Boosting Transferability and Discriminability for Time Series Domain Adaptation
Authors: Mingyang Liu
Xinyang Chen
Yang Shu
Xiucheng Li
Weili Guan
Liqiang Nie
Venue: NeurIPS 2024 poster (2024)
Keywords: Time-series; Domain Adaptation; Transferability; Discriminability; Frequency domain
Primary area: other

Abstract: Unsupervised domain adaptation excels in transferring knowledge from a labeled source domain to an unlabeled target domain, playing a critical role in time series applications. Existing time series domain adaptation methods either ignore frequency features or treat temporal and frequency features equally, which makes it challenging to fully exploit the advantages of both types of features. In this paper, we delve into transferability and discriminability, two crucial properties in transferable representation learning. It's insightful to note that frequency features are more discriminative within a specific domain, while temporal features show better transferability across domains. Based on the findings, we propose **A**dversarial **CO**-learning **N**etworks (**ACON**), to enhance transferable representation learning through a collaborative learning manner in three aspects: (1) Considering the multi-periodicity in time series, multi-period frequency feature learning is proposed to enhance the discriminability of frequency features; (2) Temporal-frequency domain mutual learning is proposed to enhance the discriminability of temporal features in the source domain and improve the transferability of frequency features in the target domain; (3) Domain adversarial learning is conducted in the correlation subspaces of temporal-frequency features instead of original feature spaces to further enhance the transferability of both features. Extensive experiments conducted on a wide range of time series datasets and five common applications demonstrate the state-of-the-art performance of ACON. Code is available at <https://github.com/mingyangliu1024/ACON>.

Boosting Transferability and Discriminability for Time Series Domain Adaptation
Mingyang Liu', Xinyang Chen les, Yang Shu Xiucheng Li Weili Guan", Liqiang Nie 'School of Computer Science and Technology. Harbin Institute of Technology (Shenzhen)
School of Data Science and Engineering, East China Normal University
School of Electronics and Information Engineering, Harbin Institute of Technology (Shenzhen) com, yshu@dase ecnu edu. fchenxinyang, htap:/aannnniiiiun lixiucheng,,,oo www.nnhennnngggilll...e. guanweili, mieliiiang) centt.ddu.ccmm cn
mingyang11iu10240gmaaa ,
Abstract
Unsupervised domain adaptation excels in transferring knowledge from a labeled source domain to an unlabeled target domain, playing critical role in time series applications. Existing time series domain adaptation methods either ignore fre- quency features or treat temporal and frequency features equally, which makes it challenging to fully exploit the advantages of both types features. In this paper, we delve into transferability and discriminability. two crucial properties in trans- ferable representation learning. It's insightful note that frequency features are more discriminative within a specific domain, while temporal features show better transferability across domains. Based on the findings, we propose Adversarial CO-learnin Networks (ACON), to enhance transferable representation learn- ing through collaborative learning manner in three aspects: (1) Considering the multi- petiodierio in time series, multi-period frequency feature learning is proposed to enhance the discriminability of frequency features; (2) Temporal- frequency domain mutual learning is proposed to enhance the discriminability of temporal features in the source domain and improve the transferability of fre- quency features in the target domain; (3) Domain adversarial learning is conducted in the correlation subspaces of temporal sppooral-frquuccyy features instead of original feature spaces further enhance the transferability of both features. Extensive experiments conducted on wide range of time series datasets and five common ap- plications demonstrate the state-of-the-art performance of ACON. Code is available at https: / github. com/
Introduction
Time series classification has achieved significant success in the deep learning era by leveraging discriminative features learned from extensive labeled data [18]. However, the presence of distribution shift may arise when deploying the model, potentially impeding the generalization ability of deep models [].]. Unsupervised domain adaptation [13], offering the potential to transfer knowledge from a labeled source domain to an unlabeled target domain, emerges as a promising solution.
Existing domain adaptation methods tailored for time series primarily focus on learning domain- invariant temporal features [30, 41, 29]. yielding promising results. Recently, the significance of frequency features for enhancing domain-invariant representation has also been recognized [16]. However, frequency features and temporal features are treated equally, and their distinct properties are overlooked, leading to the inability to fully leverage both types of features to boost transfer learning.
In this paper, we analyze the two most important properties of features in transfer learning: transfer- ability and discriminability, to investigate the characteristics of the frequency features and temporal
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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features. We find that under the premise of adopting advanced backbones in -fate-of-the-ar works [31, 16]. frequency features are more discriminative within a specific domain, while temporal features show better transferability across domains.
Based on the findings, we propose Adversarial CO-leaming Networks (ACON) maximize the po- tential of temporal features and frequency features in terms of both transferability and discriminability in collaborative learning manner. Firstly, to fully leverage the properties of multi-periodicity in time series, we propose multi-period frequency feature learning to further enhance the discriminability of frequency features. Secondly, we propose temporal-frese frequency domain mutual learning to enhance the discriminability of temporal features in the source domain and improve the transferability of fre- quency features in the target domain. Specifically, to harness the potent discriminability of frequency features within the domain, we enable the transfer of knowledge from frequency features to temporal features within the source domain via knowledge distillation. To leverage the strong transferability of temporal features across domains, we facilitate the transfer of knowledge from temporal features to frequency features in the target domain through knowledge distillation. Thirdly, we propose to learn transferable representations via domain adversarial learning in semporal-frquuene correlation correlation subspace
subspace instead of the original temporal feature space. The camporal-frqqeent not only possesses the properties of the original temporal feature space and original frequency feature space but also incorporates the correlation between the two types of features. Learning transferable representations in the temporal frequuuccyy correlation subspace can further enhance the transferability of features. Our main contributions can be summarized as follows:
We uncover the characteristies wherein temporal features and frequency features cannot be equally treated in transfer learning. Specifically, we observe that frequency features are more discriminative within a specific domain, while temporal features show better transferability across domains through empirical findings.
We design ACON, which enhances UDA in three key aspects: module to enhance the discriminability of frequency features, a -rreuuecy domain mutual learning module to enhance the discriminability of temporal features in the source domain and improve the transferability of frequency features in the target domain, and a domain adversarial learning module in enhance transferability of features.
feature learning
correlation subspace further
Experiments conducted on a wide range of time series datasets and five common applications verify the effectiveness of ACON.
2 Related Work
General Unsupervised Domain Adaptation Methods Unsupervised domain adaptation leverages the labeled source domain to predict the labels of a different but related, unlabeled target domain. It finds wide applications in computer vision [46, 15, 8] and natural language processing [40, 39, 44]. Existing UDA methods can be classified into three categories: (1) Methods based on adversarial training aim to learn domain-invarian invariant representations via the game between the feature extractor and the domain discriminator. Widely used methods include DANN [13], CDAN [26] and DIRT-T [34]. (2) Methods based on statistical divergence aim to reduce the domain discrepancy by minimizing domain discrepancy in latent feature space. Widely used methods include DAN [25], DeepCoral [36] and HoMM [5]. (3) Methods based on self-training produce pseudo-labels on unlabeled data and use confident aseudo-labels together with the labeled data to train the model. Widely used methods include PFAN[6]. CST [22] and AdaMatch [2]. However, these methods are generally designed and do not fully leverage the properties of time series. Although these methods can be applied to time series through tailored feature extractors, they often obtain suboptimal performance and UDA algorithm specially designed for time series is needed.
Unsupervised Domain Adaptation for Time Series To date, few methods have been tailored to unsupervised domain adaptation for time series data. VRADA [30] is the first UDA method for multivariate time series that uses adversarial learning for reducing domain discrepancy. In VRADA, a variational recurrent neural network (VRNN) [10] is trained in an adversarial way to learn Nomain-invarian temporal features. CoDATS [41] builds upon VRADA but uses a convolutional neural network for the feature extractor, proposing a solution for multi-source domain adaptation in
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time series classification. SASA [3] adopts LSTM [33] as feature extractors to capture the domain- invariant association, and aligns sparse associative structure between source and target domain via the minimization of maximum mean discrepancy (MMD) [38]. AdvSKM [23] modifies MMD to make more suitable for time series data. CLUDD [29] learns contextual representation via contrastive learning, and aligns features between source and target domain via adversarial training. RAINCOAT [16] is the first to introduce frequency features into domain adaptation, aligning temporal features and frequency features respectively via Sinkhorn divergence.
Research gap In general, in terms of representation learning, most methods only focus on the temporal domain or assume that the temporal domain and the frequency domain are independent of each other, hindering the full utilization of two types of features. In terms of feature adaptation, existing works only focus on aligning temporal features or adopting simple statistical divergence to align frequency features, ignoring the different properties of the temporal features and frequency features in transfer learning. terms of evaluation, the existing evaluations are conducted on several datasets of limited scale in a few specific tasks, and more general evaluations are needed.
3 Transferability and Discriminability in Time Series
3.1 Problem setup
In this paper, we study the UDA problem for time series classification. time series classification problem, the model receives set of n labeled samples {(x,,y,)) where i-th sample x; E IR CRT contains observation of variates over T time steps. We allow for both univariate and multivariate time series. In UDA setup, we are given n, labeled samples from a source domain P = {(x,, yf) and unlabeled samples from a target domain Q = {x){)] which are sampled from different distributions P and Q. Superscripts 8 and are adopted to distinguish the source domain and the target domain. UDA for time series aims to learn a time series classification model with labeled
y.))
source data P and unlabeled target data Q, which can make accurate predictions on the target domain.
In addition the source domain and target domain UDA, time series naturally can be represented in the temporal domain and frequency domain. By Fast Fourier Transform (FFT), the raw time series input x; in the temporal domain can be transformed to corresponding frequency input v, the frequency domain:
V; FFT (x;),
where the complex variable v, E CC contains observation of C' variates over [ different frequencies. Due to the conjugacy of frequency domain, we only consider the frequencies within {1, [.
3.2 Discriminability of frequency feature
Temporal data vs. Frequancy data
Chossecaiio Results
Tapprra
(a) Temporal data vs. Frequency data
(b) Source classification
(c) Target classification
Figure 1: Discriminability of frequency feature: (a) The Filectreecepphalograhyy (EEG) signal and corresponding frequency data of two classes in the CAP dataset: Wake and Rapid Eye Movement (REM). (b) Classification on the source domain: Temporal domain vs. Frequency domain. (c) Source-only and DANN: Temporal domain vs. Frequency domain.
As Figure 1(a) presented, compared to the uniform distribution of temporal data for different classes, the frequency data for different classes shows distinct differences in the dominant frequencies and peaks, which holds more discriminative information. To further investigate the discriminability of
3

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frequency features, we perform the single data domain classification task in the frequency domain and temporal domain respectively on all five data domains of the CAP [37, 14] dataset.
In order to minimize the impact of specific model structures, we adopt 3-layer ID-CNN, a generic structure the temporal feature extractor, and 1-layer linear the frequency feature extractor, which have both widely validated for their effectiveness in existing time series analysis methods [23, 16, 42, 43]. We only retain the low-frequency data ensure that the temporal feature extractor and the frequency feature extractor have comparable parameter quantities. For the classifiers, we uniformly use I-layer linear. As Figure 1(b) shown, with simple feature extractor, the frequency classification outperforms the temporal classification, demonstrating that the frequency features have better discriminability. More analysis results on different datasets are included in Appendix C.I.
3.3 Transferability of temporal feature
Another key criterion that characterizes the performance of domain adaptation transferability [7]. Transferability indicates the ability to learn invariant features across domains. Since the frequency features have better discriminability within the source domain, the frequency features also have better discriminability in the target domain?
natural to raise the question: Will
We investigate this problem starting with the comparison of four methods: (1) Source-only-F, a model trained in the frequency domain without UDA. (2) Source-only-T. a model trained in the temporal domain without UDA. (3) DANN-F, a model aligning the source features and the target features in the frequency domain via DANN. (4) DANN-T. a model aligning the source features and the target features the temporal domain via DANN. Figure I(c) shows the accuracy in the target domains of four source-targe target domain pairs from the CAP dataset. Compared with Figure 1(b), the frequency classification, which has better discriminability performance in the source domain, actually slightly underperforms in the target domain. It indicates that better discriminabilityy in the source domain does not necessarily imply better discriminability in the target domain. Compared with Source-only methods, the gap between DANN-F and DANN-T is further exacerbated. This suggests that the temporal feature extractor more easily learns domain-invann inmainninvariant features. More analysis results on different datasets are included in Appendix C.2.
The above analysis reveals two insights for time series domain adaptation: With better discriminability but worse transferubility. domain adaptation in the frequency domain obtains suboptimal performance; while with better transferability, domain adaptation in the temporal domain has the potential to achieve superior performance under the guidance of more discriminative information.
Approach
Based on the above observations, our motivation is simultaneously leverage the strong discrim- inability of frequency features and the strong transferability of temporal features to enhance domain adaptation. This inspires us learn tive learning manner.
temporal and frequency features in collabora-
Figure 2 illustrates the overall structure of Adversarial CO-learning Networks (ACON). To avoid confusion, subscripts T and are adopted to distinguish the temporal domain and the frequency domain. Specifically, in the temporal domain,
have temporal feature extractor with temporal input f = (x) and temporal classifier ýT = (f));; while in the frequency domain, we have frequency feature extractor with frequency input z = vF(v) and a frequency classifier ÿ = (z) Additionally, we have a domain discriminator 9p. which is trained to distinguish the source feature and the target feature. In the following, we will introduce three main contributions in ACON: multi-period frequency feature learning in Section 4.1, temporal-frqquecc domain mutual learning in Section 4.2, and domain adversarial learning in temporal -requeeny correlation subspace in Section 4.3.
4.1 Multi-period frequency feature learning
The real-world time series usually present multi-periodicity, which is reflected in the frequency domain as the presence of few dominant frequencies with significantly larger amplitudes. Data from different periods can have different discriminative patterns. Based on this, before performing FFT, we segment the raw time series according to the top-k significant periods, enhancing the

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9F y
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gr
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Figure 2: The architecture of ACON. ACON models temporal data (blue) and frequency data (green) simultaneously. Left part: Segment raw frequency data by period to capture different discriminative patterns. Middle part: Align distributions in -rreuulyy correlation subspace via adversarial training. Right part: Mutual learning between the temporal domain and frequency domain.
discriminability of the frequeney domain. Additionally, by seriod-based segmentation, the noises brought by meaningless high frequencies are effectively filtered out [4, 45].
To capture the overall multi-periodicityy before training, we randomly sample mini-batches from the training set to perform FFT and select the frequencies with the top-k amplitudes (/,,-.., Jk.. Given the frequency fj. the corresponding period is Pý = 771. 1- For each selected period pj in (pi.....P0 Pp) and frequency fj in the corresponding {fi..... ] perform the following transform input x,:
X Reshape,, pj (xx), j E kk.
Avg FFT X
where X E RC v ce is averaged from f, dimensions by Avg(-). In other words, we perform FFT on each segment obtained by segmenting x; with period py. and average the FFT results across segments to obtain the distribution v over the frequencies within {1..... L 2 J}. In this way, we obtain the overall frequency pattern for each period. To keep the discriminative patterns derived from different periods, we concatenate the different v/. obtaining v; as the frequency input corresponding to the temporal input x;:
V: v! e.... v JE kk.
(3)
We extend the source sample P and the target sample set Q to the frequency domain: P
{(x], vi) and Q {(x], =i To learn features in both real part and imaginary part of complex frequency data, we adopt complex-valued linear layer as the frequency feature extractor vrr. Since the phase generally does not provide strong discriminative information, we only retain the amplitudes of each frequency to construct the frequency domain feature Z,:
2: Amp (v+((v:))
where Amp(.) denotes the calculation of amplitude values. For multivariate time series, we convert v; into a single-channel vector by concatenating across different variates.
4.2 Terpuecl- domain mutual learning
Discriminability and transferability are two key criteria that characterize the goodness of feature representations to enable domain adaptation. Section 3, we reveal that the frequency features are more discriminative within the source domain, while the temporal features are more transferable across domains. Based on this discovery, we propose carporal-frequencyy domain mutual learning, aiming to leverage the respective advantages of the temporal domain and frequency domain.
The essence of domain mutual learning relies on how to transfer knowledge between the temporal domain and frequency domain. Inspired by model distillation, where the knowledge is transferred by matching the predictions between the teacher and student via the Kullback Leibler (KL) divergence [17], we focus mutual learning on the alignment between the temporal predictions and the frequency predictions. The KL divergence between two predictions pı and p2 is formulated as:
m
DKI(pillp2)
Σ m=1
P
log
(5)
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The KL divergence is asymmetric, that is, DRL(Pillp) emphasizes aligning Pa to Pt. while D D (Pallpi) emphasizes aligning Pi to P2- Based on the asymmetry, we use different alignment strategies in the source domain and target domain. Specifically, in the source domain, the frequency model serves as more discriminative teacher, helping the temporal model make more accurate predictions; conversely, in the target domain, the temporal model acts as more transferable teacher, assisting the frequency model in learning domain-invariant representations. We achieve temporal- frequency domain mutual learning by minimizing the KL Divergence. Formally, domain mutual learning is formulated as:
(V',, GT) = E (x) pl PD LM (1F. gF) = ( (VT
(6)
where y and y refer to the frequency prediction and temporal prediction in the source domain respectively; while y's and 8 refer the frequency prediction and temporal prediction in the target domain respectively. By aligning 8 to y?. the training of the temporal feature extractor and classifier is guided with more discriminative information; by aligning y1p to y the transferable knowledge contained in the temporal features is transferred to frequency domain.
4.3 Domain adversarial learning in temporal-frqquency correlation subspace
Domain adversarial learning [13] is one of the most popular transferable representation learning methods, and it can be employed to learn transferable representation in time series. The key to the effectiveness of the method lies in how fully utilize two types of features to learn transferable representations. Given time series in temporal domain and frequency domain, domain adversarial learning can be formulated Lor on the temporal feature extractor Uhy and classifier 9r, which is minimized to guarantee lower source risk of the temporal classifier; (b) Lop on the frequency feature extractor tp and classifier gr, which is minimized to guarantee lower source risk of the frequency classifier; (c) LD on the temporal feature extractor thr, the frequency feature extractor 4hy and the domain discriminator gD. which is minimized over JD but maximized over vhr and uhy:
minimax optimization problem with three competitive loss terms: (a)
(VTT ST) = E (x xt) (gT (uT (x()) yf),
(F)) E (v (gr (&e (vf)) .y)),
(7)
CD(DT, (F, = - E (x) xx) logigD (vh (xf) VE (vf))
E ( log gD (vr (xf) th (v!))..
where denotes cross-entropy loss. Different from standard domain adversarial learning, where there is only one type of feature, domain adversarial learning in time series needs to consider the temporal features and frequency features simultaneously. A simple strategy is to concatenate the temporal feature f and the frequency feature z. However, with the concatenation strategy, the adversarial game between the domain discriminator and the feature extractors can be viewed as two independent components: the game between dD and v/y and the game between and Φp. With the worse transferability, z provides ID with rich domain-label relevant information. In this case, 9D only needs to focus on the game with vhp, ignoring the domain adversarial learning in the temporal domain.
To achieve co-alignment in the temporal domain and frequency domain, we propose domain ad- versarial learning in temporal-frequeng correlation subspace. The temporal-frequency correlation subspace not only possesses statistical characteristics of the original temporal feature subspace and original frequency feature subspace but also reflects the correlation between temporal features and frequency features. Reducing the discrepancy of the only reduces the discrepancy in the cross-domain temporal and frequency features but also decreases the differences in cross-domain temporal-frequency correlations.
correlation subspace not
Formally, the vectors in temporal- freeuunncy correlation subspace can be calculated as the outer product @ between the temporal feature f and the frequency feature
2 z |z [1] f. [2] f. ....... z [1] f).
(8)
where z E RRLx By adjusting the order of dimensions, z & f equivalent to 6 z. Considering the sparsity of the frequency domain and the modeling of long-length time series, the direct outer product

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leads to dimension explosion and the sparsity in lemporal-frequency feature subspace. We address the problem by performing average pooling over z. Average pooling, which calculates the average value for the amplitudes of neighboring frequencies, yields dense frequency features with smaller dimensions. With outer product and average pooling, the adversarial loss LD formulated as:
h(x,, vi) = (x,) & P (t'F (v:)),
[oooo gu (h (x,, vI)), (9)
CD(PT, (D)) = px) (h (xf, vf)) - E (x)
where h(.)) denotes the mapping from the inputs of the overall model to the inputs of the domain discriminator, and P (-) denotes the calculation of average pooling.
4.4 Overview
During alignment, our method trains the temporal feature extractor uhy and classifier ør by minimizing the loss Lcy and trains the frequency feature extractor th and classifier OF by minimizing the loss Lc, using the source sample set Additionally, our method promotes mutual learning between the temporal domain and frequency domain by minimizing the loss LM. on the source domain and the loss LM, on the target domain. Meanwhile, our method aligns distributions of the source domain and target domain in the cemporal-frquuenc correlation subspace. With gradient reversal layers between the two feature extractors and the domain discriminator, the adversarial training is achieved by minimizing the loss LD- To simplify notation, denote OF as parameters containing op and gF. and Or is parameters containing vTr and gr. The minimax optimization problem is formulated as:
min Lc, (0r) + 0F
+ LM, (0r) + (m.(0r) (0r) CD(Vr, vrr, gD),
(10)
min (Vrr, gr.9)) sD
5 Experiments
5.1 Setup
Datasets We conduct extensive experiments using wide range of time series datasets. (1) Experi- ments using benchmark datasets in sensor- sensor-based human activity recognition (HAR) task: UCIHAR [1], HHAR [35] and WISDM[20]. For HHAR, we first split domains from the perspective of par- ticipants, denoted as HHAR-P [16, 31] dataset. Then, we split domains from the perspective of devices, denoted as HHAR-D [12] datasets. (2) Experiments using the benchmark dataset in sleep stage classification (SSC) task: CAP [14, 37]. (3) Experiments using EMG [24, 27] dataset in gesture recognition (GR) task. (4) Experiments using PCL [32, 9, 21, 19] dataset in motor imagery classification (MIC) task. (5) Experiments using FD [31] dataset in machine fault diagnosis (MFD) task. For each dataset, following the existing DA methods on time series [2, 16), we randomly sample 10 source-target domain pairs for evaluation. If the dataset has less than 10 pairs, we evaluate all available domain pairs Further details, processing and domain splits included in Appendix A.
Baselines (1) We report the performance of a model without UDA (Source-only) in the temporal domain to show the overall contribution of UDA methods. (2) We implement the following state- of-the-art baselines for UDA of time series data: CODATS[41]. AdvSKM[23), CLUDA[29] and RAINCOAT[16] (3) We additionally implement general unsupervised DA methods: CDAN [26]. DeepCoral [36], AdaMatch [2], HoMM [5] and DIRT-T [34].
Evaluation We report accuracy and Macro-F1 Score calculated using target test datasets. Accuracy computed by dividing the number of correctly classified samples by the total number of samples. Macro-F1 Score is calculated using the unweighted mean of all the per-class F1 scores.
Implementation We adopt the implementation of AdaTime [31] as benchmarking suite for domain adaptation on time series data, using ID-CNN as the temporal feature extractor and 1-lyer complex-valued linear as the frequency feature extractor. We use the same feature extractor across all algorithms, ensuring fair comparison. In all experiments, we use the prediction of the temporal classifier to calculate accuracy and Macro-FI Score. More experimental details are provided in Appendix B.
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Table 1: Average Accuracy (%) on Eight Datasets and Five Applications for UDA.
Task
GR
MFD
MI
HAR
SSC
Dataset
EMG
FD
PCL
UCIHAR
HHAR-P
WISDM
HHAR-D
CAP
Source-only
76.24
70.04
60.95
75.12
54.25
65.78
55.86
CDAN
79.89
90.56
63.36
85.78
68.73
70.05
67.33
DeepCoral
78.71
84.10
63.51
82.01
68.03
AdaMatch
80.69
82.11
57.78
76.07
65.91
69.79
HoMM
78.74
85.72
63.83
80.99
65.01
67.26
52.33
65.67
DIRT-
79.27
88.08
61.02
83.26
64.99
69.62
56.14
70.42
CLUDA
75.62
84,99
54.69
85.53
68.73
67.04
53.84
65.79
AdvSKM
78.81
83.37
63.58
83.26
66.41
66.97
$2.80
64,39
CoDATS
80.60
87.20
64.18
75.54
68.71
70.66
56.27
68.23
RAINCOAT
79.93
86.75
58.99
94.43
74.21
76.60
49.07
69.13
Ours
82.91
91.74
65.02
97.02
81.74
84.80
65.04
74.08
Improve %)
2.75
1,30
1.31
2.74
10.15
10.70
15.85
5.20
5.2 Results
Table shows the average accuracy of each method on datasets and tasks. Overall, our method has won 5 out of 5 tasks and 8 out of 8 datasets (2 metrics). Specifically, our method improves accuracy by 2.75% on GR task, 5.20% on SSC task, 1.31 on MI task, 9.86% on HAR task and 1.30% on MFD task over the advanced baseline on each dataset respectively.
Due to the limited pages, we report the results for selected target domain pairs with metric accuracy on the representative datasets EMG (GR task), CAP (SSC task) and HHAR-P (HAR task). More accuracy results are given Table 11-15. Average macro-fl score results are given in Table 16. Full macro-fl score results are given in Table 17-24.
Table 2: Accuracy (%) on CAP for unsupervised domain adaptation.
Method
0-+1
0-+3
0-+4
1-+0
1-+4
2-+3
3-+0
4-+1
4-+3
Avg
Source-only
42.44
75.75
66.09
57.98
63.26
50.75
69.47
26.88
33.90
72.09
55,86
CDAN
68.04
77.47
72.84
62.66
67.29
53.93
72.64
63.58
58.17
76.63
67.33
DeepCoral
67.44
77.34
72.33
59.18
67.71
58.09
70.66
53.02
49.12
73.94
64.88
AdaMatch
60.28
77.67
75.55
68.90
63.17
37.33
73.52
59.29
60.26
75.22
65.12
HoMM
69.89
77.11
72.27
60.36
67.89
57.96
71.58
57.61
47.52
74.49
65.67
DIRT-T
72.16
79.21
76.04
64.18
68.69
57.75
75.47
69.91
64.59
76.16
70.42
CLUDA
67.67
75.77
58.82
70.31
70.23
53.94
74.91
53.62
58,30
74.29
65.79
AdvSKM
63.88
77.04
72.17
60.61
66.09
58.00
70.93
55.26
46.64
73.32
64.39
CoDATS
70.54
78.64
70.40
67.89
72.05
57.32
76.08
53.79
60.43
75.17
68.23
RAINCOAT
70.58
72.80
73.47
65.34
69.62
56.08
71.34
70.86
70.47
70.70
69.13
Ours
75.32
80.14
76.58
70.68
73.25
57.48
77.75
75.17
75.67
78.74
74.08
Table 2 presents the results on CAP dataset. CAP contains over 40,000 samples of 3000 time steps, so adaptation on is more challenging. Our method outperforms general DA time series DA methods on 9 out of 10 source-target domain pairs, achieving an average improvement of 5.20 % over the advanced baseline, DIRT-T. Table presents the results on HHAR-P dataset. Our method significantly outperforms RAINCOAT, the state-of-the-art DA method for time series, by 10.15%.
Table 3: Accuracy (%) on HHAR-P for unsupervised domain adaptation.
Method
0-+2
1-+6
2-+4
4-+0
4-
5-+1
5-+2
7-+2
7-+5
8-34
Avg
Source-only
64.51
70.63
45.42
32.81
78.32
90.63
25.67
32.37
39.26
62.92
54.25
CDAN
76.19
92.57
52.57
29.09
97.27
96.16
35.04
37.05
75.26
96.11
68.73
DeepCoral
84.23
90.14
47.08
28.13
90.49
89.91
38.39
34.45
55.73
76.88
68.03
AdaMatch
84.78
92.31
54.50
36.45
78.45
94.20
41.96
37.65
63.80
64.69
65.91
HoMM
75.67
90.79
52.83
36.61
87.66
90.78
37.23
37.32
61.29
79.88
65.01
DIRT-T
77.83
88.54
50.69
32.22
93.16
91.86
38.62
38.10
72.46
65.83
CLUDA
79.84
93.40
45.90
38.84
94.08
95.57
33.93
37.80
77.57
96.52
69.35
AdvSKM
78.94
87,91
52.57
33.49
92.64
92.71
36.53
39.95
65.49
83.75
66
CoDATS
79.61
90.90
60.07
21.80
97.66
97.66
41.44
38.54
58.15
97.01
68.71
RAINCOAT
87.72
93.33
63.75
46.46
98.05
98.25
42.63
43.32
84.17
93.75
74.21
Ours
86.65
93.45
79.01
53.53
97.15
98.32
65.80
65.71
88.59
89.17
81.74

---

Table 4: Ablation studies: Average Accuracy (%) on UCIHAR, HHAR-P and WISDM.
Lor
Lop
Period
LM.
LM.
LD
UCIHAR
HHAR-P
WISDM
Average
75.12
54.25
65.78
65.05
66.88
51.08
56.47
58.14
d
73.47
53.16
59.10
61.91
94.05
79.49
74.19
82.58
V
90.83
57.83
67.77
72.14
97.02
81.74
84,80
87.85
5.3 Analysis
Ablation Study We conduct ablation experiments on three datasets, UCIHAR, HHAR-P and WISDM. For each datasets, we select the same 10 source-target domain pairs mentioned in Section 5.1. The ablation results (average accuracy domain pairs) are presented in Table 4. We observe that all learning modules in the proposed method effective. Further discussions included in Appendix C.3.
Sensitivity analysis on UCIHAR
Sensitivity analysis HHAR.P
Sensitivity analysis
Accuaaoys
ACON--
ACOMAo
ACCNI-A
ACOAHA
ACCON
ACON
ACON
RANNCOA
RAN.COAT
RAINCOAT
23
(a) Sensitivity analysis on UCIHAR (b) Sensitivity amalysis on HHAR (c) Sensitivity analysis on WISDM
Figure 3: Sensitivity Analysis on three different datasets: (a) UCIHAR (b) HHAR-P (c) WISDM. RAINCOAT: The advanced baseline that achieves suboptimal performance on the three datasets.
Sensitivity Analysis It's worth noting that our total loss in Equation (10) does not include any hyperparameters. UDA setup, how to search the optimal trade-offs without access to labeled target samples is still an open problem. Considering that, we choose to set all the trade-offs to 1, as it is the most intuitive choice. Without tuning the trade-offt offe, our proposed ACON still achieves significant improvements. To further investigate the sensitivity of ACON, update Equation (10) as:
min for (0r) + (0r) + DM. (Or) + Am L., (0F) ApDp(WT.Tttt..............>>>>>b (F,9D), 0p.0r
(11)
min ADC gD) go
where hyperparameters Åp. AM. and AM, control the contribution of each component. We investigate sensitivity of the model to the hyperparameters Ap, AM, and AM,- ACON-Ap refers that the currently investigated hyperparameter is Ån, and others are analogous. From Figure 3, we observe that the performance of ACON quite stable the hyperparameters setting all the trade-offs to may not achieve the optimal performance, ACON still significantly outperforms the advanced baseline. This implies that ACON can achieve superior performance on wider range of datasets without the need for careful hyperparameter tuning.
Equation (11). Although
6 Conclusion
In this paper, the phenomenon is revealed- that temporal features exhibit better transfcrability across domains, whereas frequency features tend to be more discriminative within a specific do- main. Based on the findings, Adversarial CO-learning Networks (ACON) is proposed to boost the transferability and discriminability
collaborative learning manner. Specifically, multi multi-period feature learning is proposed to enhance the discriminability of frequency features, cimporal-frequent domain mutual learning proposed to enhance the discriminability domain and improve the transferability of frequency features in the target domain; domain adversarial learning in frrquuenyy correlation subspace is proposed to further enhance transferability of features. ACON achieves state-of-ther -hr-r-rrttttt performance wide range of time series datasets.
temporal features the source

---

Acknowledgements
This work was supported by the National Natural Science Foundation China (62306085,
62206074, 62406112, 62476071, 62236003), Shenzhen College Stability Support Plan (GXWI200231133111339900 GXWD202208 1113333001,, CXWD220208174442300
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A Dataset
A.1 Detailed Statistics
We conduct extensive experiments using a wide range of time series datasets. The detailed statistics for each dataset is included in Table 5. For EMG dataset, use the processed version released by DIVERSIFY [28]. For PCL,, CAP and HHAR-D datasets, we use the processed versions released by WOODS [11]. For UCIHAR, HHAR-P, WISDM and FD datasets, we use the processed versions released by AdaTime [31].
Table 5: Summary of datasets.
Dataset
Subjects
Channels
Length
Class
Total
Task
EMG
8
200
6
6883
GR
FD
4
5120
3
10916
FD
PCL
48
750
2
22598
MIC
CAP
19
3000
40387
SSC
UCIHAR
30
9
128
6
3290
HAR
HHAR-P
3
128
6
17934
HAR
WISDM
30
128
2070
HAR
HHAR-D
500
13674
HAR
A.2 Dataset Processing
Each domain of datasets is randomly divided into 80% training, and 20% testing. We follow [31], apply 7-score normalization to both the training and testing splits of the data, using the following equation:
normalize
2G
meean
1
(12)
gatd
where N₂ for the source domain data and N, for the target domain data. Note that both the training and testing splits normalized based the training set statistics only.
B Experimental Details
The experiments conducted single NVIDIA GeForce696 RTX 4090 with 24GiB of memory. As shown in Figure 3, without tuning the trade-offs of training loss, ACON still achieves significant improvements. Here report other key hyperparameters for ACON in Table 6. Additional hyperparameters can be found in our code. In all experiments, we adopt 3-layer ID-CNN as the temporal feature extractor (the specific structure is kept consistent with the existing works [31, 16)). For frequency feature extraction, we adopt a 1-layer complex-valus linear as the frequency feature extractor.
Table 6: Key hyperparameters for ACON.
Hyperparameter
EMG
FD
PCL.
CAP
UCIHAR
HHAR-P
WISDM
HHAR-D
Epoch
50
50
50
50
50
50
Batch Size
32
32
32
32
32
32
32
32
Learning Rate
0.001
0.01
0.001
0.001
0.01
0.001
0.003
0.01
C Further Analysis
C.1 Discriminability of Frequency Feature
In Table we report the average accuracy of classification experiments under the setting Section using five different datasets: UCIAHR[1), HHAR-P(35)), WISDM[20]. CAP[1,, 37] and FD[31]. For each dataset, we collect all the domains involved in the selected 10 domain pairs as mentioned in Section 5. and perform the classification task on them.
13

---

Table 7: Classification Accuracy (%) in the source domain: Temporal domain vs. Frequency domain.
Dataset
UCIHAR
HHAR-P
WISDM
CAP
FD
Temporal domain
86.18
97.01
95.63
81.63
97.99
Frequency domain
95.69
97.77
98.01
82.73
98.83
C.2 Transferability of Temporal Feature
In Table 8, we report the average accuracy of classification experiments under the setting of Section 3.3 using three different datasets: UCIAHR[I], HHAR-P[335), WISDM[20], CAP[14, 37] and FD[3I]. For each dataset, we perform the domain adaptation and classification task on the selected 10 domain pairs as mentioned Section 5.1.
Table 8: Classification Accuracy (%) in the target domain: Temporal domain Frequency domain.
Dataset
UCIHAR
HHAR-P
WISDM
CAP
Source-only-T
75.12
54.25
65.78
70.14
70.04
Solrce-only-F
66.88
51.08
56.47
67.15
69.53
DANN-T
88.30
72.57
71.54
75.49
86.21
DANN-F
80.64
68.73
60.99
70.76
81.46
C.3 Ablation Study
C.3.1 Ablation Study on different modules
We conduct ablation experiments on three datasets, UCIHAR, HHAR-P and WISDM. For each datasets, we select the same 10 source-target domain pairs mentioned in Section 5.1. The ablation results (average accuracy of 10 domain pairs) are presented in Table 9, We verify the effectiveness of all learning modules in the proposed method by answering the following questions.
Can multi-period frequency feature learning enhance the discriminability of frequency featurre comparing the 2nd and 3rd rows, the makes more accurate predictions on the target domain. Meanwhile, compared with 1st row, even with multi-period frequency feature learning, the performance the target domain is still inferior to the classification on the temporal domain, which is consistent with our conclusion in Section 3.3 that the temporal features have better transferability.
observe that with multi-period frequency feature learning,
Can aligning distributions in frrpuryl subspace effectively learn domain-invariant features? By comparing the 1st, 3rd and 4th rows, we observe that distribution alignment significantly improves the performance. It indicates that by aligning the distributions in the temporal- frequency subspace, the model learns more domain-invarian invariant features.
Can temporal-frequency domain mutual learning leverage the respective advantages? ? By compar- ing the 1tt, 3rd and 5th rows, we can observe that the model with domain mutual learning outperforms the model using only the temporal domain or only the frequency domain. It demonstrates that via domain mutual learning, the temporal domain and frequency domain successfully transfer meaningful knowledge, leveraging their respective advantages.
Can the different modules mutually promote each other? By comparing the 3rd, 4th, 5th and 6th rows, we can observe that with all modules, the model achieves the optimal performance. Specifically, with multi-perin -eriodd frequency feature learning, the frequency domain transfers more discriminative knowledge to the temporal domain; with aligning distribution temporal domain transfers more transferable knowledge to the frequency domain; with aligning distribution in campporl--rrquencyy subspace and temporal domain as a more tranferbale teacher, both the temporal domain and frequency domain learn domain-invariant features; with domain mutual learning, the frequency domain and the temporal domain enhance each other in the transfer progress, achieving synergistic effect.
capporal-frequnce subspace, the
14

---

Table 9: Ablation study on different modules: Average Accuracy (%) on UCIHAR, HHAR-P and WISDM.
Cor
Cor
Period
LM,
LM..
Lp
UCIHAR
HHAR-P
WISDM
Average
75.12
54.25
65.78
65.05
66.88
51.08
56.47
58.14
f
73.47
53.16
59.10
61.91
94.05
79.49
74.19
82.58
90.83
57.83
67.77
72.14
97.02
81.74
84.80
87.85
D Limitations
Although ACON boosts transferability and discriminability for time series Domain adaptation, like
existing DA methods, it still unstable enough in time series with relatively large variances. This is a problem that needs to be solved urgently in the future.
E Broader Impacts
We investigate how to boost Transferability and discriminability domain adaptation time series classification. We reveal that the frequency features are more discriminative, while the temporal features are more transferable. Upon this, we propose multi-period frequency feature learning, domain mutual learning, and distribution alignment in remporal-frequenee feature subspace. The purpose of our research is to advance the research progress in the relevant community without any negative social impact.
F
Full Resluts
We present all experimental results in this section. Notably, our model achieves superior performance, yielding improvements of more than 6% in terms of accuracy and 4% in terms of Macro-F1 across cross-domain time series datasets and common applications on average.
Table 10: Accuracy (%) on EMG for unsupervised domain adaptation.
Method
0-11
0-+2
0-+3
1-+2
1-+3
2-+0
2-+1
2-+3
3-+1
3-
Avg
Source-onl only
84.94
74.38
73.38
74.38
73.88
73.88
82.16
73.69
79.38
72.31
76.24
CDAN
87.84
76.63
77.63
77.44
81.63
73.94
87.10
75.13
83.98
77.63
79.89
DeepCoral
87.50
76.44
76.19
77.63
77.63
74.69
84.72
75.50
81.93
74.88
78.71
AdaMatch
89.03
75.94
79.38
76.94
80.00
76.31
81.31
84.26
73.81
HoMM
87.61
76.50
75.75
77.00
77.94
73.94
75.88
82.61
75.31
78.74
DIRT-T
89.77
75.25
78.69
75.88
80.06
70.63
84.77
77.69
83.30
76.69
79.27
CLUDA
78.18
75.00
76.75
74.75
74.19
75.94
79.43
70.00
76.88
75.13
75.62
AdvSKM
86.42
75.94
76.25
77.25
78.00
74.88
85.06
77.25
81.76
75.31
78.81
CoDATS
88.24
77.44
78.31
78.44
81.81
73.75
86.65
78.88
84.43
78.06
80.60
RAINCOAT
89.60
77.00
78.56
78.25
83.13
73.06
85.68
76.88
83.13
74.00
79.93
Ours
92.50
79.06
81.75
80.13
83.13
77.94
90.91
79.75
85.11
78.88
82.91
15

---

Table 11: Accuracy (%) on PCL for unsupervised domain adaptation.
Method
0-+1
0-+2
1->0
1-+1
2->0
2-+1
Avg
Sourcc-only
65.68
57.79
59.65
60.65
56.51
65.46
60.95
CDAN
68.37
59.77
62.79
62.44
57.50
69.27
63.36
DeepCoral
67.66
60.08
62.59
63.58
57.76
63.51
AdaMatch
66.11
54.92
58,30
58.73
53.75
57.78
HoMM
68.28
60.27
62.80
63.75
58.71
63.83
DIRT-T
61.69
57.29
60.77
62.13
56.79
67.47
61.02
CLUDA
56.60
53,46
60.13
57.79
49.78
50.35
54.69
AdvSKM
67.62
59,90
63.06
64.15
58.07
68.68
63.58
CoDATS
70.52
57.83
65.10
64.
57.83
69.62
64.18
RAINCOAT
58.46
54.04
59.88
60.81
57.63
63.14
58.99
Ours
70.63
60.58
63.42
64.63
60.32
70.53
65.02
Table 12: Accuracy (%) on FD for unsupervised domain adaptation.
Method
0-+1
0-+2
0-+3
1-+0
1 1-+2
2-+0
2-+1
2-+3
3-+0
3-+2
Avg
Source-only
62.21
53.71
62.41
63.91
73.95
64.08
93.17
95.54
57.08
74.31
70.04
CDAN
91.29
71.83
90.13
96,50
90.09
83.10
99.38
99.98
95. 95.40
87.95
90.56
DeepCoral
75.54
71.79
76.03
89.13
83.55
76.34
98.84
98.55
87.50
83.71
84.10
AdaMatch
67.81
55.38
62,88
92.21
98.57
79.08
89.96
90.40
87.23
97.57
82.11
HoMM
81.54
71.63
78.17
89.89
84.78
76.03
98.71
99.55
90.94
85.96
85.72
DIRT-T
75.94
70.85
76.36
98.10
90.27
81.92
100.0
99.98
97.06
90.29
88.08
CLUDA
90.47
82.63
88.68
89.06
92.23
61.92
93.91
90.80
82.01
78.17
84.99
AdvSKM
74.71
66.05
73.30
87.86
86.29
76.85
98.66
99.38
84.89
85.74
83.37
CoDATS
81.79
73.26
83.15
89.22
88.68
81.43
99.89
100.0
85.47
89.00
87.20
RAINCOAT
85.18
79.40
89.04
78.84 84
90.11
81.43
95.18
96.81
77.39
94.08
86.75
Ours
86.52
69.00
97.92
99.80
84.29
98.62
97.72
97.66
91.74
Table 13: Accuracy (%)
on UCIHAR for unsupervised domain adaptation.
Method
2-+11
6-+23
7-+13
9-+18
12-+16
13-+19
18-+21
20-+6
23-+13
24-+12
Avg
Source-only
76.56
67.36
83.68
24.65
61.11
88.89
100.0
94.10
71.18
83.68
75.12
CDAN
85.42
87,50
92.01
58.86
66.67
96.52
100.0
95.13
82.64
93.40
85.78
DeepCoral
90.63
84.38
87.50
46.88
65.28
95.49
100.0
95.49
69.79
87.50
82.01
AdaMatch
75.00
80.20
85.76
56.59
49.65
94.79
100.0
84.37
68.75
70.83
76.07
HoMM
74.06
82.71
73.96
70.21
96.67
98.75
73.33
77.71
80.63
80.99
DIRT-T
80.21
74.31
82.99
59.03
67.01
99.30
98.61
92.36
74.72
94.27
83.26
CLUDA
81.77
92.01
99.31
67.71
65.28
94.44
98.96
97.22
72.92
99.31
AdvSKM
98.96
88.54
92.71
74.65
69.44
93.05
100.0
85.41
79.51
96.87
83.26
CoDATS
68.23
74.31
77.43
63.89
66.32
94.09
99.65
70.49
56.25
82.81
75.54
RAINCOAT
100.0
95.83
100.0
75.69
86.52
100.0
100.0
93.41
86.52
93.75
94.43
Ours
100.0
96.25
99.16
91.66
85.63
100.0
100.0
97.50
100.0
100.0
97.02
Table 14: Accuracy (%)
WISDM for unsupervised domain adaptation.
Method
2-+32
4-+15
7-+30
12-+7
12-+19
18-+20
20-+30
21 21-+31
25-
26-+2
Avg
Source-only
81.16
79.86
89.32
71.53
$4.29
83.74
67.96
21.29
26.11
82.52
65.78
CDAN
89.37
65.97
84.79
70.48
51.01
88.62
77.02
46.58
44.33
83.33
70.05
DeepCoral
87.92
62.50
91.26
79.86
51.77
64.23
81.88
54.62
53.89
77.44
70.80
AdaMaich
74.39
78.47
89.64
73.26
55,30
75.20
74.76
31.32
57.78
87.20
69.79
HoMM
77.10
74.58
78.64
68.13
50.61
71.22
72.82
56.39
57.00
66.10
67.26
DIRT-T
77.78
70.83
90.61
70.20
51.51
85.36
71.84
54.41
60.04
66.46
69.62
CLUDA
73.91
67.36
86.40
65.97
49.24
83.74
72.49
49.97
35.00
86.47
67.04
AdvSKM
70.83
95.85
93.85
77.08
47.47
81.30
21.28
44.45
74.79
74.95
66.97
CoDATS
77.29
70.83
83.20
70.17
47.47
76.01
82.85
52.61
53.89
83.29
70.66
RAINCOAT
79.71
97.91
91.28
89.80
85.00
92.23
91.66
59.09
82.97
83.50
76.60
Ours
89.86
86.25
98.06
98.13
77.73
83.66
91.26
63.61
60.00
99.51
84.80
16

---

Table 15: Accuracy (%) on HHAR-D for unsupervised domain adaptation.
Method
0-11
0-+2
0-+3
0-+4
1-:0
1-43
1-+4
2-+1
3-44
4-+1
Avg
Source-only
65.48
33.59
31.71
39.79
34.69
44.83
49.54
38. 17
86.17
44.23
46.82
CDAN
69.86
48.28
38.22
48.42
48.75
60.48
51.33
47.84
87.33
48.89
54.94
DeepCoral
68.94
42.88
40.67
47.96
35.63
55.31
56.21
44.71
87.25
45.96
52.55
AdaMatch
71.78
39.60
39.74
47.50
52.50
55.48
58.33
46.49
85.83
41.15
53.84
HoMM
69.66
40.51
39.16
50.42
35.94
55.02
57.13
42.36
86.79
46.35
52.33
DIRT-T
68.37
42.14
47.21
52.92
41.25
60.14
55.63
46.73
92.25
54.81
56.14
CLUDA
71.78
39.60
39.74
47.50
52.50
55.48
58.33
46.49
85.83
41.15
53.84
AdvSKM
67.93
40.71
40.19
47.33
37.19
55.65
59.54
42.69
87.46
49.33
52.80
CoDATS
72.50
43.35
50.79
45.50
58.44
62.24
54.54
40.14
89.63
45.53
56.27
RAINCOAT
74.47
36.52
48.82
35.29
51.25
41.49
41.50
34.28
88.58
38.46
49.07
Ours
77.50
61.36
54.69
65.46
69.38
71.30
62.13
50.10
93.63
44.86
65.04
Table 16: Average Macro-F1 Score on Eight Datasets and Five Applications for UDA.
Task
GR
MFD
MI
HAR
SSC
Datasct
EMG
FD
PCI.
UCIHAR
HHAR-P
WISDM
HHAR-D
CAP
Source-only
0.76
0.65
0.60
0.73
0,50
0,52
0.43
0.52
CDAN
0.80
0.92
0.63
0.86
0.68
0.54
0.53
0.62
DeepCorul
0.79
0.81
0.63
0.82
0.62
0.52
0.49
0.59
AdaMatch
0.81
0.78
0.56
0.76
0.62
0.54
0.51
0.57
HoMM
0.79
0.81
0.64
0.79
0.64
0,49
0.49
0,60
DIRT-T
0.79
0.88
0.61
0.81
0.64
0.54
0.53
0.64
CLUDA
0.75
0.82
0.48
0,86
0.67
0.57
0.51
0.59
AdvSKM
0.79
0.80
0.63
0.87
0.65
0.55
0.49
0.59
CoDATS
0.81
0.88
0.63
0.72
0.63
0.56
0.55
0.62
RAINCOAT
0.80
0.89
0.59
0.93
0.75
0.74
0.47
0.59
Ours
0.83
0.93
0.65
0.97
0.80
0.74
0.62
0.67
Table 17: Macro-F1 Score on EMG for unsupervised domain adaptation.
Method
0-+1
0-+2
0-+3
1-+2
1-+3
2-+0
2-+1
2-+3
3-+1
3-+2
Avg
Source-only
0.85
0.74
0.74
0.74
0.75
0.75
0.82
0.74
0.78
0.72
0.76
CDAN
0.88
0.77
0.78
0.78
0.82
0.74
0.87
0.76
0.84
0.78
0.80
DeepCoral
0.87
0.76
0.76
0.78
0.78
0.75
0.84
0.76
0.82
0.75
0.79
AdaMatch
0.89
0.76
0.79
0.77
0.80
0.76
0.90
0.81
0.84
0.74
0.81
HoMM
0.87
0.77
0.76
0.77
0.78
0.74
0.84
0.76
0.82
0.75
0.79
DIRT-T
0.90
0.75
0.79
0.76
0.80
0.71
0.84
0.78
0.83
0.77
0.79
CLUDA
0.78
0.75
0.77
0.75
0.74
0.76
0.79
0.70
0.75
0.75
0.75
AdvSKM
0.86
0.76
0.76
0.77
0.78
0.76
0.85
0.77
0.81
0.75
0.79
CoDATS
0.88
0.77
0.78
0.79
0.82
0.74
0.86
0.79
0.84
0.78
0.81
RAINCOAT
0.89
0.77
0.83
0.73
0.85
0.83
0.74
Ours
0.92
0.79
0.83
0.78
0.85
Table 18:
Macro-F1 Score on CAP for unsupervised domain adaptation.
Method
0-+1
0-+3
0-44
1-+0
1-+4
2-+3
3-+0
3-+1
4-+1
4-33
Avg
Source-only
0.39
0.71
0.61
0.50
0.54
0.45
0.63
0.30
0.33
0.69
0.52
CDAN
0.62
0.73
0.66
0.58
0.59
0.48
0.68
0.61
0.55
0.73
0.62
DeepCoral
0.61
0.73
0.65
0.54
0.58
0.53
0.66
0.44
0.44
0.70
0.59
AdaMatch
0.52
0.73
0.64
0.58
0.55
0.29
0.66
0.52
0.51
0.67
0.57
HoMM
0.62
0.73
0.65
0.56
0.59
0.54
0.66
0.50
0.48
0.71
0.60
DIRT-T
0.65
0.75
0.69
0.57
0.59
0.50
0.69
0.67
0.59
0.71
0.64
CLUDA
0.58
0.71
0.51
0.63
0.61
0.44
0.67
0.50
0.55
0.68
0.59
AdvSKM
0.58
0.73
0.65
0.55
0.59
0.53
0.66
0.48
0.41
0.69
0.59
CoDATS
0.64
0.75
0.65
0.63
0.51
0.51
0.54
0.71
RAINCOAT
0.58
0.65
0.61
0.55
0.56
0.50
0.63
0.60
0.61
0.59
Ours
0.64
0.76
0.68
0.62
0.63
0.54
0.71
0.72
0.70
0.74
0.67

---

Table 19: Macro-F1 Score on PCL for unsupervised domain adaptation.
Method
0-+1
0-+2
1->0
1-+1
2-
2-+1
Avg
Sourcc-only
0.65
0.57
0.58
0.60
0.55
0.64
0.60
CDAN
0.68
0.59
0.62
0.62
0.57
0.69
0.63
DeepCoral
0.68
0.60
0.62
0.63
0.57
0.69
AdaMatch
0.66
0.53
0.58
0.57
0.53
0.56
HoMM
0.60
0.63
0.63
0.58
0.64
DIRT-T
0.57
0.61
0.62
0,56
CLUDA
0.55
0.49
0.59
0.56
0.33
0.36
0,48
AdvSKM
0.67
0.60
0.63
0.63
0.58
0.69
0,63
CoDATS
0.70
0.55
0.65
0.64
0.57
0.69
0,63
RAINCOAT
0.58
0.54
0.59
0.61
0.57
0.63
0.59
Ours
0.71
0.60
0.63
0.64
0.60
0.71
0.65
Table 20: Macro-Fl Score on FD for unsupervised domain adaptation.
Method
0-+1
0-+2
0-+3
1-+0
1 1-+2
2-+0
2-+1
2-+3
3-+0
3-+2
Avg
Source-only
0.41
0.33
0.41
0.65
0.77
0.64
0.95
0.97
0.59
0.78
0.65
CDAN
0.91
0.76
0.90
0.95
0.92
0.86
1.00
1.00
0.94
0.91
0.92
DeepCoral
0.61
0.62
0.62
0.90
0.87
0.77
0.99
0.99
0.89
0.88
0.81
AdaMatch
0.50
0.45
0.46
0.91
0.98
0.80
0.93
0.93
0.87
0.97
0.78
HoMM
0.61
0.52
0.62
0.91
0.88
0.78
0.99
1.00
0.91
0.89
0.81
DIRT-T
0.80
0.62
0.70
0.97
0.93
0.84
1.00
1.00
0.96
0,93
0.88
CLUDA
0.84
0.80
0.79
0.88
01.33
(.50
0.95
0.90
0.84
0.80
0.82
AdvSKM
0.55
0.54
0.57
0.89
0.89
0.76
0.99
1.00
0.87
0.89
0.80
CoDATS
0.80
0.69
0.87
0.90
0.92
0.86
1.00
1.00
0.87
0.92
0.88
RAINCOAT
0.89
0.84
0.81
0.92
0.85
0.98
0.81
0.94
0.89
Ours
0.86
0.75
0.89
0.96
1.00
0.88
0.99
0.96
0.98
Table 21: Macro-FI Score on UCIHAR for unsupervised domain adaptation.
Method
2-+11
6-+23
7-+13
9-+18
12-+16
13-+19
18-+21
20-+6
23-+13
24-s12
Avg
Source-only
0.69
0.63
0.84
0.17
0.58
0.91
1.00
0.94
0.71
0.84
0.73
CDAN
0.85
0.88
0.91
0.61
0.64
0.97
1.00
0.95
0.82
0.92
0.86
DeepCoral
0.91
0.81
0.87
0.44
0.65
0.95
1.00
0.95
0.70
0.88
0.82
AdaMatch
0.73
0.81
0.86
0.55
0.48
0.94
1.00
0.84
0.67
0.70
0.76
HoMM
0.73
0.78
0.81
0.69
0.69
0.96
0.71
0.75
0.78
DIRT-T
0.81
0.68
0.58
0.62
0.99
0.92
0.74
0.93
0.81
CLUDA
0.81
0.92
0.99
0.67
0.64
0.94
0.99
0.98
0.71
0.99
AdvSKM
0.99
0.87
0.92
0.73
0.68
0.93
1.00
0.84
0.77
0,96
0.87
CoDATS
0.66
0.71
0.78
0.60
0.64
0.93
0.99
0.65
0.54
0.81
0.72
RAINCOAT
1.00
0.96
1.00
0.76
0.86
1.00
1.00
0.94
0.86
0.94
0.93
Ours
1.00
0.97
0.99
0.91
0.86
1.00
1.00
0.98
1.00
1.00
0.97
Table 22: Macro-F1 Score HHAR-P for unsupervised domain adaptation.
Method
0-+2
1-+6
2-+4
4-+0
4-+5
5-+1
5-+2
7-+2
7-+5
8-44
Avg
Source-only
0.60
0.64
0.32
0.29
0.78
0.90
0.19
0.31
0.36
0.58
CDAN
0.70
0.93
0.52
0.27
0.98
0..88
0.35
0.32
0.76
0.97
DeepCoral
0.86
0.91
0.45
0.26
0.90
0.90
0.36
0.32
0.50
0.73
AdaMaich
0.83
0.93
0.46
0.32
0.76
0.94
0.40
0.37
0.60
0.61
0.62
HoMM
0.70
0.91
0.45
0.37
0.88
0.91
0.34
0.40
0.61
0.79
0.64
DIRT-T
0.76
0.86
0.51
0.30
0.93
0.90
0.36
0.34
0.73
0.64
0.64
CLUDA
0.82
0.94
0.44
0.40
0.94
0.96
0.37
0.36
0.65
0.84
0.67
AdvSKM
0.72
0.88
0.44
0.33
0.93
0.92
0.35
0.41
0.64
0.83
0.65
CoDATS
0.73
0.90
0.46
0.20
0.96
0.94
0.41
0.36
0.59
0.95
0.63
RAINCOAT
0.87
0.93
0.59
0.45
0.98
0.98
0.41
0.44
0.86
0.94
0.75
Ours
0.86
0.93
0.74
0.52
0.97
0.98
0.62
0.65
0.89
0.89
0.80
18

---

Table 23; Macro-Fl Score on WISDM for unsupervised domain adaptation.
Method
2-+32
4-+15
7-+30
12-7
12-+19
18-+20
20-+30
21 21-+31
25 +5-+29
26-+2
Avg
Source-only
0.68
0.52
0.77
0.53
0.36
0.81
0.56
0.10
0.15
0.69
0.52
CDAN
0.72
0.44
0.70
0.50
0.31
0.87
0.64
0.31
0.23
0.71
0.54
DeepCoral
0.71
0.42
0.85
0.67
0.35
0.63
0.67
0.27
0.25
0.64
0.52
AdaMatch
0.59
0.54
0.76
0.67
0.38
0.66
0.54
0.16
0.24
0.74
0.54
HoMM
0.63
0.42
0.62
0.55
0.39
0.63
0.60
0.30
0.26
0.54
0.49
DIRT-T
0.65
0.41
0.78
0.56
0.39
0.67
0.65
0.28
0.21
0.54
0.54
CLUDA
0.64
0.61
0.81
0.59
0.41
0.70
0.70
0.27
0.26
0.75
0.57
AdvSKM
0.55
0.53
0.35
0.71
0.28
0.55
0.55
CoDATS
0.66
0.41
0.37
0.76
0.30
0.30
0.70
RAINCOAT
0.68
0.98
0.86
0.72
0.78
0.92
0.87
0.43
0.44
0.75
Ours
0.81
0.65
0.99
1.00
0.63
0.76
0.87
00.36
0.28
1.00
0.74
Table 24: Macro-F1 Score on HHAR-D for unsupervised domain adaptation.
Method
0-+1
0-+2
0-+3
0-+4
1-+0
1-+3
1-+4
2-+1
3-+4
4-+1
Avg
Source-only
0.61
0.27
0.25
0.33
0.44
0.43
0.46
0.32
0.85
0.38
0.43
CDAN
0.67
0.42
0.35
0.42
0.66
0).7
0.50
0.44
0.88
0.44
0.53
DeepCoral
0.65
0.34
0.33
0.40
0.48
0.53
0.53
0.39
0.86
0.41
0.49
AdaMaich
0.69
0.36
0.36
0.41
0.60
0.49
0.56
0.41
0.86
0.36
0.51
HoMM
0.66
0.33
0.31
0.41
0.47
0.52
0.53
0.37
0.86
0.42
0.49
DIRT-T
0.66
0.38
0.40
0.44
0.52
0.60
0.53
0.39
0.93
0.49
0.53
CLUDA
0.69
0.36
0.36
0.41
0.60
0.49
0.56
0.41
0.86
0.36
0.51
AdvSKM
0.63
0.32
0.31
0.38
0.46
0.54
0.56
0.36
0.86
0.44
0.49
CoDATS
0.71
0.38
0.39
0.70
0.61
0.38
0.90
0.44
RAINCOAT
0.72
0.32
0.42
0.32
0.56
0.39
0.38
0.31
0.89
0.35
Ours
0.76
0.53
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Reviews:
[{"review_id": "OtX3iOJ3UP", "reviewer": "Reviewer_uayq", "summary": "This paper uncovers an empirical insight in time series domain adaptation - frequency features are more discriminative within a specific domain, while temporal features show better transferability across domains. Based on this insight, it develops ACON (Adversarial CO-learning Networks), which achieves clear improvement over baselines.", "questions": "See weakness.", "limitations": "The limitation of stability has been discussed.", "rating": 7, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- Empirical insight: it is great to see such empirical analysis to provide an interesting insight about the properties of frequency/temporal features.\n- Technical solution, which leverages the insight to improve accuracy.\n- Experiments: it is good to see solid experimental efforts in the paper and appendix.", "weaknesses": "- It would be better to explain (or explore) “why” behind the insight? Is it because the distinguished frequency patterns shift across domains dramatically?\n\n- Usually, neural networks can capture some frequency patterns from time series data. Why it avoids most distinguished frequency patterns, but extracts more transferable ones?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your helpful feedback! We are grateful that the reviewer highlights our empirical insight, technical solution and solid experiments. We would be delighted to explore the underlying reasons behind the empirical insight with the reviewer. \n\n### W1: Why the frequency features have worse transferability? Is it because the distinguished frequency patterns shift across domains dramatically?\n\nA1: \n\nHere we provide an intuition from the perspective of energy. \n\nAccording to Parseval-Plancherel identity [1], the energy of a time series in the temporal domain is equal to the energy of its representation in the frequency domain. By FFT, the energy of raw temporal signals in Euclidean space is transformed to the frequency data in Hilbert space. In Euclidean space, the energy is allocated to every time step, while in Hilbert space, the energy is mainly allocated to several dominant frequencies. \n\nThis means that in the frequency domain, the model needs to focus its attention on a local region to capture the dominant frequencies, while in the temporal domain, the model needs to distribute its attention globally to extract discriminative patterns. When a shift happens, the frequency model with local attention may encounter **a dramatical local shift** (e.g. a shift in the dominant frequencies of a certain class), leading to worse transferability. In contrast, the temporal features with a more evenly distributed energy are more resistant to the shift and exhibit better transferability.\n\n### W2: Why the temporal model avoids to capture most distinguished frequency patterns?\n\nA2: \n\nAs mentioned in A1, with a more evenly distributed energy, the temporal model needs to distribute its attention globally to extract discriminative patterns (eg. multi-period or trend). This global extraction ability is often highly correlated with the model architecture and depth, which makes the temporal modeling still challenging. In contrast, in the frequency domain,  the discriminative patterns have been \"**pre-extracted**\" via FFT, which makes the frequency model more easily extract discriminative features. \n\nOur experimental results also support this point. We compare the sota models of temporal modeling (TimesNet [2] and DLinear [3] ) with 1D-CNN on source domain classification (results are presented in the following table), and it was surprisingly found that these more complex models do not show a significant improvement in UDA settings. This indicates that the existing temporal models still do not have an ideal ability to extract the most discriminative patterns. \n\nBased on intuition and empirical insight, we believe the mutual enhancement between the temporal domain and the frequency domain can be a promising solution.\n\n| Temporal model | UCIHAR | HHAR-P | WISDM |\n| -------------- | ------ | ------ | ----- |\n| 1D-CNN         | 86.18  | 97.01  | 95.63 |\n| TimesNet       | 89.85  | 95.07  | 88.42 |\n| DLinear        | 67.18  | 67.03  | 75.30 |\n\n[1] Plancherel, Michel, and Mittag Leffler. \"Contribution à ľétude de la représentation d’une fonction arbitraire par des intégrales définies.\" *Rendiconti del Circolo Matematico di Palermo*, 1910.\n\n[2] Wu, Haixu, et al. \"TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis.\" *ICLR*, 2023.\n\n[3] Zeng, Ailing, et al. \"Are transformers effective for time series forecasting?\" *AAAI*, 2023.\n\nThank you again for providing insightful comments which helped us to improve our paper, and we hope our responses were able to address any remaining concerns. Please do let us know if you have any further questions as well as what would be expected for score improvement.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "9XTL84E5Gr", "reviewer": "Reviewer_5Lht", "summary": "The paper shows that temporal features and frequency features should not be equally treated in model training, the expression of those features are different. Frequency features show strong discriminability and temporal features show strong transferability. Then the author propose the Multi-period frequency feature learning; Temporal-frequency domain mutual learning and Domain adversarial learning in temporal-frequency correlation subspace to leverage the advantages. The proposed results are impressively good.", "questions": "See weaknesses.", "limitations": "The authors have addressed the limitations.", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The proposed differences of frequency feature and temporal feature is interesting. \nThe proposed methods are novel.\nThe results are impressively good.", "weaknesses": "The motivation of the proposed methods should be clarified.\n\n1. Why the alignment between the temporal predictions and the frequency predictions can leverage the respective advantages of the temporal domain and frequency domain? There is no guarantee to keep both advantages.\n2. Why the Multi-period frequency feature learning can enhancing the discriminability of the frequency domain?\n3. Why Domain adversarial learning can let the model learn transferable representations?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your valuable feedback! We are grateful that the reviewer highlights our method's novelty and solid experiments. We would be happy to explain the motivations behind the different components in more detail.\n\n### W1: Why the alignment between the temporal predictions and the frequency predictions can leverage the respective advantages of the temporal domain and frequency domain?\n\nThe alignment between the temporal predictions and the frequency predictions is inspired by knowledge distillation (KD). KD aligns the student model's predictions to the teacher model's predictions to transfer knowledge from teacher to student. Existing studies have proven that learning to mimic the teacher is easier than learning the target function directly, and the student can match or even outperform the teacher [1]. \n\nGiven the respective advantages of the frequency domain and temporal domain,  ACON allows the frequency domain and temporal domain to each become a teacher with different advantages. By minimizing the KL divergence with different directions, the respective advantages of the frequency domain and temporal domain are transferred to each other. In this way, the temporal domain and the frequency domain can not only learn the true label but also learn each other's secondary quantities (e.g. their estimates of the probabilities of the next most likely classes) [2], enhancing the discriminability and transferability.\n\n[1] Romero, Adriana, et al. \"Fitnets: Hints for thin deep nets.\" *ICLR*, 2015.\n\n[2] Hinton, et al. \"Distilling the knowledge in a neural network.\" *Deep Learning Workshop in NeurIPS*, 2014.\n\n### W2: Why the Multi-period frequency feature learning can enhance the discriminability of the frequency domain?\n\nThe real-world time series usually presents multi-periodicity, which is reflected in the frequency domain as the presence of a few dominant frequencies with significantly larger amplitudes. Data from different periods can have different discriminative patterns. By multi-period frequency feature learning, ACON extracts these discriminative patterns derived from different periods.\n\n### W3: Why Domain adversarial learning can let the model learn transferable representations?\n\nWe provide explanations from two perspectives: intuition and theory. \n\n- Intuitively, adversarial learning is a two-player game between the domain discriminator and the feature extractor. The domain discriminator is trained to distinguish source features from target features and the feature extractor is trained simultaneously to confuse the discriminator. When the game reaches equilibrium, the domain discriminator can no longer distinguish the source features from the target features. At this point, the extracted features are invariant to the change of domains. \n\n- Theoretically, according to [1], the $\\mathcal{H}\\Delta \\mathcal{H}$-Divergence between the source feature distribution $P$ and target feature distribution $Q$ can be estimated by training the domain discriminator $D$: \n\n   $L_D= \\max\\limits_{D}\\mathbb E_{f\\sim P}[D(f)=0]+\\mathbb E _{f\\sim Q}[D(f)=1]$    （1）\n\n  \n\n  The objective of the feature extractor is to minimize the source error as well as the $\\mathcal{H}\\Delta \\mathcal{H}$-Divergence bounded by Equation (1), resulting in transferable representations.\n\n  [1] Ben-David, et al. \"A theory of learning from different domains.\"  *Machine learning*, 2010.\n\nThank you again for the valuable feedback! We hope our responses were able to address any remaining concerns. Please do let us know if you have any further questions as well as what would be expected for score improvement.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "xNhNTvBEH3", "reviewer": "Reviewer_U97c", "summary": "This paper studies the Unsupervised Domain Adaptation (UDA) problem in time series classification. The authors first proposed an insight that temporal features enhance transferability while frequency features enhance discriminability. Based on the insight, the authors designed a model that leverages temporal and frequency features. Other techniques include but not limited to Knowledge Distillation and Domain Adversarial Learning. The evaluations show SOTA performance, and the ablation study indicates that the designed components are helpful.", "questions": "It’s a great idea to exploit the advantages of both temporal and frequency features using distillation. But I also wonder why a simple fusion of temporal and frequency features is not used and compared. Will the fused features maintain both good transferability and discriminability?", "limitations": "Yes", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1.\tEmpirical insights into temporal and frequency features of time series data in terms of transferability and discriminability.\n2.\tIt is interesting to see how the authors managed to achieve better transferability and discriminability through knowledge distillation.\n3.\tThe designed temporal-frequency subspace for domain adversarial learning showed notable performance increase.", "weaknesses": "1.\tThis paper is derived from the empirical insight of temporal and frequency features. It would be better if the authors can explain a little bit about why temporal or frequency features excel in different properties. \n2.\tThe preliminary experiment on transferability and discriminability could use more datasets and more analysis to justify the motivation of the paper.\n3.\tSince there are other papers utilizing temporal and frequency features as mentioned in the related work, it would be better if the author can illustrate the differences and the advantages of the current design compared to other works.\n4.\tIt would be helpful to improve clarity if the author can explain the “index” in figure 1.\n5.\tDuring the illustration of the model proposed, the author did not cover the design of the domain discriminator.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you very much for your valuable feedback! The additional results are presented in **the PDF attached to Author Rebuttal** and we summarize the original weaknesses or questions.\n\n### W1: The intuition behind empirical insight\n\nHere we provide an intuition from the perspective of energy. \n\nAccording to Parseval-Plancherel identity [1], the energy of a time series in the temporal domain is equal to the energy of its representation in the frequency domain. By FFT, the energy of raw temporal signals in Euclidean space is transformed to the frequency data in Hilbert space. In Euclidean space, the energy is allocated to every time step, while in Hilbert space, the energy is mainly allocated to several dominant frequencies. \n\nThis means that in the frequency domain, the model needs to focus its attention on a local region to capture the dominant frequencies, while in the temporal domain, the model needs to distribute its attention globally to extract discriminative patterns, which makes the temporal modeling still challenging. In contrast, in the frequency domain,  the discriminative patterns have been \"**pre-extracted**\" via FFT, which makes the frequency model more easily extract discriminative features.\n\nWhen a shift happens, the frequency model with local attention may encounter **a dramatical local shift** (e.g. a shift in the dominant frequencies of a certain class), leading to worse transferability. In contrast, the temporal features with a more evenly distributed energy are more resistant to the shift and exhibit better transferability.\n\n[1] Plancherel, et al. \"Contribution à ľétude de la représentation d’une fonction arbitraire par des intégrales définies.\" 1910.\n\n### W2: More datasets for preliminary study\n\nWe conduct a comprehensive preliminary study on a wide range of datasets (**5 datasets from 3 tasks**). The results are comprehensively presented in **Table 1-2 of PDF**. Among them, (1) Results of SSC task (CAP dataset) are included in Section 3 of the paper. (2) Results of HAR task (UCIHAR, HHAR-P and WISDM datasets) are included in Appendix C.1. (3) We conduct additional experiments on FD task (MFD dataset) in rebuttal to further justify the motivation. \n\nFrom Table 1 and 2, we can observe **general** experimental phenomena:\n\n- Frequency features have better discriminability.\n- Temporal model has a better ability to learn invariant features in the progress of alignment. \n\nThe phenomena of different types of data consistently support our empirical insights, demonstrating its generalizability.\n\n### W3: Comparison with other works\n\nTo our knowledge, RAINCOAT is currently the only work that introduces the frequency domain into time series domain adaptation. \n\nFor the extraction of frequency features, RAINCOAT treats amplitudes and phases equally, while ACON discards the phase and proposes multi-period frequency feature learning to enhance discriminability. \n\nFor the utilization of temporal and frequency features, RAINCOAT assumes them are independent and treats them equally, resulting in the improvement brought by the frequency domain being incremental. In contrast, based on the respective advantages, ACON proposes temporal-frequency domain mutual learning and co-alignment in temporal-frequency correlation subspace, achieving a performance boost.\n\n### W4 & W5: Index & Design of domain discriminator\n\nThank you very much for pointing out the confusion and the missing. \n\nFor Figure 1(a), the index refers to time steps or frequencies. For Figure 1(b), the index refers to different domains contained in the CAP dataset. For Figure 1(c), the index refers to different source-target pairs selected from the CAP dataset. \n\nWe adopt a 3-layer linear as the domain discriminator and ReLU as the activation function, which is consistent with existing UDA works. We will add the explanations in the later version.\n\n### Q1: Comparision with a simple fusion\n\nWe conduct exploratory experiments to verify whether a simple fusion in classification or alignment module can produce better performance. The results are presented in Table 3 of the PDF. Due to limited space, a more detailed explanation is included in **the caption of Table 3**. \n\nIn classification module, by comparing the 4th, 5th and 6th rows in Table 3, we can observe that concatenation features do not achieve better performance. Intuitively, when we use the concatenation feature for classification, the final prediction is **a simple average** of the temporal prediction and the frequency prediction. Ideally, the extracted features can only maintain suboptimal discriminability and suboptimal transferability. In contrast, our mutual learning allows the frequency domain and temporal domain to become teachers with different advantages, and transfer knowledge to each other. In this way, each other's secondary quantities (e.g. the estimates of the probabilities of the next most likely classes) are transferred [1], enhancing the discriminability and transferability.\n\nIn alignment module, by comparing the 3rd and 6th rows, we can observe that with the concatenation DANN significantly underperforms our method. Intuitively, when we use the concatenation feature for alignment, $\\mathbf f_F$ with the worse transferability provides $g_D$ with rich domain-label relevant information. In this case, $g_D$ only needs to focus on the game with $\\psi_{F}$ in the frequency domain, ignoring the domain adversarial learning in the temporal domain. Based on the experimental performance and intuition, we discard the simple fusion and opt for co-alignment in the temporal-frequency correlation subspace.\n\n[1] Hinton, et al. \"Distilling the knowledge in a neural network.\" *Deep Learning Workshop in NeurIPS*, 2014.\n\nWe hope our responses were able to address any remaining concerns. Please do let us know if you have any further questions as well as what would be expected for score improvement.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "A5WXUrTmdJ", "reviewer": "Reviewer_ggDU", "summary": "The paper introduces Adversarial CO-learning Networks (ACON) to improve unsupervised domain adaptation (UDA) for time series classification by enhancing the transferability and discriminability of temporal and frequency features. The proposed approach incorporates multi-period frequency feature learning, temporal-frequency domain mutual learning, and domain adversarial learning in temporal-frequency correlation subspaces. Extensive experiments demonstrate ACON's superior performance over existing methods on various time series datasets.", "questions": "1. The preliminary study assumes that low-frequency components are the most discriminative. However, the choice between phase and amplitude for frequency feature extraction can significantly impact results. Why were only the human activity recognition datasets used for this preliminary study, and how might this assumption affect other types of time series data?\n2. The ablation study indicates that the domain loss contributes more significantly to the model's performance than the two KL losses. Could you explain why this is the case, and provide more insights into the individual contributions of each loss component?\n3. The paper proposes domain adversarial learning to align features in both source and target domains. However, this seems to conflict with the novel aspect of different alignment strategies based on domain-specific characteristics. Could you clarify how these two approaches are reconciled in your framework?\n\n~~4. How are classification predictions made during inference? The paper mentions a voting mechanism, but additional details on how the final prediction is derived from the individual components would be helpful.~~  \n\n5. In Section 4.1, how is the value of k (the number of top amplitudes) determined for multi-period frequency feature learning? Is it dataset-specific, or is there a general guideline for selecting this parameter?\n\n~~6. Can you provide more details on what the learned latent variables represent? Do they capture the essential features that define each class, and how can this be validated?~~\n\n(The issues in Questions 4 and 6 were errors that occurred while I was switching between different pages during the review process of multiple articles. I sincerely apologize to the authors for this.)", "limitations": "The authors acknowledge that while ACON enhances transferability and discriminability for time series domain adaptation, it remains unstable when dealing with time series data that exhibit relatively large variances. Addressing this instability is a critical challenge that needs to be tackled in future research.", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "- The introduction of Adversarial CO-learning Networks (ACON) that integrates multi-period frequency feature learning, temporal-frequency domain mutual learning, and domain adversarial learning is a novel and promising direction for enhancing unsupervised domain adaptation (UDA) in time series classification.  \n- The paper demonstrates extensive experiments across a wide range of time series datasets and five common applications, providing strong empirical evidence of the proposed method's effectiveness.  \n- The paper effectively highlights the distinct properties of temporal and frequency features, proposing mechanisms to leverage their respective strengths for improved transfer learning.", "weaknesses": "- Methodological Complexity: The proposed ACON framework is highly complex, involving multiple components and phases (multi-period frequency feature learning, temporal-frequency domain mutual learning, and domain adversarial learning). This complexity may hinder reproducibility and practical implementation, especially in real-world applications.\n- Insufficient Scalability Analysis: The paper lacks a detailed discussion on the scalability and computational efficiency of ACON. It remains unclear how the model performs with larger datasets and whether it introduces significant computational challenges.\n- Presentation and Clarity Issues: Some sections of the paper are dense and difficult to follow. Simplifying the language and providing clearer explanations would improve readability and accessibility.\n- Lack of Detailed Comparative Analysis: While the paper includes experiments against various baselines, it falls short in providing a detailed comparative analysis. More in-depth discussion on why ACON outperforms other methods and the specific contributions of its individual components would strengthen the paper.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your helpful feedback! Due to limited space, additional results are in **PDF attached to Author Rebuttal** and we summarize the weaknesses and questions below.\n### W1: Reproducibility and implementation in real\n- Compared with existing works, ACON has the widest evaluation scope (8 datasets and 5 common applications) and the sota performance, exhibiting greater potential in solving real problems.\n- Existing UDA methods for time series usually need careful hyperparameter tuning, while ACON fixes all hyperparameters in total loss, making the implementation easier. \n- Code was provided to ensure reproducibility. \n### W2: Scalability and computational challenges\n- Larger datasets\n  - Comparisons of evaluation scope are in **Table 4 of PDF**. ACON expands the evaluation scope to **more common tasks and more datasets** (8 datasets and 5 common applications) with **longer lengths and more channels**. Performance of ACON on larger and more complex datasets demonstrates its scalability.\n- Computational challenges: \n  - Comparisons of training time are in **Table 5 of PDF**. ACON performs the best, with the second fastest speed, slightly slower than the fastest method. Thus ACON does not introduce additional computational challenges.\n### W3: Presentation\nWe will refine the expression. If the reviewer could point out the specific sections, we would be more grateful and make more targeted improvements.\n### W4: More in-depth discussion on ACON and other methods\nExisting works are in two categories: general UDA and UDA for time series. \n- General UDA methods ignore the special properties of time series, while ACON fully leverages the respective advantages of temporal and frequency features. \n- Most UDA methods for time series ignore frequency domain. RAINCOAT introduces frequency domain into UDA and assumes that temporal domain and frequency domain are independent, treating them equally. As a result, the improvement brought by frequency domain is incremental. Guided by empirical insight, we propose ACON to fully utilize the advantages of temporal domain and frequency domain: \n  - multi-period feature learning to enhance the discriminability of frequency features \n  - temporal-frequency domain mutual learning to leverage the respective advantages \n  - domain adversarial learning in temporal-frequency correlation subspace to align the source and target distribution\n### Q1: Only HAR datasets are used in preliminary study\nWe apologize for any confusion that may lead the reviewer to think that only HAR datasets are used. We conduct a comprehensive preliminary study on **5** datasets. The results are presented in **Table 1-2 of PDF**. Among them, (1) Results of CAP dataset (SSC task) are in Section 3 of the paper. (2) Results of UCIHAR, HHAR-P and WISDM datasets (HAR task) are in Appendix C.1. (3) We conduct additional experiments on MFD dataset (FD task) in rebuttal to justify the motivation further. \n\nTo analyze the impact of phase and amplitude, results of frequency classification experiments using three strategies are in **Table 6 of PDF**. \n\nFrom Table 1, 2 and 6,  **general** phenomena are observed:\n- Frequency features have better discriminability.\n- Temporal model is more skilled at learning invariant features with domain alignment. \n- Phase can not provide strong discriminative information. \n\nPhenomena of diverse scenarios consistently support our assumption.\n### Q2: KL losses's improvements are smaller than domain loss\nDomain loss is the key to improving transferability. Without domain loss, transferability of temporal features is weak and cannot significantly enhance transferability of frequency features using KL losses.\n### Q3: Adversarial learning seems to conflict with mutual learning\nDifferent mutual learning strategies in source and target domain do not conflict with adversarial learning between source and target. The reasons are:\n- Mutual learning is an alignment (1) between temporal and frequency space (2) at the **sample** level. \n\n  Adversarial learning is an alignment (1) between source and target domain (2) at the **distribution** level. \n- The alignment direction of mutual learning (temporal <-> frequency) is orthogonal to that of adversarial learning (source <-> target). Therefore, mutual learning is not contradictory to adversarial learning in reducing the divergence between source and target.\n- Mutual learning enhances the transferability of frequency features, assisting the alignment of adversarial learning in frequency space.\n- Mutual learning enhances the discriminability of temporal features, enhancing the discriminability of the invariant features learned through adversarial training.\n\nIn all, mutual learning and adversarial training share the same goal — to learn domain invariant and discriminative features. To avoid potential confusion caused by the repetition of \"alignment\" both in mutual learning and adversarial learning, we will change \"alignment\" in mutual learning to \"match\".\n### Q4: A voting mechanism\nThe \"voting mechanism\" did not appear in our paper. We would be grateful if the reviewer could provide more information. To make classification predictions, we apply softmax to the output of the classifier and take the class with the highest score as the final prediction.\n### Q5: How is the value of k determined?\nIn ACON, the original time series length is set as a default period to capture the global information. Upon this, according to the amplitude distribution after min-max normalization, we choose the one with the amplitude ratio > 0.9 as the dominant frequencies. We will add explanations in the next version.\n### Q6: Latent variables\nThe \"latent variables\" did not appear in our paper. To our knowledge, latent variables refer to the learned representation in Bayesian Generative Models, which is irrelevant to our paper. We would be grateful if the reviewer could provide more information.\n\nWe hope our responses were able to address any remaining concerns.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:
Thank you to all reviewers for the thoughtful feedback.

We are pleased that all four reviewers agree with our empirical insight, method novelty and solid experiments. We are also delighted that reviewers recognized this study as a promising solution to UDA for time series.

In response to reviewers' comments, we perform 4 additional experiments and organize the results into 6 new tables. Due to the limited space, the new tables are included in **the PDF attached to this Author Rebuttal**. We hope these updates address all key concerns and clarify the significance of our work.

We respond to all your comments below in the individual replies, where we directly address comments raised by individual reviewers. Please note that in our response, all experimental results are presented in the PDF attached to this Author Rebuttal.  In addition, we carefully proofread the paper and edit the paper for clarity. We will include further details in the next version (new revisions during the rebuttal are not allowed).

Thank you again for your thoughtful feedback. If you have any further concerns or questions, please do not hesitate to let us know.

**Table 1-2**: More datasets for preliminary study (Reviewer U97c and Reviewer ggDU)

**Table 3**: Comparison with a simple fusion  (Reviewer U97c)

**Table 4**: Comparison of evaluation scope (Reviewer ggDU)

**Table 5**: Comparison of accuracy and speed (Reviewer ggDU)

**Table 6**: Three different strategies in the frequency domain (Reviewer ggDU)

Meta-review: Reviewers agree on acceptance based on meaningful empirical insights, effective technical solutions, and notable performance. The authors are encouraged to include discussions and results in the rebuttal to the final version.
Decision: Accept (poster)