PTB-XL
FLAAP
UCI-HAR
Metric
Accuracy
F1
Accuracy
F1
Accuracy
F1
Accuracy
F1
nk = 3
99.84
99.84
73.08
62.44
80.05
79.45
94.10
94.08
nk 5
99.86
99.86
73.57
62.51
80.31
79.83
94.64
94.69
nkk = 7
99.90
99.90
73.80
63.43
80.81
80.35
95.62
95.64
nk 9
99.76
99.76
73.35
62.51
80.58
80.25
95.38
95.42
nk = 11
99.39
99.39
73.49
62.73
80.29
79.86
94.38
94.45
Periodic Window Sizes. To evaluate the effectiveness of periodic window selection, we analyze the frequency-donee domain representations of each main dataset and select the top-5 frequencies with the highest amplitudes (excluding the full sequence length) as candidate periods. The corresponding periodic windows for each dataset are as follows: TDBRAIN (26, 128, 29, 32). FLAAP (50, 34, 25, 20), UCI-HAR (64, 32, 26, 19), and PTB-XL (84, 125, 63, 36). We then compare the model performance under these different periodic settings. As shown in Table IT the model achieves slightly better performance under the first two period values, though the difterences across configurations remain relatively small. This demonstrates the robustness of our model and validates the effectiveness of the proposed periodic mechanism for extracting multi-scale temporal information.
Table 11: Analysis of hyperparameter sensitivity concerning periodic window sizes main datasets.
Dataset
TDBrain
PTB-XL
FLAAP
UCI-HAR
Metrie
Accuracy
F1
Accuracy
F1
Accuracy
F1
Accuracy
FI
periodic window No.1
99.90
99.90
73.34
62.54
80.81
80.35
93.88
93.95
periodic window No.2
99.69
99.69
73.56
63.65
79.08
78.66
95.62
95.64
periodic, window No.3
99.58
99.58
72.91
61.59
79.24
78.77
93.95
93.97
periodic wiiddww No.4
99.79
99.79
73.09
62.48
77.45
76.94
94.50
94.49
30

---

E
Efficiency Analysis
We conduct a comprehensive comparison between SGN and several representative models, including Reformer [48), Crossformer [25), FEDformer [14], iTransformer [24]. PatchTST [22), MICN [[7]. Modern 19) and TimesNet T8 from the perspectives of classification performance, training speed, and memory usage. As illustrated in Figure |
SGN achieves well-balanced trade-off between accuracy, training time, and memory consumption on the TDBRAIN and FLAAP datasets. These results highlight the efficiency and effectiveness of our proposed method in handling multivariate time series data under resource-constrained settings.
Figure Model efficiency comparison under TDBRAIN and FLAAP Datesets.
300
158 Zen
0C
SHMM 17hes
95
MICN
BSGME 9aan
S13tmm
S0
20033E8
AcunooyN))
Hefommer
Accuracy
Mudicr
1844 7ams
6C
Timosei
2482348 $2mm
CrasdSerte
Flan
JUNRMI
55
PaulISTT
MICNS
Memsury Footgrint
BCC
100
200
200
400
500
500
700
800
900
Training
Tairing (mseiter)
FLAAP
TDBRAIN
F
Additional Visualization Results
In Figure 10 we visualize the temporal correlations across different layers of the model on various datasets. is evident that in the lower layers, temporal dependencies are mostly confined nearby timestamps. However, with the integration of the PWSM module, which progressively merges low-level features from short-period windows into high-level representations of long-period windows, the temporal correlations in the upper layers extend across the entire window. This demonstrates the effectiveness our multi-level periodic fusion mechanism in capturing comprehensive global temporal patterns.
Figure 10: The temporal correlation on TDBRAIN, FLAAP and PTB-XL. Datasets.
15
Time Stop
08
Thes
37
Time Shp
Thms Last Layer
Time Step
Firs Layer
Firtt Layer
Last Layer
TDBRAIN
FLAAP
67
TeTe Shpp
65
Time Sizp
First Layer
Last Layer
PTB-XL
31

---

G
Discussion
In this paper, we propose the SGN architecture, which introduces novel perspective for modeling variable relationships by transforming them into pirr- and inter-group interactions through variable grouping- Additionally, leverage the periodic nature of time series to perform hierarchical and multi-scale temporal feature extraction. Our method achieves state-of-the multiple datasets from various domains, demonstrating its generalizability and effectiveness. Despite its strong empirical results and contributions to time series modeling, SGN still has certain limitations and leaves room for further exploration.
performance across
While SGN demonstrates strong performance improvements and achieves outstanding results on several datasets, its applicability other time series tasks such as forecasting and imputation remains to be further explored. Moreover, the use of intrinsic similarity to generate the assignment matrix introduces additional computational overhead. This preprocessing step, although beneficial for modeling accuracy, may hinder deployment in real-time scenarios, and thus requires further optimization and acceleration.
Limitation.
Future Work. Future research can gradually extend SGN to other domains, such as industrial monitoring and healthcare, where multivariate time series play crucial role. In addition, exploring alternative strategies for generating the assignment matrix, potentially guided by domain knowledge, could improve the flexibility and interpretability of variable grouping. Furthermore, enhancing the design of periodic windows, including the integration of multiple window candidates or adaptive selection mechanisms, may further boost the model's effectiveness and generalization across diverse datasets.
Broader Impacts. The proposed SGN model holds promising potential for positive societal impact. By enhancing the accuracy and efficiency of multivariate time series classification, SGN can benefit a wide range of critical applications. For instance, in the healthcare domain, can help detect diseases early by analyzing patient ECG signals, leading to timely interventions and improved outcomes. In meteorology, SGN can assist in making informed decisions based complex environmental data, ultimately contributing to risk reduction and public safety. These capabilities demonstrate the model's value in supporting well-being and societal resilience across multiple sectors.
32


Reviews:
[{"review_id": "Z43pkyGuLA", "reviewer": "Reviewer_86Jq", "summary": "The paper introduces SwinGroupNet (SGN), a novel framework for multivariate time series (MTS) classification that explicitly models both intra- and inter-variable dependencies using a grouped embedding approach and hierarchical temporal feature extraction. By combining three components—Variable Group Embedding (VGE), Multi-Scale Group Window Mixing (MGWM), and Periodic Window Shifting and Merging (PWSM)—SGN aims to preserve semantic structures, address heterogeneous variable types, and exploit periodic temporal patterns. Experimental results on multiple benchmark datasets show promising improvements over prior work.", "questions": "1- How does the computational cost (in terms of FLOPs, training time, inference time, and memory usage) of SGN compare to the baseline models?\n2- Does the model generalize well to datasets with fewer variables or less clear periodic structure?\nThe reliance on periodic patterns in PWSM might not apply broadly.", "limitations": "no", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "# Strengths \n\n1. **Clear Motivation**: The paper convincingly discusses the limitations of univariate decomposition and full multivariate modeling approaches in MTS.\n2. **Novel Architecture**: The use of group-based embeddings and hierarchical temporal modeling (through PWSM and MGWM) is an interesting and original idea.\n3. **Strong empirical results**: Demonstrates consistent state-of-the-art performance across diverse benchmarks with a reported 4.2% improvement on average.\n4. **Code Availability**: Open-sourcing the implementation increases reproducibility and community impact.\n \n# Weaknesses\n- **Architectural Complexity Without Computational Justification**\n    \n    While SGN demonstrates strong performance, the proposed design—incorporating Variable Group Embedding (VGE), Multi-Scale Group Window Mixing (MGWM), and Periodic Window Shifting and Merging (PWSM)—introduces considerable architectural complexity. However, the paper **does not provide any analysis of computational cost** (e.g., training/inference time, parameter count, FLOPs, or GPU memory usage), which is critical when evaluating practical deployment, especially for long multivariate sequences. Without this, it is difficult to assess the **efficiency vs. performance tradeoff** compared to simpler or more lightweight baselines.\n    \n- **Lack of Controlled Comparison With Existing Channel Dependency Methods**\n    \n    Although the motivation for capturing inter-variable dependency is valid, the paper does not thoroughly compare SGN with **alternative methods for modeling channel correlations**. For instance, prior work like MSGNet (AAAI 2024) has explored efficient multi-scale inter-series correlation modeling. Additionally, **no study is conducted using a common architectural backbone** to test whether simpler methods (e.g., channel attention, global attention, temporal convolutions) underperform consistently compared to SGN.\n    \n- **Scalability**: No discussion is included on the computational complexity, especially for large MTS with many variables and long sequences.", "was_revised": true, "final_justification": "The authors have clarified more detailed about implementation and baseline comparison", "rebuttal": "Many thanks for your valuable and encouraging feedback. We sincerely appreciate that you found our paper to be well-motivated, with a novel architecture and strong empirical performance. We would like to provide further clarifications to address your comments in more detail.\n\n---\n\n**W1. Architectural Complexity Without Computational Justification**\n\n**A1**. We appreciate the reviewer’s concern regarding computational efficiency. For the input time series data $X \\in \\mathbb{R}^{d_{\\text{m}} \\times \\text{group} \\times L}$, where $d_{\\text{m}}$​ denotes the embedding dimension and *L* is the temporal length (with $L>>d_{\\text{m}}$​​). We adopt a combination of **depthwise and pointwise convolutions** for feature extraction. This design allows for efficient modeling with the following complexity: **Time complexity** $\\mathcal{O}(L \\cdot d_{\\text{m}}^2)$ and **Space complexity** $\\mathcal{O}(d_{\\text{m}}^2)$. A comparison with other methods is detailed in the table below:\n\n| Methods     | Time Complexity                                  | Space complexity  |\n| ----------- | ------------------------------------------------ | ----------------- |\n| SGN（Ours）   | $O(Ld_m)$                                        | $O(Ld_m)$         |\n| TVNet       | $O(Ld_m^2)$                                      | $O(d_m^2 + Ld_m)$ |\n| MICN        | $O(Ld_m^2)$                                      | $O(Ld_m^2)$       |\n| FEDformer   | $O(L)$                                           | $O(L)$            |\n| Crossformer | $O\\left(\\frac{d_m}{L_{\\text{seg}}^2} L^2\\right)$ | $O(Ld_m)$         |\n\n\nWe have also conducted a detailed comparison with baseline methods in terms of **FLOPs** and **GPU memory usage**, as shown in **Appendix E**. The results confirm that our approach achieves favorable computational efficiency while maintaining strong performance.\n\n  \n---\n\n**W2. Lack of Controlled Comparison With Existing Channel Dependency Methods.**\n\n  \n**A2**. We sincerely appreciate your insightful suggestion. Following your advice, we have included additional baseline methods for a more comprehensive comparison. Specifically, we categorized these methods into the following groups:\n\n- **Multi-scale methods**: MSGNet, MedFormer\n- **Channel attention methods**: iTransformer, Crossformer\n- **Global attention methods**: Transformer, PatchTST\n- **Temporal convolution methods**: TCN, ModernTCN\n\nThis categorization allows for a more structured evaluation, and the extended comparisons further demonstrate the effectiveness and robustness of our proposed method. The specific results are shown in the following table:\n\n| Dataset       | TDBRAIN  |          | **FLAAP** |           | **UCI-HAR** |           | **PTB-XL** |           |\n| ------------- | :------: | :------: | :-------: | :-------: | :---------: | :-------: | :--------: | :-------: |\n| Metric        | Accuracy |    F1    | Accuracy  |    F1     |  Accuracy   |    F1     |  Accuracy  |    F1     |\n| MSGNet        |  85.64   |  85.63   |   74.38   |   74.01   |    92.43    |   92.84   |   69.96    |   57.64   |\n| Medformer     |  89.62   |  89.62   |    74     |   73.84   |    90.17    |   90.27   |   72.87    |   62.02   |\n| Crossformer   |  81.56   |   81.5   |   76.33   |   76.14   |    90.66    |   90.68   |    73.3    |   62.59   |\n| iTransformer  |  74.67   |  74.65   |   75.83   |   75.57   |    93.47    |   93.46   |   69.28    |   56.2    |\n| TCN           |   88.5   |  88.42   |   76.11   |   75.79   |    92.72    |   92.66   |   72.67    |   62.04   |\n| MordenTCN     |   87.6   |  87.54   |   71.66   |   71.37   |    92.75    |   92.8    |   72.85    |   61.33   |\n| Transformer   |  87.17   |   87.1   |   74.14   |   73.71   |    90.68    |   90.69   |   70.59    |   59.05   |\n| PatchTST      |  79.25   |   79.2   |   56.23   |   55.57   |    86.83    |   87.17   |   73.23    |   62.61   |\n| **SGN(ours)** | **99.9** | **99.9** | **80.81** | **80.35** |  **95.62**  | **95.64** |  **73.8**  | **63.43** |\n\n\n---\n\n  \n**W3. No discussion is included on the computational complexity, especially for large MTS with many variables and long sequences.**\n\n\n**A3**. We sincerely thank the reviewer for the thoughtful suggestion. Our SGN model effectively reduces computational complexity by combining **periodic windowing and fusion mechanisms** for long sequences, along with the use of **depthwise and pointwise convolutions**. \nAs shown in **Table 7 of Appendix C.3**, our method outperforms other baselines even on challenging datasets such as EthanolConcentration(with a sequence length of 1751) and FaceDetection(with 144 variables), demonstrating strong performance on both long sequences and high-dimensional multivariate data.\n\n\n---\n\n**Q1. How does the computational cost (in terms of FLOPs, training time, inference time, and memory usage) of SGN compare to the baseline models** \n\n**A4.** We have provided the corresponding response in **A1 of W1**.\n\n---\n\n**Q2. Does the model generalize well to datasets with fewer variables or less clear periodic structure? The reliance on periodic patterns in PWSM might not apply broadly.**\n\n\n**A5**. Thanks for your valuable insight. We would like to respond from the following two perspectives:\n\n1. In the **UEA datasets used in Table 7 of Appendix C.3**, there are several datasets with **few variables** and **weak periodicity**, such as _EthanolConcentration_ and _Handwriting_, each containing only three variables. Despite these challenges, our method consistently outperforms baseline models, demonstrating its robustness in low-dimensional and weakly periodic settings.\n2. While SGN is designed to leverage periodic patterns, it does **not rely rigidly on periodicity**. Instead, we incorporate a **dynamic shifting mechanism** that enables **local context fusion across windows**, allowing the model to remain effective even when the underlying periodic structure is weak or inconsistent."}, {"review_id": "7H43LDY0vV", "reviewer": "Reviewer_Tx33", "summary": "This paper proposes SwinGroupNet (SGN), a novel approach for multivariate time series (MTS) classification, with key innovations including: Variable Group Embedding (VGE): A dynamic grouping strategy based on Brownian Distance Covariance (BDC) that partitions variables into clusters, enabling separate modeling of intra-group and inter-group dependencies to balance the trade-offs between independent and mixed variable modeling paradigms. Integrated periodic analysis and multi-scale convolution for simultaneous feature extraction across both temporal and variable dimensions. Periodic window shifting to enhance cross-window interactions and mitigate limitations of localized modeling.", "questions": "The proposed PWSM module exhibits strong dependence on periodic assumptions through its FFT-based windowing mechanism. This architectural choice may degrade model performance when processing non-periodic signals (e.g., white noise), (b) transient events (e.g., fault spikes in industrial data), or (c) irregular sampling scenarios - all common in real-world time series applications. What considerations did the author have regarding this?", "limitations": "1.Regarding the selection of baseline methods, we recommend incorporating state-of-the-art Multivariate Time Series representation approaches.\n2. Evaluating the method's generalizability through additional experiments on fundamental time-series tasks such as forecasting and anomaly detection.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1. It demonstrates relatively excellent performance in multivariate time series classification tasks.\n\nWeaknesses:\n1. The architecture presented in Figure 2 is difficult to interpret. especially for the subfigures. \n2. Line 142.  the final loss includes the L_task, in fact, the experimental validation appears limited to classification tasks.", "was_revised": true, "final_justification": "Thanks for the responses.. I'll maintain my original rating.", "rebuttal": "Thank you for your positive feedback. We're glad that you find our method demonstrates relatively excellent performance in multivariate time series classification tasks. We would like to provide some clarifications in the hope of addressing your concerns.\n\n  \n\n---\n\n\n**W1. The architecture presented in Figure 2 is difficult to interpret. especially for the subfigures.**\n\n  \n**A1**. We apologize for the lack of clarity in the original model illustration, and we thank the reviewer for bringing this to our attention. Below, we provide a more detailed explanation of the SGN model architecture, which consists of **three main modules**: **VGE**, **MSWM**, and **PSPM**.\n\n- **VGE (Variable Grouping and Embedding)**:  \n    - This module serves two purposes. First, it computes an **assignment matrix** based on intrinsic variable similarity, which is used to **fuse variables into groups**. These groups are then encoded using **group embeddings** to obtain compact representations.  \n    - Second, the module applies **FFT** to estimate dominant periods and uses them to segment the time series into **periodic windows**.\n    \n- **MSWM (Multi-Scale Window Module)**:  \n    This module performs joint feature extraction along both the **temporal** and **variable** dimensions.\n    \n    - First, in the temporal dimension, it applies **multi-scale depthwise convolutions** using multiple kernel sizes.\n        \n    - Next, in the variable dimension, it performs **group-wise intra/inter pointwise convolutions** to capture both within-group and across-group interactions.\n        \n- **PSPM (Period Shifting and Merging Module)**:  \n    This module includes two components:\n    \n    - **Period Merging**, which fuses features across adjacent windows to enhance temporal continuity.\n        \n    - **Period Shifting**, which introduces dynamic offsets to the window boundaries, helping the model adapt to imperfect or misaligned periodicity.\n        \n\nWe hope this explanation provides a clearer understanding of our model architecture and its components.\n\n  \n---\n\n  \n\n**W2. Line 142. the final loss includes the $\\mathcal{L}_{\\text{task}}$, in fact, the experimental validation appears limited to classification tasks.**\n \n\n**A2**. We apologize for the confusion. To clarify, the SGN model is primarily designed for **multivariate time series classification**.\n\n- $\\mathcal{L}_{\\text{task}}$​ corresponds to the **classification loss**, which serves as the main supervision signal. We will correct the symbols in subsequent versions.\n    \n- $\\mathcal{L}_{\\text{sim}}$​ is a **similarity-based regularization term**, which encourages more structured and meaningful variable grouping by penalizing inconsistent similarity patterns.\n\n  \n\n---\n\n  \n\n**Q1. The proposed PWSM module exhibits strong dependence on periodic assumptions through its FFT-based windowing mechanism. This architectural choice may degrade model performance when processing non-periodic signals (e.g., white noise), (b) transient events (e.g., fault spikes in industrial data), or (c) irregular sampling scenarios - all common in real-world time series applications. What considerations did the author have regarding this?.**\n  \n**A3**. Thanks for your valuable insight. We would like to respond from the following two perspectives:\n\n1. In the **UEA datasets used in Table 7 of Appendix C.3**, there are several datasets with **few variables** and **weak periodicity**, such as _EthanolConcentration_ and _Handwriting_, each containing only three variables. Despite these challenges, our method consistently outperforms baseline models, demonstrating its robustness in low-dimensional and weakly periodic settings.\n2. While SGN is designed to leverage periodic patterns, it does **not rely rigidly on periodicity**. Instead, we incorporate a **dynamic shifting mechanism** that enables **local context fusion across windows**, allowing the model to remain effective even when the underlying periodic structure is weak or inconsistent.\n\nIn addition, we have included more **multivariate datasets** and conducted comparisons against a broader range of **state-of-the-art multivariate methods** to further validate the effectiveness of our approach. The specific results are shown in the following table. **Wins/Draws/Losses** indicate the number of datasets (out of 30) on which the SGN method achieves higher, equal, or lower accuracy compared to the corresponding baseline methods. As shown, SGN consistently achieves **a greater number of first-place results and better average ranking** compared to state-of-the-art methods, demonstrating its robustness and generalization across diverse datasets.\n\n\n| Data/Model                | W.MUSE   | M.FCN |  TapNet  | ShapeNet | TodyNet  |   SVPT   | Shapeformer | MPTSNet  |   SGN(Ours)    |\n| ------------------------- | -------- | ----- | :------: | :------: | :------: | :------: | :---------: | :------: | :------: |\n| ArticularyWordRecognition | 99       | 97.3  |   98.7   |   98.7   |   98.7   | **99.3** |     99      |   97.7   |    99    |\n| AtrialFibrillation        | 33.3     | 26.7  |   33.3   |    40    |   46.7   |    40    |    53.3     |   53.3   | **66.7** |\n| BasicMotions              | **100**  | 95    | **100**  | **100**  | **100**  | **100**  |   **100**   | **100**  | **100**  |\n| CharacterTrajectories     | 99       | 98.5  | **99.7** |    98    |   N/A    |    99    |    99.2     |   N/A    |   99.6   |\n| Cricket                   | **100**  | 91.7  |   95.8   |   98.6   | **100**  | **100**  |    94.4     |   94.4   | **100**  |\n| DuckDuckGeese             | 57.5     | 67.5  |   57.5   | **72.5** |    58    |    70    |     64      |    68    |    64    |\n| EigenWorms                | 89       | 50.4  |   48.9   |   87.8   |    84    | **92.5** |     N/A     |   N/A    |   85.5   |\n| Epilepsy                  | **100**  | 76.1  |   97.1   |   98.7   |   97.1   |   98.6   |    98.6     |   97.1   |   97.8   |\n| EthanolConcentration      | 13.3     | 37.3  |   32.3   |   31.2   |    35    |   33.1   |    41.1     |   43.3   | **44.5** |\n| ERing                     | 43       | 13.3  |   13.3   |   13.3   |   91.5   |   93.7   |    87.4     |   94.4   | **95.9** |\n| FaceDetection             | 54.5     | 54.5  |   55.6   |   60.2   |   62.7   |   51.2   |    65.8     |   69.8   | **70.3** |\n| FingerMovements           | 49       | 58    |    53    |   58.9   | **67.6** |    60    |     55      |    64    |    64    |\n| HandMovementDirection     | 36.5     | 36.5  |   37.8   |   33.8   |   64.9   |   39.2   |    41.9     |   63.5   | **75.7** |\n| Handwriting               | **60.5** | 28.6  |   35.7   |   45.1   |   43.6   |   43.3   |    30.2     |   34.4   |   50.4   |\n| Heartbeat                 | 72.7     | 66.3  |   75.1   |   75.6   |   75.6   |    79    |  **81.5**   |   75.6   |   77.1   |\n| InsectWingbeat            | N/A      | 16.7  |   20.8   |    25    |   N/A    |   18.4   |    31.4     |   N/A    |  **68**  |\n| JapaneseVowels            | 97.3     | 97.6  |   96.5   |   98.4   |   N/A    |   97.8   |  **99.2**   |   98.6   |   98.9   |\n| Libras                    | 87.8     | 85.6  |    85    |   85.6   |    85    |   88.3   |  **95.5**   |   87.2   |   83.9   |\n| LSST                      | 59       | 37.3  |   56.8   |    59    |   61.5   | **66.6** |    63.8     |   60.4   |   63.7   |\n| MotorImagery              | 50       | 51    |    59    |    61    |    64    |  **65**  |     N/A     |  **65**  |  **65**  |\n| NATOPS                    | 87       | 88.9  |   93.9   |   88.3   |   97.2   |   90.6   |    96.1     |   94.4   | **98.3** |\n| PenDigits                 | 94.8     | 97.8  |    98    |   97.7   |   98.7   |   98.3   |  **99.1**   |   98.9   | **99.1** |\n| PEMS-SF                   | N/A      | 69.9  |   75.1   |   75.1   |    78    |   86.7   |     N/A     | **94.2** |   88.4   |\n| PhonemeSpectra            | 19       | 11    |   17.5   |   29.8   | **30.9** |   17.6   |    29.3     |   14.4   |   23.1   |\n| RacketSports              | **93.4** | 80.3  |   86.8   |   88.2   |   80.3   |   84.2   |    88.8     |   87.5   | **93.4** |\n| SelfRegulationSCP1        | 71       | 87.4  |   65.2   |   78.2   |   89.8   |   88.4   |    91.8     |   92.8   | **93.9** |\n| SelfRegulationSCP2        | 46       | 47.2  |    55    |   57.8   |    55    |    60    |    56.1     |   57.2   | **60.6** |\n| SpokenArabicDigits        | 98.2     | 99    |   98.3   |   97.5   |   N/A    |   98.6   |  **99.7**   |   99.5   | **99.7** |\n| StandWalkJump             | 33.3     | 6.7   |    40    |   53.3   |   46.7   |   46.7   |  **66.7**   |   53.3   |   53.3   |\n| UWaveGestureLibrary       | 91.6     | 89.1  |   89.4   |   90.6   |    85    | **94.1** |     90      |   88.1   |   92.2   |\n| Average rank              | 5.57     | 7.17  |   6.13   |   4.80   |   4.27  |   3.70   |    3.19     |   3.74   | **2.13** |\n| Number of top-1           | 5        | 0     |    2     |    2     |    4     |    7     |      7      |    3     |  **15**  |\n| Wins                      | 20       | 28    |    27    |    23    |    21    |    19    |     15      |    20    |    -     |\n| Draws                     | 4        | 0     |    1     |    2     |    2     |    3     |      5      |    4     |    -     |\n| Loses                     | 4        | 2     |    2     |    5     |    3     |    8     |      7      |    3     |    -     |"}, {"review_id": "u16kINJJYx", "reviewer": "Reviewer_eNCr", "summary": "This paper proposes SwinGroupNet (SGN), a novel framework for multivariate time series classification, which integrates three key components: Variable Group Embedding (VGE), Multi-scale Group Window Mixing (MGWM), and Periodic Window Shifting and Merging (PWSM). By combining these modules, SGN effectively captures both intra-group and inter-group variable dependencies across multiple temporal scales from raw multivariate time series data. Extensive experiments on four medical multivariate time series datasets and ten benchmark datasets from the UEA archive demonstrate that SGN achieves state-of-the-art classification performance.", "questions": "1. The UEA archive does not provide predefined validation sets for its sub-datasets. However, in the provided source code (data_loader.py, lines 723–725), it appears that a validation set is being generated. Could the authors clarify the strategy used to create the validation sets for the UEA datasets? Additionally, the released code does not include experimental scripts for running on the UEA datasets—would the authors consider making them publicly available to ensure reproducibility?\n\n2. Regarding the results shown in Figure 4, were all baseline results (e.g., ROCKET, TimesNet) re-implemented and re-evaluated by the authors under the same experimental setup? If so, could the authors provide details on how the reproduction was performed, including any modifications or hyperparameter settings used?\n\n3. Given the experimental settings adopted in [R8, R9] on the full UEA 30 time series dataset, could the authors report the classification performance of SGN under the same setting, using the published results from [R8, R9] as baselines (without the need to re-run those methods if time and resources are limited)? Such a comparison would provide a clearer understanding of SGN’s effectiveness relative to recent state-of-the-art approaches.\n\n4. The weaknesses outlined above—including concerns about incremental novelty, unclear interactions among proposed modules, limited UEA dataset coverage, and insufficient comparison with recent related methods—require further clarification and justification.\n\n\n[R9] MPTSNet: Integrating multiscale periodic local patterns and global dependencies for multivariate time series classification. AAAI, 2025.", "limitations": "Yes.", "rating": 4, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths：\n\n1. The proposed VGE, MGWM, and PWSM modules are thoughtfully designed to address key aspects of multivariate time series analysis, including variable-wise dependency modeling, multi-scale feature extraction, and frequency-domain periodicity—factors that are central to advancing current time series research.\n\n2. The figures and tables are clearly presented and enhance the interpretability of the proposed method.\n\n3. The related work section is well-organized and comprehensive, providing a clear overview of the field’s recent advancements.\n\nWeaknesses：\n\n1. The overall novelty of the proposed SGN appears incremental, as it primarily integrates ideas from existing works. For instance, the core concept of the VGE module has been previously summarized and discussed in [R1], and shares similarities with contributions from [R2, R3]. Likewise, the multi-scale mixing strategy in MGWM resembles the approach adopted in TimeMixer [R4].\n\n2. Although VGE, MGWM, and PWSM are individually designed to capture distinct characteristics of multivariate time series, the conceptual and functional relationships among them are not clearly articulated. In particular, MGWM already captures multi-scale temporal patterns, which often include periodic structures. It remains unclear how the additional periodic modeling via PWSM complements or interacts with MGWM, and what underlying mechanism ensures their synergy.\n\n3. The authors claim in the abstract that existing methods either ignore inter-variable dependencies or model all variables jointly. However, a number of prior works have explicitly addressed inter-variable dependency modeling in multivariate time series classification [R5, R6], which are not discussed or empirically compared in the paper.\n\n4. For multivariate time series classification, the UEA 30 dataset is a widely accepted benchmark [R7, R8]. The authors evaluate their method on only 10 selected datasets, raising concerns about potential cherry-picking and limited generalizability of the results.\n\n\n[R1] A Comprehensive Survey of Deep Learning for Multivariate Time Series Forecasting: A Channel Strategy Perspective. arXiv, 2025.\n\n[R2] Crossformer: Transformer utilizing cross-dimension dependency for multivariate time series forecasting. ICLR, 2023.\n\n[R3] From similarity to superiority: Channel clustering for time series forecasting. NeurIPS, 2024.\n\n[R4] Timemixer: Decomposable multiscale mixing for time series forecasting. ICLR, 2024.\n\n[R5] SVP-T: A shape-level variable-position transformer for multivariate time series classification. AAAI, 2023.\n\n[R6] Fully-Connected Spatial-Temporal Graph for Multivariate Time Series Data. AAAI, 2024.\n\n[R7] The great multivariate time series classification bake off: a review and experimental evaluation of recent algorithmic advances. DMKD, 2021.\n\n[R8] Shapeformer: Shapelet transformer for multivariate time series classification. KDD, 2024.", "was_revised": true, "final_justification": "Based on the author's clarification,  I have decided to raise my score to Borderline Accept.", "rebuttal": "Many thanks for your thoughtful and encouraging comments. We sincerely appreciate your recognition of the design and motivation behind our proposed VGE, MGWM, and PWSM modules. We would like to offer further clarifications to enhance the understanding of our contributions.\n\n---\n**W1. The novelty of SGN seems incremental, as its core components (VGE, multi-scale mixing) closely resemble ideas from prior works such as [R1–R3].**\n\n**A1**. We would like to clarify the design and motivation behind our modeling of variable dependencies. We have observed in our experiments that performing variable aggregation based solely on intrinsic similarity at the **initial stage** fails to capture the **complex dependencies** among variables (see the ablation results in Table 3). To address this, we propose a **two-stage variable dependency modeling strategy** in SGN.\n\nIn the **first stage**, **VGE** module leverages pairwise similarity to group variables and perform group embedding. However, our goal here is to obtain a **coarse segmentation of variables**, analogous to patching along the temporal axis, allowing for more efficient downstream processing. In the **second stage**, we explicitly model **major variable dependencies** within and across variable groups. This allows for deeper and more expressive modeling of intra- and inter-group variable relationships.\n\nCompared with existing methods:\n\n- [R1] treats variable dependency modeling as a **plugin aggregation module** and does not further explore dependencies after grouping. In contrast, SGN performs **continued hierarchical interactions** after the initial grouping.\n    \n- [R2] applies operations to all variables **individually**, without leveraging variable grouping as an inductive bias. This may lead to **over-smoothing** and less structured dependency modeling.\n    \nRegarding **multi-scale strategies**, [R3] applies linear projections to generate multiple temporal views. In contrast, **SGN leverages the strong local feature extraction capability of convolutions** and employs multiple 1D convolutional kernels with different receptive fields to extract **multi-scale patterns** within periodic windows.\n    \n[R1] From similarity to superiority: Channel clustering for time series forecasting. NeurIPS, 2024.\n\n[R2] Crossformer: Transformer utilizing cross-dimension dependency for multivariate time series forecasting. ICLR, 2023.\n\n[R3] Timemixer: Decomposable multiscale mixing for time series forecasting. ICLR, 2024.\n\n---\n**W2. The conceptual distinctions and interactions among VGE, MGWM, and PWSM are unclear, particularly regarding how PWSM complements MGWM’s existing multi-scale temporal modeling.**\n\n**A2**. We appreciate the opportunity to further clarify the **interactions among SGN’s core modules**.\n\n- The **VGE module** serves as the foundation by constructing both the **periodic windows** and **variable groups**, enabling structured and localized modeling.\n    \n- Built upon the VGE outputs, the **MGWM module** operates **within each periodic window**, performing **feature extraction along both the temporal and variable dimensions**. \n    \n- While MGWM focuses on **within-window modeling**, PWSM is designed to **capture dependencies across windows**, thereby enabling global information flow and alignment across different temporal windows.\n\nThese three components are **mutually supportive and closely coupled**.\n\n---\n**W3. The paper overlooks prior works that explicitly model inter-variable dependencies, despite claiming a gap in existing methods without proper discussion or comparison.**\n\n**A3**. We divide variable interactions into three main categories: **variable-independent modeling**, **variable aggregation**, and **variable mixing**. These three strategies have been explicitly discussed in the _Related Work_ section to highlight their conceptual differences and practical trade-offs. We appreciate the reviewer’s attention to this aspect and **will incorporate additional relevant literature** in the final version to provide a more comprehensive overview of related approaches.\n\n---\n**W4. Evaluating on only 10 selected datasets from the UEA archive, rather than the full 30, raises concerns about cherry-picking and limits the generalizability of the results.**\n\n**A4**. We evaluate the effectiveness of SGN on four major datasets. To further assess the robustness and generalizability of SGN under diverse datasets—such as long sequences and weak periodicity—we additionally conduct experiments on ten UEA multivariate time series datasets. These datasets are commonly used in prior studies such as [R4-R6]. We have added results on all 30 UEA datasets and compared SGN with more baseline methods, as summarized in the table below.\n\n[R4] TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis. ICLR, 2023.\n\n[R5] ModernTCN: A Modern Pure Convolution Structure for General Time Series Analysis. ICLR, 2024.\n\n[R6] TimeMixer++: A General Time Series Pattern Machine for Universal Predictive Analysis. ICLR, 2025.\n\n---\n**Q1. The paper lacks clarity on the validation set construction for UEA datasets, as the code suggests a custom split despite no predefined sets. Moreover, the absence of experimental scripts for UEA datasets hinders reproducibility.** \n\n**A5.** We adopt a fixed random seed and utilize the **StratifiedShuffleSplit** method to ensure that the class distribution in the split subsets remains consistent with the original dataset. Specifically, we reserve **20% of the training set as the validation set**, and use the remaining **80% for model training**.\nDue to NIPS policy, we are unable to upload our UEA implementation script to the Anonymity link. However, we will make the code publicly available after the review process to ensure full reproducibility.\n\n---\n**Q2. Figure 4 lacks clarity on whether baselines were re-implemented under a consistent setup; details on reproduction, modifications, and hyperparameter settings are needed.**\n\n**A6.** We directly follow the data used in their paper. However, unlike their setting where the **test set is directly used as a validation set**, we adopt a more rigorous strategy by **reserving 20% of the training set as a validation set**, which helps prevent information leakage and better simulates real-world scenarios.\n\n---\n**Q3. To better assess SGN’s effectiveness, the authors are encouraged to report its performance under the same experimental settings used in [R7, R8] on the full UEA 30 dataset, using published results as baselines if re-running those methods is impractical.**\n\n**A7.** To further validate the effectiveness of the SGN method, we have supplemented additional comparison results under the same experimental settings with methods such as **Shapeformer** and **MPTSNet** on the **full UEA dataset**.  \nDue to time constraints, we were only able to reproduce a subset of the existing methods. The detailed results are provided in the following table. As shown, SGN consistently achieves **a greater number of first-place results and better average ranking** compared to state-of-the-art methods, demonstrating its robustness and generalization across diverse datasets.\n**Notably**, the **SGN#** column reports results using 20% of the training set as a validation set, **rather than directly using the test set for training as in other settings**, and still demonstrates strong performance. \n\n|Data/Model|W.MUSE|M.FCN|TapNet|ShapeNet|TodyNet|SVPT|Shapeformer|MPTSNet|SGN|SGN#|\n|--|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|\n|AW|99|97.3|98.7|98.7|98.7|**99.3**|99|97.7|99|98|\n|AF|33.3|26.7|33.3|40|46.7|40|53.3|53.3|**66.7**|53.3|\n|BasicMotions|**100**|95|**100**|**100**|**100**|**100**|**100**|**100**|**100**|**100**|\n|Character|99|98.5|**99.7**|98|N/A|99|99.2|N/A|99.6|97.8|\n|Cricket|**100**|91.7|95.8|98.6|**100**|**100**|94.4|94.4|**100**|98.6|\n|DDG|57.5|67.5|57.5|**72.5**|58|70|64|68|64|62|\n|EWorms|89|50.4|48.9|87.8|84|**92.5**|N/A|N/A|85.5|80.2|\n|Epilepsy|**100**|76.1|97.1|98.7|97.1|98.6|98.6|97.1|97.8|97.1|\n|EC|13.3|37.3|32.3|31.2|35|33.1|41.1|43.3|**44.5**|**44.5**|\n|ERing|43|13.3|13.3|13.3|91.5|93.7|87.4|94.4|**95.9**|91.9|\n|FaceDetection|54.5|54.5|55.6|60.2|62.7|51.2|65.8|69.8|**70.3**|**70.3**|\n|FingerMove|49|58|53|58.9|**67.6**|60|55|64|64|57|\n|HandMove|36.5|36.5|37.8|33.8|64.9|39.2|41.9|63.5|**75.7**|60.8|\n|Handwriting|**60.5**|28.6|35.7|45.1|43.6|43.3|30.2|34.4|50.4|43.2|\n|Heartbeat|72.7|66.3|75.1|75.6|75.6|79|**81.5**|75.6|77.1|77.1|\n|Insect|N/A|16.7|20.8|25|N/A|18.4|31.4|N/A|**68**|66.2|\n|JV|97.3|97.6|96.5|98.4|N/A|97.8|**99.2**|98.6|98.9|98.9|\n|Libras|87.8|85.6|85|85.6|85|88.3|**95.5**|87.2|83.9|83.9|\n|LSST|59|37.3|56.8|59|61.5|**66.6**|63.8|60.4|63.7|60.8|\n|MI|50|51|59|61|64|**65**|N/A|**65**|**65**|57|\n|NATOPS|87|88.9|93.9|88.3|97.2|90.6|96.1|94.4|**98.3**|95.6|\n|PenDigits|94.8|97.8|98|97.7|98.7|98.3|**99.1**|98.9|**99.1**|98.7|\n|PEMS-SF|N/A|69.9|75.1|75.1|78|86.7|N/A|**94.2**|88.4|88.4|\n|Phoneme|19|11|17.5|29.8|**30.9**|17.6|29.3|14.4|23.1|20.4|\n|RS|**93.4**|80.3|86.8|88.2|80.3|84.2|88.8|87.5|**93.4**|91.4|\n|SCP1|71|87.4|65.2|78.2|89.8|88.4|91.8|92.8|**93.9**|91.1|\n|SCP2|46|47.2|55|57.8|55|60|56.1|57.2|**60.6**|57.8|\n|SA|98.2|99|98.3|97.5|N/A|98.6|**99.7**|99.5|**99.7**|**99.7**|\n|StandWalkJump|33.3|6.7|40|53.3|46.7|46.7|**66.7**|53.3|53.3|40|\n|UWave|91.6|89.1|89.4|90.6|85|**94.1**|90|88.1|92.2|90.3|\n|Average rank|6.21|8.03|6.13|5.30|4.69|4.13|3.56|4.30|**2.13**|4.40|\n|Number of top-1|5|0|2|2|4|7|7|3|**15**|4|\n|Wins|20|28|27|23|21|19|15|20|-||\n|Draws|4|0|1|2|2|3|5|4|-||\n|Loses|4|2|2|5|3|8|7|3|-||\n\n[R7] MPTSNet: Integrating multiscale periodic local patterns and global dependencies for multivariate time series classification. AAAI, 2025.\n\n[R8] Shapeformer: Shapelet transformer for multivariate time series classification. KDD, 2024.\n\n---\n\n**Q4. The weaknesses outlined above require further clarification and justification.** \n\n**A8.** We have provided the corresponding responses in **Answers A1–A4** above."}, {"review_id": "Op2SwRQQfQ", "reviewer": "Reviewer_6yyx", "summary": "This paper proposes SwinGroupNet (SGN), a novel framework for multivariate time series (MTS) classification that addresses limitations of existing methods by integrating structured variable grouping and hierarchical temporal feature extraction. The model comprises three core modules: 1) Variable Group Embedding (VGE), which partitions variables into groups based on similarity to capture intra-group and inter-group dependencies; 2) Multi-Scale Group Window Mixing (MGWM), which extracts multi-scale temporal features via periodic window partitioning and convolutional operations; 3) Periodic Window Shifting and Merging (PWSM), which leverages sequence periodic patterns to enable hierarchical temporal interaction. Extensive experiments on diverse benchmarks show SGN achieves state-of-the-art performance, with an average 4.2% accuracy improvement over existing methods.", "questions": "--- In the Variable Group Embedding module, BDC (Brownian Distance Covariance) is used to model dependencies between variables. However, referring to Equation (11), its essence still relies on Euclidean distance. Does this approach genuinely capture better non-linear dependencies? Is there any performance improvement compared to other methods? Additionally, when calculating dependencies between variables, do you use the entire time series of that variable?\n--- \"Considering the extensibility of periodic patterns, we further incorporate multiple scales by merging additional period windows corresponding to the remaining Top-K dominant frequencies.\" (page=5, lines 155-157) This statement mentions merging period windows corresponding to the remaining frequencies in Top-K. Could you elaborate in detail on how this merging process is implemented?\n--- While moving and merging periodic windows enhances the capture of cross-window dependencies, what specific offset value and window size after merging yield optimal results? \n--- In Section 4.2, the authors selected 10 multivariate time series datasets from the UEA. Many research reports have shown the performance of all datasets. How does your work perform on all datasets? Additionally, the hyperparameter sensitivity analysis lacks an evaluation of the regularization parameter $\\beta$.", "limitations": "The applicability of SGN in other time series tasks such as forecasting and imputation remains to be further explored. Moreover, the use of intrinsic similarity to generate the assignment matrix introduces additional computational overhead.", "rating": 4, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths:\n1. This paper introduces a novel perspective transforming multivariate interactions into structured intra/inter-group relationships, effectively balancing fine-grained dependency capture and over-smoothing avoidance.  \n2. Experimental validation covers domains including healthcare and human activity recognition, demonstrating consistent superiority over baselines.\n\nWeaknesses:\n1. In the Variable Group Embedding module, BDC (Brownian Distance Covariance) is used to model dependencies between variables. However, referring to Equation (11), its essence still relies on Euclidean distance. Does this approach genuinely capture better non-linear dependencies? Is there any performance improvement compared to other methods? Additionally, when calculating dependencies between variables, do you use the entire time series of that variable?\n2. \"Considering the extensibility of periodic patterns, we further incorporate multiple scales by merging additional period windows corresponding to the remaining Top-K dominant frequencies.\" (page=5, lines 155-157) This statement mentions merging period windows corresponding to the remaining frequencies in Top-K. Could you elaborate in detail on how this merging process is implemented?\n3. In the \"Multi-Scale Group Window Extracting\" section (Lines 159–172), operations of intra-group and inter-group pointwise convolutions are not explained. Mathematical formulations are needed to clarify channel dimension transformations. \n4. While moving and merging periodic windows enhances the capture of cross-window dependencies, what specific offset value and window size after merging yield optimal results? Please provide a quantitative analysis of this. \n5. In Section 4.2, the authors selected 10 multivariate time series datasets from the UEA. Many research reports have shown the performance of all datasets. How does your work perform on all datasets? Additionally, the hyperparameter sensitivity analysis lacks an evaluation of the regularization parameter $\\beta$.  \n6. Notation inconsistency: $k_i$ in Equation (6) conflicts with $n_k$ in Line 699 of Appendix D, causing confusion. Notation should be unified.", "was_revised": true, "final_justification": "I have increased my rating considering the work from authors to clarify and improve the paper.", "rebuttal": "We sincerely appreciate your recognition of our novel perspective on modeling multivariate interactions through structured intra/inter-group relationships, as well as your acknowledgment of the strong empirical validation across diverse domains. We would like to provide some clarifications in the hope of addressing your concerns.\n\n---\n\n\n**W1. While the VGE module employs BDC to model inter-variable dependencies, Equation (11) reveals its reliance on Euclidean distance, raising questions about its ability to truly capture non-linear relationships. Clarification is needed on whether this offers performance gains over other dependency measures, and whether the full time series of each variable is used in the computation.**\n\n\n**A1**. We thank the reviewer for the insightful question regarding our similarity metric.  \nIn our method, we adopt BDC to measure similarity, where a positive value of **dCov(X, Y) > 0** indicates the existence of statistical dependence—including **non-linear** relationships.\nTo validate its effectiveness, we compare **BDC** with **Pearson correlation** on both the FLAAP and UCI-HAR datasets. As shown in the table below, BDC demonstrates a **slight improvement in performance**.  \nNotably, BDC computes similarity over the **entire time series**, allowing it to better preserve the temporal structure during the similarity estimation process.\n\n| Dataset |  FLAAP   |       | UCI-HAR  |       |\n| ------- | :------: | :---: | :------: | :---: |\n| Metric  | Accuracy |  F1   | Accuracy |  F1   |\n| Pearson |  79.64   | 78.94 |  95.52   | 95.55 |\n| BDC     |  80.81   | 80.35 |  95.62   | 95.64 |\n\n---\n\n**W2. The paper mentions merging period windows from the remaining Top-K frequencies, but it lacks details—could the authors clarify how this merging is implemented in practice?**\n\n**A2.**  In our experiments, we observed that the **top-k dominant periods** in time series often exhibit a **multiple relationship**. Based on this insight, we design our model to start with a **small base period window**, and then progressively **fuse multiple windows** to reach larger period lengths.  \nThis periodic window fusion strategy allows SGN to capture diverse periodic patterns effectively across various temporal resolutions.\n****\n\n**W3. In the \"Multi-Scale Group Window Extracting\" section (Lines 159–172), operations of intra-group and inter-group pointwise convolutions are not explained. Mathematical formulations are needed to clarify channel dimension transformations.**\n\n**A3.** Given the input data tensor **$X \\in \\mathbb{R}^{num \\times (d_{\\text{model}} \\times v_{\\text{group}}) \\times T}$**, where `num` is the number of temporal windows, `T` is the periodic window length, $v_{\\text{group}}$​​ is the number of variable groups, and $d_{\\text{model}}$​​ is the feature dimension per group:\n\n- We first apply **group-wise pointwise convolutions** by setting the number of convolution groups to $v_{\\text{group}}$​​, enabling **intra-group interaction**.\n- Next, we **transpose the $v_{\\text{group}}$ and $d_{\\text{model}}$​​ dimensions**, resulting in a shape of **num × ($v_{\\text{group}}$​​ x $d_{\\text{model}}$​​) × T**.\n- Then, we apply another pointwise convolution with **$d_{\\text{model}}$​​** groups, allowing **inter-group feature interactions** across different variable embeddings.\n\nThis two-stage group-wise and inter-group convolution design enhances both **local specialization** and **global coordination** across variable groups.\n\n---\n\n**Q4. What are the specific offset and merged window size values that optimize cross-window dependency capture, and could you provide quantitative analysis supporting these choices?**\n\n**A4.** We provide detailed ablation results on the effect of **shift offsets** according to the window length T in the table below. As shown, different offset values yield similar performance, indicating that the essential contribution lies in enabling **information exchange across shifted temporal windows**, rather than relying on a specific offset.\n\n| Shift_offset  |   0   |  T/4  |  T/2  | 3/4T  |\n| ------- | :---: | :---: | :---: | :---: |\n| FLAAP   | 78.05 | 80.07 | 80.81 | 79.48 |\n| UCI-HAR | 87.05 | 94.74 | 95.62 | 94.62 |\n| TDBRAIN | 99.79 | 99.91 | 99.9  | 99.75 |\n| PTB-XL  | 73.32 | 73.75 | 73.8  | 74.19 |\n\nFor the **window merging** strategy, we adopt a doubling-based merging approach, where the merged window size is a multiple of the original. The corresponding results and in-depth analysis are presented in **Table 10 of Appendix E**, demonstrating the effectiveness of our period merging design.\n\n\n---\n**Q5. The evaluation on only 10 UEA datasets is limited; how does the method perform on the full set? Also, the hyperparameter sensitivity analysis omits the regularization parameter.**\n\n**A5.** We have supplemented the results on the full UEA multivariate time series classification benchmark. Under the **same experimental settings**, we compare SGN with a broader range of recent state-of-the-art methods (see the Table). **Wins/Draws/Losses** indicate the number of datasets (out of 30) on which the SGN method achieves higher, equal, or lower accuracy compared to the corresponding baseline methods. As shown, SGN consistently achieves **a greater number of first-place results and better average ranking** compared to state-of-the-art methods, demonstrating its robustness and generalization across diverse datasets.\n\n|Data/Model|W.MUSE|M.FCN|TapNet|ShapeNet|TodyNet|SVPT|Shapeformer|MPTSNet|SGN(Ours)|\n|---|:--:|:--:|:--:|:--:|:--:|:--:|:--:|:--:|:--:|\n|ArticularyWordRecognition|99|97.3|98.7|98.7|98.7|**99.3**|99|97.7|99|\n|AtrialFibrillation|33.3|26.7|33.3|40|46.7|40|53.3|53.3|**66.7**|\n|BasicMotions|**100**|95|**100**|**100**|**100**|**100**|**100**|**100**|**100**|\n|CharacterTrajectories|99|98.5|**99.7**|98|N/A|99|99.2|N/A|99.6|\n|Cricket|**100**|91.7|95.8|98.6|**100**|**100**|94.4|94.4|**100**|\n|DuckDuckGeese|57.5|67.5|57.5|**72.5**|58|70|64|68|64|\n|EigenWorms|89|50.4|48.9|87.8|84|**92.5**|N/A|N/A|85.5|\n|Epilepsy|**100**|76.1|97.1|98.7|97.1|98.6|98.6|97.1|97.8|\n|EthanolConcentration|13.3|37.3|32.3|31.2|35|33.1|41.1|43.3|**44.5**|\n|ERing|43|13.3|13.3|13.3|91.5|93.7|87.4|94.4|**95.9**|\n|FaceDetection|54.5|54.5|55.6|60.2|62.7|51.2|65.8|69.8|**70.3**|\n|FingerMovements|49|58|53|58.9|**67.6**|60|55|64|64|\n|HandMovementDirection|36.5|36.5|37.8|33.8|64.9|39.2|41.9|63.5|**75.7**|\n|Handwriting|**60.5**|28.6|35.7|45.1|43.6|43.3|30.2|34.4|50.4|\n|Heartbeat|72.7|66.3|75.1|75.6|75.6|79|**81.5**|75.6|77.1|\n|InsectWingbeat|N/A|16.7|20.8|25|N/A|18.4|31.4|N/A|**68**|\n|JapaneseVowels|97.3|97.6|96.5|98.4|N/A|97.8|**99.2**|98.6|98.9|\n|Libras|87.8|85.6|85|85.6|85|88.3|**95.5**|87.2|83.9|\n|LSST|59|37.3|56.8|59|61.5|**66.6**|63.8|60.4|63.7|\n|MotorImagery|50|51|59|61|64|**65**|N/A|**65**|**65**|\n|NATOPS|87|88.9|93.9|88.3|97.2|90.6|96.1|94.4|**98.3**|\n|PenDigits|94.8|97.8|98|97.7|98.7|98.3|**99.1**|98.9|**99.1**|\n|PEMS-SF|N/A|69.9|75.1|75.1|78|86.7|N/A|**94.2**|88.4|\n|PhonemeSpectra|19|11|17.5|29.8|**30.9**|17.6|29.3|14.4|23.1|\n|RacketSports|**93.4**|80.3|86.8|88.2|80.3|84.2|88.8|87.5|**93.4**|\n|SelfRegulationSCP1|71|87.4|65.2|78.2|89.8|88.4|91.8|92.8|**93.9**|\n|SelfRegulationSCP2|46|47.2|55|57.8|55|60|56.1|57.2|**60.6**|\n|SpokenArabicDigits|98.2|99|98.3|97.5|N/A|98.6|**99.7**|99.5|**99.7**|\n|StandWalkJump|33.3|6.7|40|53.3|46.7|46.7|**66.7**|53.3|53.3|\n|UWaveGestureLibrary|91.6|89.1|89.4|90.6|85|**94.1**|90|88.1|92.2|\n|Average rank|5.57|7.17|6.13|4.80|4.27|3.70|3.19|3.74|**2.13**|\n|Number of top-1|5|0|2|2|4|7|7|3|**15**|\n|Wins|20|28|27|23|21|19|15|20|-|\n|Draws|4|0|1|2|2|3|5|4|-|\n|Loses|4|2|2|5|3|8|7|3|-|\n\nIn addition, we conduct an ablation study on the **β parameter** (see Table Y). The results reveal a **non-monotonic trend**: as β increases, the performance initially improves and then gradually declines, indicating that an appropriate choice of β is crucial for balancing the similarity regularization term.\n\n| β       |   0   |  0.1  |  0.2  |  0.3  |\n| ------- | :---: | :---: | :---: | :---: |\n| FLAAP   | 80.24 | 80.81 | 79.4  | 80.09 |\n| UCI-HAR | 94.86 | 95.62 | 94.05 | 94.42 |\n| TDBRAIN | 99.88 | 99.9  | 99.75 | 99.88 |\n| PTB-XL  | 70.84 | 73.8  | 73.84 | 73.8  |\n\n---\n\n**W6. Notation inconsistency:  in Equation (6) conflicts with  in Line 699 of Appendix D, causing confusion. Notation should be unified**\n\n**A6.** We denote $k_{\\text{i}}$​​ as the kernel size and $n_{\\text{k}}$​​​ as the number of convolution kernels. For example, when $n_{\\text{k}}$​​=6, we use multiple convolution kernels with sizes $k_{\\text{i}}$​​∈{1,3,5,7,9,11}. This design enables the model to capture temporal patterns at multiple scales effectively.\n\n\n---\n\n**Q. The problem is the same as the weakness.** \n\n**A7.** We have provided the corresponding responses in **Answers A1–A6** above."}]

Author rebuttal:

Meta-review: The paper proposes a method for multivariate timeseries classification which works by grouping features, modeling inter and intra-group dependencies and learning multi-scale features. Most reviewers praised the paper's novelty, strong empirical results and clarity of presentation.

The comparison against other channel dependency methods is appreciated, as are the additional experimental results presented in response to reviewers eNCr and 6yyx.

During the response period, the authors addressed the reviewer's concerns, leading to a unanimous decision to accept the paper.
Decision: Accept (poster)