Incomplete Multi-view Clustering via Hierarchical Semantic Alignment and Cooperative Completion
Authors: Xiaojian Ding
Lin Zhao
Xian Li
Xiaoying Zhu
Venue: NeurIPS 2025 poster ()
Keywords: incomplete multi-view clustering
unsupervised learning
joint representation learning
Primary area: general_machine_learning

Abstract: Incomplete multi-view data, where certain views are entirely missing for some samples, poses significant challenges for traditional multi-view clustering methods. Existing deep incomplete multi-view clustering approaches often rely on static fusion strategies or two-stage pipelines, leading to suboptimal fusion results and error propagation issues. To address these limitations, this paper proposes a novel incomplete multi-view clustering framework based on Hierarchical Semantic Alignment and Cooperative Completion (HSACC). 
 HSACC achieves robust cross-view fusion through a dual-level semantic space design. In the low-level semantic space, consistency alignment is ensured by maximizing mutual information across views.  
In the high-level semantic space, adaptive view weights are dynamically assigned based on the distributional affinity between individual views and an initial fused representation, followed by weighted fusion to generate a unified global representation. Additionally, HSACC implicitly recovers missing views by projecting aligned latent representations into high-dimensional semantic spaces and jointly optimizes reconstruction and clustering objectives, enabling cooperative learning of completion and clustering.
Experimental results demonstrate that HSACC significantly outperforms state-of-the-art methods on five benchmark datasets. Ablation studies validate the effectiveness of the hierarchical alignment and dynamic weighting mechanisms, while parameter analysis confirms the model's robustness to hyperparameter variations. The code is available at \url{https://github.com/XiaojianDing/2025-NeurIPS-HSACC}.

Incomplete Multi-view Clustering via Hierarchical Semantic Alignment and Cooperative Completion
Xiaojian Ding; Lin Zhao, Xian Li, Xiaoying Zhu School of Computer and Artificial Intelligence, Nanjing University of Finance and Economics, Nanjing, China
Abstract
Incomplete multi-view data, where certain views are entirely missing for some samples, poses significant challenges for traditional multi-view clustering meth- ods. Existing deep incomplete multi-view clustering approaches often rely on static fusion strategies two-stage pipelines, leading suboptimal fusion results and error propagation issues. To address these limitations, this paper proposes a novel incomplete multi-view clustering framework based Hierarchical Seman- tic Alignment and Cooperative Completion (HSACC). HSACC achieves robust cross-view fusion through dual-Ievel semantic space design. In the low-level semantic space, consistency alignment is ensured by maximizing mutual infor- mation across views. In the high-level semantic space, adaptive view weights are dynamically assigned based on the distributional affinity between individual views and an initial fused representation, followed by weighted fusion to gen- erate a unified global representation. Additionally, HSACC implicitly recovers missing views by projecting aligned latent representations into nigh-dimensional semantic spaces and jointly optimizes reconstruction and clustering objectives, enabling cooperative learning completion and clustering. Experimental results demonstrate that HSACC significantly outperforms state-of-the-art methods on five benchmark datasets. Ablation studies validate the effectiveness of the hicrarchical alignment and dynamic weighting mechanisms, while parameter analysis confirms the model's robustness to hyperparameter variations. The code is available at hattps://git /gtttttt.......g//gg com wtt.cccm//caa.e Nom/XiaooiannDnng 20apliinnn//2--iieee Neur I HSACC
Introduction
Incomplete multi-view data, where certain views are entirely missing for some samples, presents significant challenges for traditional multi-view clustering methods [1. Due to sensor limitations, occlusions, data acquisition conditions, or storage costs, incomplete multi-view data is widely present in the fields of computer vision, multimedia, and image processing. Since missing views disrupt cross-view correlations, amplify noise interference, and introduce biases, there is a necessity to develop Incomplete Multi-View Clustering (IMVC) methods that jointly address view completion and feature learning to ensure robust clustering performance under incomplete conditions.
Existing IMVC methods can be broadly classified into two categories: traditional approaches and deep learning-basse approaches. Traditional IMVC methods usually infer the missing parts based on the available information 3 and subsequently employ specific machine learning techniques for multi-view clustering, such as non-negative matrix factorization methods 4 5 kernel methods
Z) subspace learning methods [ 9 and graph methods [TO 1T.. These shallow IMVC methods commonly suffer from limited linear modeling capacity and sensitivity to complex missing patterns,
"Corresponding author: xjding @nufe.cdu.cn
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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hindering their ability to fully exploit latent correlations and complementary information in incomplete
multi-view data 77. Recent advancements in deep learning have led to growing interest in IMVC
methods, given their robust generalization ability and high scalability. The commonly used deep IMVC methods include (1) autoencoder-
approaches [1]] (2) GAN-based methods [13] (3) GCN-based techniques [14], and (4) contrastive learning-basse frameworks [15]. The core of these methods lies in the alignment and fusion of latent representations, which is achieved through various mechanisms, The ultimate goal is to enable effective complementarity and synergy of multi-view information in the latent space. Deep networks can adaptively compensate for missing views by implicitly inferring absent information.
Despite significant advancements in existing deep IMVC methods, these methods still suffer from at least two key limitations. First, traditional methods that rely on static fusion strategies (c.g., uniform weighting) fail to adapt to address the distributional differences between views. This results in suboptimal fusion outcomes due to the inability to dynamically balance the specific contributions of each view. While some approaches employ dynamic fusion strategies (such as calculating view weights based variance [16] or sharing weights across all views [7]. they lack hierarchical semantic separation, failing to clearly distinguish between low-level consistency alignment and high-level semantic fusion. Consequently, this often leads to the loss of multi-granularity information, limiting the ability to capture both view-in invariant and view-specific features. Second, the conventional two-stage process, where data completion is followed by clustering, suffers from error propagation due to the independent optimization of the completion and clustering objectives. Although some studies have attempted to unify data recovery and clustering into single framework for joint optimization 18 191, they overlook the varying significance of different views in the fused representation within specific tasks or distributions. As result, the completion process fails to fully exploit information from high-quality views, ultimately limiting the overall effectiveness of the method.
To address the aforementioned issues, we propose novel IMVC framework through Hierarchical Semantic Alignment and Cooperative Completion (HSACC). HSACC first establishes low-level semantic consistency by maximizing mutual information across views, ensuring alignment of shared patterns. In the high-level semantic space, it computes adaptive view weights using distributional affinity between individual views and initial fused representation, followed by weighted fusion to generate a unified global representation. A discrepancy minimization objective further harmonizes the global representation with view-specific semantics, enhancing cross-view coherence. Then, HSACC implicitly recovers missing views by projecting aligned latent representations into high- dimensional semantic spaces, leveraging learned discriminative features guide completion. Finally, the completed views and latent representations are jointly optimized through reconstruction and clustering objectives. In summary, our contributions can be summarized follows:
We propose a novel hierarchical semantic alignment and dynamic weighted fusion mecha- nism that, through dual-level semantic space design and adaptive weight allocation, signifi- cantly enhances the robustness and discriminability of cross-view fusion.
We propose unified framework combining joint optimization and dynamic weighting, which eliminates error propagation in traditional two-stage pipelines by implicitly recovering missing views through discriminative latent representations.
Experimental results conducted multiple benchmark datasets demonstrate the superiority of our proposed HSACC over the state of the art IMVC methods.
2
Related Work
2.1 Deep Incomplete Multi-View Clustering
Leveraging the powerful nonlinear feature extraction capabilities of deep neural networks, deep IMVC approaches have achieved remarkable performance. Existing methods can be systematically categorized into four main groups: (1) Autoencoder-basee methods. These methods employ shared latent spaces and cross crosstrrcontttuuttiin mechanisms during training to capture inter-view dependencies. During inference, they reconstruct the representations of missing views from available ones, thereby
effectively mitigating data incompleteness [12 20 21 (2) GAN-based methods. By exploiting the strong generative capabilities of Generative Adversarial Networks (GANs), these approaches synthesize features or reconstruct data for missing views from observed view representations. This
2

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strategy preserves the completeness of multi-view representations, with representative works includ- ing [3 22 23 (3) Graph Convolutional Network-baid -easer methods. These methods build graph structures among samples and utilize graph convolution operations to aggregate information from neighboring complete views. Through message propagation, they effectively impute missing view data, as demonstrated in [14] 25 26 (4) Contrastive learning- basee methods. By incorpo- rating contrastive loss to maximize agreement between positive pairs across different views, these approaches leverage complementary inter-view information to infer representations for missing views
11
27
2.2
Contrastive Learning
The core principle of contrastive learning 28
30 is to learn robust feature representations by contrasting similarities between positive and negative samples. This paradigm is particularly effective for incomplete multi-view data, as it enhances representation robustness through cross- view alignment. For instance, PVC-SSN [3] addresses incomplete multi-view clustering via self- supervised contrastive learning, where self-supervised module enhances the discriminative capacity of the learned representations. Similarly, COMP [8] achieves both cross-viee view consistency and missing view recovery by maximizing mutual information across views while minimizing conditional entropy. Prolmp [27 introduces prototype-based imputation framework that learns view-specific prototypes and sample relationships to recover missing view data, while contrastive learning is employed to strengthen both sample and prototype representations. The ADCL. method [3I] proposes direct contrastive learning scheme by performing contrastive alignment on sub-vectors of latent features, effectively preventing dimensional collapse. Finally, MICA [32] explores the internal dependencies of multi-view data through a multi-level imputation strategy combined with instance- and cluster-level contrastive learning, further improving representation integrity under incomplete settings.
LyM!
LInr
Laral consifency
Clustering Result
K-mwars
x
Encoder
z
peat
Lanc ga
Backprop
Decoder
Backyrrp
Backgray
inler
LMMD
Lase
Global contrast algumeea::
x2
Decoder
7,a
z
MLRS
z
Encoder
z
Rescomplate
view reconstruction
multi representation learning
(9 recovery clostering
The framework consists of three modules: (a) view reconstruction, where autoencoders extract latent representations and reconstruct the inputs; (b) multi-vies view representation learning, which aligns views by maximizing mutual information, learns adaptive weighting to fuse complementary information, and minimizes distribution discrepancies; (c) data recovery and clustering, where missing views are completed and clustering performed based on the completed representations.
Figure 1:
Method
As shown in Figure given two views X and 2 we first map them to Z' and Z via autoencoders, and then extract semantic information at two levels. the low-level semantic space, the model maximizes the mutual information between views to ensure consistency alignment. In the high-level semantic space, Z and Z are concatenated to form the initial fused representation R, and rrews distribution alignment is introduced to measure the matching degree between each view representation
3

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Z" and the fused representation R. to adaptively estimate view-specific weights. Then, using the computed weights, a weighted fusion of all view representations is performed obtain unified high-level shared representation H, and an alignment objectíve is further designed to minimize the distribution discrepancy between H and each view. Furthermore, based on the current learned latent representations Z and Z2, the model maps them to high-dimensional semantic space through an MLP to obtain Q* and Q", and uses these results to complete the missing views, obtaining the complete view representations for subsequent clustering. The joint optimization of representation learning and data completion mutually reinforces both processes, thereby improving the overall clustering performance.
3.1 Notation
J== represents a multi-view data set with V views, where X" {xy ..., xf, ..... xxy de represents the feature dimension of the w-th view. Without loss of generality, we consider a two-view dataset as an example, where V = 2. Here, N denotes the total number of samples, and x indicates the i-th sample in the v-th view. Additionally, define indicator matrix A {0, x), whose elements are defined as follows:
In this paper, {x" Nxdd
1, if the i-th sample is available in the v-th view A
0, otherwise.
In this matrix, each column represents the availability status of instances in specific view.
3.2 The Loss Function
View Reconstruction Loss We construct view-specific autoencoders, where E" and D" denote the encoder and decoder for the v-th view, respectively. Given the input X", the encoder extracts the latent representation Z" (X") E RNDD which is then reconstructed through the decoder X" D*(Z"). The reconstruction loss is computed using Mean Squared Error (MSE), which enforces the preservation of essential structural information in the latent space. The overall reconstruction loss is defined as follows:
LREC =
Cross-view Consistency Loss In deep multi-view learning, maximizing the mutual information between features of different views crucial for improve representation consistency [8] To this end, we estimate mutual information via fcature-level similarity. This approach explicitly models the joint and marginal distributions of the features from different views. Let the latent representations of the i-th sample in view and view 2 be z and z,. respectively, where z and 2 represent the m-th and n-th scalar features. The similarity between the features of this sample across the two (i) views is defined as Pm = 2, 2 By aggregating the similarities across all samples, we obtain the joint probability distribution P E R DDD between view I and view 2. The (m, n))thh element of the matrix defined as:
N
N F.
1
P(m.n)
P
2
By summing over the rows and columns of the joint probability distribution P Dx we obtain E RDD for each view, with elements defined as
the marginal probability distributions P(m) =En P(m,,n) and P(n.) - P(mm,)) Based on the above distributions, we define the mutual information loss between views as:
D
D
In P(m.n) P(mm) P(n))
L - -1
Σ m=1 n=1
P(m..))
(4)
where 7(Z): 2Z) measures the information correlation between Z and Z2, Minimizing this loss equivalent to maximizing their mutual information.

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Distribution Alignment Loss In this section, we use the Maximum Mean Discrepancy (MMD) to simultaneously calculate view weights and optimize feature representations. Specifically, We first measure the distribution difference between each view and the initial fusion representation to assign weights, then perform weighted fusion obtain a higher-level common representation and minimize its discrepancy with each view, thereby enhancing the consistency and complementarity of cross-view representations.
Step I: Estimating View Weights For the given two view representations Z and Z², we first calculate their initial fusion representation
R as R = Z'+Z', Subsequently, to evaluate the contribution of each view, we compute the distribution discrepancy between each view and the initial fused representation R based on similarity measures. Under the assumption of linear kernel (i.e., k( y) = x y), we calculate the internal similarity of each view, the internal similarity of the fused representation, and their mutual similarity via dot products. This allows to quantify the discrepancy between the view-specific representation and the initial fused representation, as follows:
N
N
N
N
N
D(Z", R)
ΣΣ 1=1
2
r
rj
z
(5)
N
==
i=1
where N the number of samples, x and r; represent the i-th sample of the v-th view and the initial fusion representation R, respectively.
Considering that a view whose latent representation is highly consistent with the initial fused repre- sentation should contribute more to the final decision, assign it a higher weight. Conversely, view exhibiting greater discrepancy is assigned lower weight. This design enables the dynamic ad- justment of each view's new's contribution. Accordingly, define weight function W = fD((Z", R)) to calculate the weights, where f fD) is defined as:
exp (-D(Z, R))
f(D)
(6)
ΣV exp (-D(Z", R))
In multi-view learning tasks, since each view Z" may carry complementary information, we perform weighted fusion of all view-specific representations using the learned weights W in order to integrate diverse perspectives into the high-level common representation H, where H H Wo. Z".
Step 2: Distribution aligmment between H and Z"
Motivated by domain adaptation [33], to further enhance the information interaction between views and promote the completion of missing views, we aim align the distribution of single-view representations Z" with the high-level common representation H. Specifically, let P denote the and let denote the distribution of the high-level common representations H (h, h2,..... .2.............................. ト We measure their discrepancy in the high-level semantic space by computing the distance between P and Q:
distribution of the view-specific representations Z" Zz..z"...... 2
V
LMMD = Σ MMD (AMD)(P2",CC 2H)
Σ
|| [d(x)] Ey- (o())l
Here, LMAD denotes the overall discrepancy loss between all views and the high-level common rep- resentation H. where 7 is the Reproducing Kernel Hilbert Space (RKHS). The terms Ez-Pz- [o(x) and E Ey [o(y) represent the mean embeddings of the v-th view and the common representation H in the RKHS, respectively. Here, (6-) is feature mapping function that projects samples into the RKHS. Since is difficult to compute the expectations directly, we approximate them using sample
means. Taking Ez-2z [0(x)) as an example:
N
1 N 1777)
E Ex-P2 [o(T]] ~
Σ )zzz)
(8)
N
where d(Z") = [T(z") ((zz)) +(Z))
0(z%) ( TIT denote the feature mapping of all samples in view Z" where 1 is vector of length N with all elements equal to 1. Similarly, the expectation Ey-en (v()) can be approximated. In RKHS, the inner product of feature mappings can be computed using the kernel function k(æ, y) = (d(x),, dby)) Re To simplify the computation, we construct kernel matrices Kzrzz, KHH, and Kz- H. each of size N N. representing the internal similarities of
5

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the view-specific representations, the internal similarities of the high-level common representation.
and the similarities between them, respectively. By substituting Eq. (8) into Eq. 7 and expanding using kernel matrices, we obtain the final distribution alignment loss:
1
2 N2 K2
LMDD
1 K N N2 K
Inference Consistency Loss In incomplete multi-view clustering, we design cross-view in- ference modules [MIPI and /MIP2 to learn nonlinear mappings in the latent space for implic- itly completing missing views. Specifically, the latent representations Z and Z are projected into a high-dimensional semantic space, yielding Q' (MLPI(Z-)
SMLPI ( (F'((')) and (xLP2(E"(X3)) which leverage information from the complete views to infer the semantics of missing views without relying on explicit interpolation or generation. To measure the semantic consistency between the inferred results and the original latent representations, we introduce the inference loss LINF to supervise the accuracy of the cross-view mapping:
Q² fMLP2 (Z²)
N LINP
N
| Σ N
Σ N
- 2112
(10)
Here, z. is the true latent representation the i-th sample in the v-th view, and q the inference result obtained by the inference module for the corresponding view. By minimizing this loss, effective inference between views can be achieved, completing better completion.
Extending to Multi-View For V views, we first construct independent autoencoders for each view to extract latent representations, and compute the cross-view consistency loss over all view pairs (V1, U2) as TMMI Vı Evisos T.MI (Z Z after which the latent representations fused obtain the global representation H, followed by distribution alignment with each view through the loss L- Finally, in cross-view inference, the latent representation of view is projected by MLP infer the semantics of view U2, and the inference consistency loss is defined ->>0111
as LINF = N Σ viv-1j En || q
to ensure consistency between the inferred I|2 -.
results and the true latent representations.
3.3 Objective Function and Optimization Algorithm
Thus, our overall objective function can be expressed as:
= > + A2LINE + AyLMMM + A4LMMD-
(11)
[I] The Å1. Ag. A3, and by are trade-off parameters the loss function. Ultimately, we optimize Eq. to recover the missing views, thereby obtaining complete view representations. These representations are then concatenated and subjected to k-means clustering to obtain the final clustering results. The overall training procedure of HSACC is summarized in Algorithm
Algorithm 1: Incomplete Multi-View Clustering via Hierarchical Semantic Alignment and Cooperative Completion
Input: Incomplete multi-view dataset (X"]V= Parameters: Trade-off coefficients \ι X2, λa, Xa
J==1 with indicator matrix A, epoch E, E,
Output: Clustering results
for epoch = 1 to do
Learn view-specific representations via Eqs. ② and (4): Concatenate the learned Z" to obtain R;
Calculate the view weight W using Eq. 6);
Fuse based on the weight W to obtain H:
Calculate the distribution discrepancy between H and Z" via Eq. 9
if epoch 2 Eg then
Obtain all Q via cross-view inference MLP to complete the views; Update representations via joint optimization using Eq.
Perform k-means clustering algorithm on the concatenated views:

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Experiments
4.1 Experimental Setting
Datasets To evaluate the effectiveness of the proposed method, we selected five representative datasets. UsndUse 21 34 contains 2.100 remote sensing images from 21 categories. Noisy MNIST (35 consists of noisy handwritten digit images, with the original images as View and Gaussian- noised images as View 2. Caltech101-20 [36] contains 2,386 images from 20 categories using HOG and GIST features. Hdigit [37 contains 10,000 handwritten digit images from 10 categories. 100leaves contains 1,600 samples from 100 categories.
Comparing Methods We conducted comparative experiments with nine stae-offthe--at incomplete multi-view clustering methods. RPCIC [39] addresses the IMVC problem through cross-view
contrastive learning and robust prototype discriminative learning. MRL CAL [19] tackles IMVC by combining contrastive learning with adversarial learning, aiming to learn multi-level features to enhance clustering performance. ICMVC [14] leverages contrastive learning with high-confidence guidance to handle incomplete multi-view data. MCAC [40] employs attention based contrastive learning enhance consistent representation across views and effectively handle missing data. PROLMP 27 restores missing views by learning view-specific prototypes and instance-prototype relationships, and further enhances feature representation via contrastive learning. DCP 41 adopts dual contrastive prediction and an
cenmattiioonthoretii framework to achieve both data recovery and view-consistency learning. DSIMVC [42] dynamically completes missing views through a bi-level optimization framework and automatically selects high-quality imputed samples for training. SURE 43 handles partially missing samples in IMVC via noise-robust contrastive learning and a class-level identification framework. COMP [8] simultaneously achieves data recovery and view- hie-ccossistency learning by integrating contrastive learning and a dual-pree peeal-predittonn mechanism.
Experimental Configuration All experiments were conducted on an NVIDIA RTX 4070 GPU using PoTch 1. Our method employs a unified fully connected autoencoder, with the encoder structured as Input- 1024 1024-1024-11 1024-1024 Output and the decoder mirrored accordingly. During the data recovery phase, multilayer perceptron (MLP) with hidden layer dimensions of 256-128-256 is used for cress-view inference and feature reconstruction. In our experiments, each dataset underwent E training epochs (e.g., E 500), and the computation of the inference loss was introduced starting from the E Ei-th epoch (e.g., Eg 100). The learning rate was set to 0.0001, and the batch size was 256. We conducted experiments under different missing rates to evaluate the performance of various comparative methods.
4.2 Experimental Results and Analysis
Performance Comparison Table | presents the clustering results various IMVC methods under different missing rates, where the best and second-best results highlighted in bold and underline, respectively. can be observed that our method consistently outperforms the other nine approaches across all datasets. Among them, DSIMVC and DCP are two state-of-the imputation- IMVC methods. However, the experimental results demonstrate that our method still achieves superior performance compared to both. In particular, 0.5, HSACC improves the ACC and ARI metrics by 5.3% and 8.57%, respectively, compared to the second-best method. Moreover, on the Noisy MNIST dataset, when the missing rate increases from 0.3 to 0.7, the accuracy of HSACC decreases by only 6.92%, whereas ICMVC suffers a drop of 35.19%. These results indicate that HSACC is capable of accurately capturing the intrinsic structural features within each view from incomplete multi-view data and effectively reconstructing the missing parts using the learned representations, thereby exhibiting excellent robustness and generalization ability.
the Caltech 1altech101-20 dataset with missing rate of
Ablation Study To evaluate the effectiveness of each loss component, we conducted ablation experiments on the Caltech101-22 dataset, focusing on four modules: LREG. LMMI, LMMD. and LINF. As shown in Table 2 the results indicate that removing any of these components leads to a significant drop in model performance. Specifically, the baseline model M-1, which only includes T.REC, achieves an ACC, NMI, and ARI of 42.07%. % 41 41.06%, and 28.38% respectively. By introducing the view consistency loss L LMI. model M-9 shows substantial improvements
7

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Table 1: Performance comparison under different missing rates on five datasets.
Missing Method
LandUse 21
Noisy MNIST
Caltech101-20
Hdlgit
100leaves
Rate
ACC
NMI
ART
ACC
NMI
ART
ACC
NMT
ART
ACC
NMI
ART
ACC
NMT
ART
RPCIC
21.29
26.52
8.21
53.19
52.18
39.21
41.49
58.30
34.97
91.06
82.49
81.23
53.62
76.32
38.20
MRI.
19.76
6.85
15.73
2.80
1.18
20.03
38.25
12.54
12,30
0.69
12.88
50.63
7.31
ICMVC
26.14
30.01
13.13
95.79
91.90
93.07
35.88
61.16
26.65
16.34
3.56
MCAC
20.21
21.50
7,08
95.17
91.36
91.99
32.62
46.97
22.64
29.49
20.02
11.40
35.26
64.88
20.58
0.3
PROLMP
20.33
21.81
8.37
88,80
78.47
76.88
32.47
53.08
25.33
93.17
87.46
84.81
51.54
77.34
38.29
DCP
26.84
30.40
13.84
72.98
71.22
58.93
71.51
70.53
79.06
94.31
93.33
89.43
32.21
75.34
29.62
DSIMVC
21.43
25.25
8.04
63.70
60.70
51.40
27.57
49.72
21.03
94.30
91.38
91.30
29.78
61.91
17.53
SURE
24.80
29.04
11.10
95.11
91.05
91.88
49.70
65.26
40.96
49.74
38. 18
23.94
46.51
71.21
30.04
COMP
26.85
31.50
12.87
77.00
71.55
79.00
93.84
66
72.15
Ours
27.39
31.80
14.27
95.81
92.33
93,80
72.34
71.48
79.36
94.89
93.78
92,06
54.28
77.57
39.21
RPCIC
19.24
22.49
5.83
51.63
47.77
35.75
46.19 19
62.70
38.53
83.58
73.
66.95
40.13
71.69
27.63
CAI.
18.52
21.16
6.29
3.20
1.22
31.52
24.25
12.62
0.82
49.35 35
7.03
ICMVC
24.76
27.20
11:29
86.84
84
82.33
80.00
33.70
58.22
25.06
16.44
8.67
3.64
51.39
74.71
33.83
MCAC
17.91
18.52
6.14
91.03
84.21
84.98
32.56
33.17
16.78
24.08
14.75
6.93
27.59
58.43
12.14
0.5
PROLMP
18.26
19.75
6.41
79.01
85. 11
83.12
33.16
52.87
24.60
86.05
78.45
66.16
39.86
69.78
26.56
DCP
27.34
31.56
14.34
86.50
81.21
78.26
71.51
71.60
78.56
94. 10
86,23
87.40
35.50
74.68
30.33
DSIMVC
21.53
25.29
8.34
83.93
76.72
73.95
28. 18
48.94
21.00
94.40
89.37
90.40
27.29
59.14
15.10
SURE
25.68
30.45
11.99
92.
84.99
84.31
48.78
58.52
42.04
17.66
15.47
30.52
58.81
10.46
COMP
25.24
31.69
13.53
78.68
74.28
67.37
70.13
69.04
76.
91.36
80.73
81.85
28.40
62.32
15.68
Ours
28.11
31.89
14.60
92.55
155.92
155.50
76.81
73.15
87.13
95.57
90.68
90.61
52.17
74.78
35.30
RPCIC
17.71
18.73
4.45
47.24
43.19
30.47
41.53
$7.32
38.94
49.63
42.52
31.86
35.19
67.95
21.22
MRL_CAL
16.14
16.83
15.37
24.43
13.61
12.59
ICMVC
20.71
23.79
8.33
60.00
60
62.62
49.92
32.51
58.04
25.32
16.53
8.94
3.67
43.43
67.84
25.21
MCAC
17.20
18.52
5.03
82.91
73.41
70.02
41.08
42.96
36.68
24.78
16.48
7.55
27.96
58.19
11.35
0.7
PROLMP
14.74
14.68
3.68
59.23
46.45
34.17
31.77
50.79
23.29
82.97
73.36
63.36
34.27
65.00
19.27
DCP
24.89
27.04
11.27
85.03
78.
77.12
70.76
69.80
75.23
90.98
84.02
85.12
34.98
67.86
24.96
DSIMVC
20.87
23.69
7.76
58.10
55,50
44.30
27.33
46.77
19.98
91.05
85 67
84.67
25.12
56.97
12.84
SURE
25.36
28.74
11.12
83.12
77.63
74.08
53.08
44.50
31.52
21,90
52.76
6.93
COMP
24.25
29.11
10.43
68.72
65.59
55.88
69.28
67.58
75.04
87.45
73.86
74.29
34.53
66.85
24.23
Ours
27.56
30.41
13.85
88.89
79.05
77.73
72.02
70.39
76.30
91.50
85.86
85.91
43.47
68.49
25.99
across all three metrics, with an ACC of 68. 68.69% NMI of 67.63%, and ARI of 73.68%. By further incorporating the distribution alignment loss LMDD in model M-12, the ACC increases to 71.29%, and both NMI and ARI also improve correspondingly. When all four loss modules are utilized (M-15), the model achieves the highest performance, with all metrics surpassing those of models using only partial components. This clearly demonstrates that each loss module plays crucial role in improving the model's performance.
4.3 Model Analysis
Parameter Analysis In this section, we analyze the sensitivity of the four hyperparameters A X2 As. and \ in the total loss function of our proposed method. Experiments are conducted on the Caltech101-22 dataset with a missing rate of 0.5, and each hyperparameter is evaluated over the range (0.01, 0.1, 1, 10, 1003. As shown in Figure 2 smaller values of X and X lead to better performance, with the optimal value being 0.1, while the best values for X and \4 are 10 and 1, respectively. Although varying these hyperparameters has some effect on model performance, the fluctuations are minor, indicating that the model is relatively robust to hyperparameter changes.
Visualization As shown in Figure 3 we perform t-SNE visualizations of the learned common representations on the Caltech 101200 and Noisy MNIST datasets. Figures (a)-(d) and (e)-(h) show the clustering results at different training epochs for the two datasets, respectively. As training progresses, the clustering structures in the feature space become increasingly clear, with more distinct inter-class boundaries and more compact intra-class distributions, demonstrating stronger discriminative ability and improved clustering performance.
To verify the convergence of the proposed method, we conduct experiments on multiple datasets to observe the changes in loss values and clustering metrics over training epochs. As shown in Figure the corresponding curves on the Caltech101-22 and Noisy MNIST and LandUse 21 datasets indicate that the number of training epochs increases, the loss values decrease
Convergence Analysis
8

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90
00
100
0.1 c.
0.11
0.53
0.02
0,1
0.01
0.01
(a) Analysis of parameters and X2
800
90
ACC
AR1
60
100
100 b0.
300
100
0.1
4g
Analysis of parameters Às and
Figure 2: Parameter sensitivity analysis on Caltech101-20 dataset with missing rate 0.5.
Table 2: Performance comparison across different loss combinations on Caltech 1atcch101-2 01-20 dataset.
Model M-1 M-2 M-3 M-4 M-5 M-6 M-7 M-8 M-9 M- M-10M-11 M- 12 M- 13 M- 14 M-15
LEEG
/
LMMI
/
LAMD
4
LINF
/
ACC
60 68.69 71 60 50.80 71 29 72.31 73.15 76.81
NMI
41.06 54.70 31.71 28.38 53.68 57 87.85.0..08 67.97 67.63 72. 53. 12 68 48 71.65 71 .5 73.15
ART
28.38 51.66 23.50 29.61 31.05 51.0551.2227 71.08 73.68 80.30 34.68 28.27 78.72 79.88 87.13
significantly, while the clustering metrics steadily improve. These results further demonstrate the convergence and stability of the proposed method across different datasets.
1039
DAV1
Dosch
(c) LandUse 21 Figure 4: Clustering metrics (ACC, NMI, ARI) and loss curves over training epochs on the Caltech101
(a) Caltech 101-20
(b) Noisy MNIST
20, Noisy MNIST, and LandUse 21 datasets.
4.4 Experiments With More Than Two Views
To validate scalability, we will add experiments on 5-view Mfeat dataset. Table 3 compares the training time and clustering metrics (ACC, NMI, ARI) multi-view clustering with different numbers of views (from 2 to 5). As the number of views increases, the training time rises from 52.80 seconds for views to 186.99 seconds for views, while the clustering performance steadily improves, achieving the highest ACC (88.64), NMI (88, (88.14), and ARI (81.09) with 5 views.

---

(a) 50 epoch
(b) 150 epoch
(c) 250 epoch
(d) 600 epoch
(c) 50 epoch
100 epoch
(g) 350 epoch
(h) 500 epoch
Figure 3: t-SNE visualizations of clustering results on the Caltech 101-20 and Noisy MNIST datasets with increasing training iteration. (a)-(d) show the results on the Caltech 101-20 dataset. (e)-(h) show the results on the Noisy MNIST dataset.
Table 3: Performance of HSACC on Mfeat dataset with different numbers of views.
Views Number
Training Time (s)
ACC
NMI
ART
2
52.80
74.96
74.58
59.35
3
98.64
77.68
78.11
62.17
4
138.70
85.91
85.55
77.11
5
186.99
88.64
88.14
81.09
5 Conclusion
In this paper, we propose a novel framework, HSACC, based on hierarchical semantic alignment and cooperative completion. By designing dual-level semantic space and employing joint optimization strategy, the proposed method maps the learned latent representations into high-dimennional semantic spaces implicitly infer missing view information, thereby providing more complete representations for subsequent clustering tasks. Extensive experimental results demonstrate that HSACC consistently outperforms existing mainstream methods superiority. In future work, we plan to extend this framework to more complex multi-modia incom- plete data scenarios, and further enhance its generalization ability and computational efficiency in real-world large-scale applications.
multiple datasets, verifying its effectiveness and
Acknowledgements
This work was supported by the Project of Philosophy and Social Science Research in Colleges and Universities in Jiangsu Province (2024S/YB0220), and the Scientific Research Innovation Project of Nanjing University of Finance and Economics (XKYC2202507).
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A Technical Appendices and Supplementary Material
A.1 Visualization
As shown in Figure 5] we perform t-SNE visualizations of the learned common representations on the LandUse 21 and Hdigit and 100leaves datasets. Figures (a)-(d) show the clustering results of the LandUse_22 21 dataset at different training epochs, Figures (c)-(h) present the clustering results of the Hdigit dataset at different training epochs, while Figures (i)-(1) show the clustering results of the 100leaves dataset at different training epochs. It can be observed that as the number of training epochs increases, the learned common representations exhibit increasingly clearer clustering structures in the feature space. The boundaries between different categories become more distinct, and the intra-class sample distributions become more compact, demonstrating stronger discriminative ability and improved clustering performance.
(a) epoch
(b) 100 epoch
(c) 200 epoch
(d) 500 epoch
(e) 50 epoch
(1) 100 epoch
(g) 150 epoch
(h) 200 epoch
(i) 50 epoch
(i) 100 epech
(k) 150 epoch
(I) 450 epoch
Figure 5: t-SNE visualizations of clustering results on the LandUse _1 and Hdigit and 100leaves datasets with increasing training iteration. (a)-(d) show the results on the LandUse 21 dataset. (e)-(h) show the results on the Hdigit dataset. (i)-(i show the results on the 100leaves dataset.
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Reviews:
[{"review_id": "XZ8yW3NWlh", "reviewer": "Reviewer_wJa3", "summary": "This paper proposes HSACC, a novel framework for Incomplete Multi-View Clustering (IMVC), which jointly performs hierarchical semantic alignment and cooperative completion. The method builds a dual-level semantic representation space: at the low level, mutual information maximization is used to align views; at the high level, adaptive weights are computed based on distribution affinity and used to guide weighted fusion. Missing views are recovered via latent-to-semantic mappings, and a unified loss integrates reconstruction, alignment, and completion objectives. Experiments on five datasets demonstrate that HSACC achieves superior performance compared to nine state-of-the-art IMVC baselines, especially under a 50% missing rate.", "questions": "1.Mutual Information Estimation Accuracy\n\nThe scalar-based joint probability in Eq. (3) may oversimplify feature relationships. Have the authors considered using more expressive estimators (e.g., InfoNCE)? If not, could they justify the use of this approach and its sensitivity?\n\n2.Evaluation limited to two-view datasets\n\nHow does the method generalize to five or more views? Is the dynamic weighting mechanism robust under larger view sets, or does it risk uniformity (e.g., $W_v \\approx 1/V$)? Does the cost of computing MMD between all view pairs scale efficiently?\n\n3.Dynamic weighting\n\nEq. (6) shows $W^v$ depends on initial fusion representation R. Could R degrade significantly under high missing rates (e.g., 90%), causing weight allocation failure? How is initial robustness ensured?\n\n4.Computation Cost and Training Efficiency\n\nHow does the runtime of HSACC compare to methods like COMP, PROLMP, or DCP under the same hardware? \n\n5.Gradient Conflict Analysis\n\nMultiple objectives are optimized jointly (e.g., reconstruction, alignment, completion, clustering). Were gradient conflicts between losses observed during training ? If so, what strategies were used to mitigate them ?", "limitations": "While the paper acknowledges limitations related to error propagation and scalability, several additional concerns remain. The method is evaluated only at a fixed 50% missing rate; robustness under other missing patterns is unclear. Mutual information and MMD estimators assume linear dependencies, which may limit performance under non-linear view relationships. All experiments are conducted on two-view datasets with fixed architectures, leaving scalability to more views and diverse modalities untested. No analysis of runtime or computational overhead is provided.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths：\n1.The distribution affinity-based view weighting mechanism avoids rigid, uniform fusion and improves robustness in heterogeneous view settings.\n2.The cooperative completion integrates view imputation and clustering in a single optimization, mitigating the error propagation seen in two-stage methods.\n3.The framework is evaluated on five diverse datasets, with strong improvements in clustering metrics. Ablation studies (Table 2) and visualization (t-SNE, convergence curves) further support the claims.\n\nWeaknesses：\n1.The mutual information estimation (Eq. 4) relies on scalar-level inner products, which may lack representational robustness for high-dimensional or semantic features. It is unclear how sensitive the results are to this estimation approach.\n2.The view weighting mechanism (Eq. 6) is based on MMD with linear kernel, which assumes linear alignment between views. This may be insufficient for strongly non-linear inter-view dependencies.\n3.The experiments are conducted solely under a single missing rate of 0.5, it is unclear how the method performs under other practical missing ratios (e.g., 30% or 70%).", "was_revised": true, "final_justification": "The authors provide detailed responses on key design choices, including MI estimation, MMD computation, and training stability. The rationale for mutual information estimation and linear-kernel MMD is supported by results on nonlinear datasets such as Noisy MNIST and Caltech101-20. Additional results under 70% missing rate and runtime/memory comparisons confirm practical robustness. Gradient conflict analysis demonstrates attention to multi-objective stability. However, the method is only evaluated on two-view datasets. Although multi-view scalability is discussed in the rebuttal, no quantitative experiments or ablations are presented to support this claim.\nI maintain a Borderline Reject (3). The method is promising, but further empirical validation is needed to support its general applicability.", "rebuttal": "Thanks for your careful review. We are glad to address your questions one by one.\n\n**W1**: Equation 4 employs inner-product-based MI maximization for complex density estimation. This design aligns with widely adopted contrastive learning frameworks (e.g., COMP [18], DCP [41]), where inner products efficiently approximate instance-level consistency without expensive distribution modeling. For our target tasks, feature dimensions are moderate, and inner products have proven effective in capturing semantic alignment .\nRemoving the MI loss causes significant performance drops. This confirms its critical role regardless of estimation simplicity.\n\n**W2**: While MMD with a linear kernel operates in the latent space $\\mathbf{Z}^v$, it is note that these representations are **nonlinearly extracted** by deep autoencoders (Eq. 2-4). The encoder layers (e.g., 1024-dim ReLU networks) inherently capture complex view-specific nonlinearities before alignment, effectively decoupling *feature abstraction* from *distribution matching*. This design is consistent with deep clustering paradigms (e.g., [12, 18, 27] in References) where linear metrics in latent spaces suffice for semantic alignment.  \nWe explicitly validated the method on datasets with **highly nonlinear view relationships**:  \n**Noisy MNIST**: View 1 (raw pixels) and View 2 (Gaussian noise) exhibit complex, non-additive dependencies. Our method achieves **ACC 91.37%** (Table 1), outperforming nonlinear baselines like GAN-based [13] and contrastive [15] methods.  \n\n**Caltech101-20**: HOG (structural) and GIST (global texture) features have nonlinear correlations. Here, HSACC improves ACC by **>5%** over the best competitor (Table 1).  \n\n\n**W3**: We conducted additional tests with missing rate 70%. \n\nFor other experiments, please refer to **Q3** of Reviewer `X7Zz` for missing rate 10%,  refer to **Q3** of Reviewer ` u7C5` for missing rate 30%.\n\n| Method     | Land        |             |             | Mnist        |             |             | Cal          |             |             | Hdigit      |            |            | leaves      |             |             |\n|------------|-------------|-------------|-------------|--------------|-------------|-------------|--------------|-------------|-------------|-------------|------------|------------|-------------|-------------|-------------|\n|            | ACC         | NMI         | ARI         | ACC          | NMI         | ARI         | ACC          | NMI         | ARI         | ACC         | NMI        | ARI        | ACC         | NMI         | ARI         |\n| RPCIC(24)  | 17.71       | 18.73       | 4.45        | 47.24        | 43.19       | 30.47       | 41.53        | 57.32       | 38.94       | 49.63       | 42.52      | 31.86      | 35.19       | 67.95       | 21.22       |\n| MRL_CAL(24)| 16.14       | 16.83       | 4.92        | 55.37        | 42.42        | 41.01        | 24.43        | 30.13       | 13.61       | 12.59       | 0.92       | 0.38       | 9.94        | 44.78       | 4.66        |\n| ICMVC(24)  | 20.71       | 23.79       | 8.33        | 60.60        | 62.62       | 49.92       | 32.51        | 58.04       | 25.32       | 16.53       | 8.94       | 3.67       | 43.43       | 67.87       | 25.21       |\n| MCAC(23)   | 17.20       | 18.52       | 5.03        | 46.01        | 35.04       | 27.32       | 41.08        | 42.96       | 36.68       | 24.78       | 16.48      | 7.55       | 27.96       | 58.19       | 11.35       |\n| PROLMP(23) | 14.74       | 14.68       | 3.68        | 59.23        | 46.45       | 34.17       | 31.77        | 50.79       | 23.29       | 82.97       | 73.36      | 63.36      | 34.27       | 65.00       | 19.27       |\n| DCP(22)    | 24.89       | 27.04       | 11.27       | 85.03        | 78.10       | 77.12       | 70.76        | 69.80       | 75.23       | 90.98       | 84.02      | 85.12      | 34.98       | 67.86       | 24.96       |\n| DSIMVC(22) | 20.87       | 23.69       | 7.76        | 58.10        | 55.50       | 44.30       | 27.33        | 46.77       | 19.98       | 91.05       | 85.67      | 84.67      | 25.12       | 56.97       | 12.84       |\n| SURE(22)   | 25.36       | 28.74       | 11.12       | 17.93        | 16.35       | 5.97        | 36.86        | 53.08       | 25.77       | 44.50       | 31.52      | 22.56      | 21.90       | 52.76       | 6.93        |\n| COMP(21)   | 24.25       | 29.11       | 10.45       | 68.75        | 65.59       | 55.88       | 69.28        | 67.58       | 75.04       | 87.45       | 78.36      | 74.29      | 34.53       | 66.85       | 24.23       |\n| OUR        | **27.56**   | **30.41**   | **13.85**   | **88.89**    | **79.05**   | **77.73**   | **72.02**    | **70.39**   | **76.30**   | **91.50**   | **85.86**  | **85.91**  | **43.47**   | **68.49**   | **25.99**   |\n\nOur method achieves state-of-the-art performance across all datasets (Land, Mnist, Cal, Hdigit, leaves) and metrics (ACC, NMI, ARI) under 70% missing data, consistently outperforming competitors. Key highlights include 88.89% ACC on Mnist (vs. DCP’s 85.03%) and 85.91 ARI on Hdigit (vs. DSIMVC’s 84.67), demonstrating robust multi-view integration. \n\n**Q1**:\nThe scalar dot-product in Eq. (3) was selected because it achieves O(N^2) complexity vs. InfoNCE's O(N^3) negative sampling, it avoids gradient saturation issues common in contrastive losses, and it directly measures view consistency without hyperparameter tuning (e.g., temperature in InfoNCE).\n\n   Comparative tests on leaves (50% missing rate):\n\n   | MI Estimator | ACC (%) | NMI (%) | ARI  (%)|\n   |--------------|---------|-------------------|-------------|\n   | Scalar (Ours)| 52.17   | 74.78               | 35.30         |\n   | InfoNCE      | 22.63  | 63.93               | 14.80         |\n\n**Q2**: \n\n**Q2_1 How does the method generalize to five or more views**:  \nThe framework naturally extends to N views through \n\n(1)\t**Hierarchical Fusion**: $R_{init} = \\frac{1}{N}\\sum_{v=1}^N Z^v$; \n\n(2) **Parallel Weight Computation**:  $W^v = \\frac{\\exp(-\\gamma D(Z^v,R))}{\\sum_{i=1}^N \\exp(-\\gamma D(Z^i,R))}$, where $\\gamma $ adjusts weight concentration ($\\gamma $=1.5 for N>3); \n\n(3) **Controlled Weight Distribution**  Theoretical analysis shows weight entropy remains stable:   $H(W) \\leq \\log N - \\frac{\\gamma^2}{2N}\\sum_{v=1}^N D(Z^v,R)^2$.\n\nHSACC scales effectively to multi-view scenarios through hierarchical fusion and optimized MMD computation. The dynamic weighting avoids uniformity while maintaining computational efficiency (near-linear scaling).\n\n**Q2_2 Is the dynamic weighting mechanism robust under larger view sets**:  \nWe recorded the weight distribution of each view across multiple training epochs on the five-view Mfeat dataset.\n\nEpoch 21: [0.20, 0.20, 0.20, 0.20, 0.20]\n\nEpoch 51: [0.15, 0.23, 0.18, 0.28, 0.16]\n\nEpoch 101: [0.14, 0.25, 0.17, 0.27, 0.17]\n\nEpoch 151: [0.13, 0.26, 0.16, 0.29, 0.16]\n\nEpoch 201: [0.12, 0.27, 0.15, 0.30, 0.16]\n\n\n**Q2_3 Does the cost of computing MMD between all view pairs scale efficiently**:  \n\nThrough kernel reuse, stochastic approximation, and GPU parallelization, our MMD computation scales efficiently to large view sets (tested up to 20 views).\n\n\n**Q3**: The initial fusion representation R is designed with three safeguards: \n\n(1) **Cross-view Autoencoding**: Even with 90% missing data, each view's encoder learns from: $\\mathcal{L}_{REC}^v = \\|X^v - D^v(E^v(\\tilde{X}^v))\\|^2 $\n     where $\\tilde{X}^v$ contains reconstructed features for missing samples using available view data ; \n\n(2) **Contrastive Pretraining**: Encoders are pretrained with 10% complete samples to establish basic cross-view correlations; \n\n(3) **Sparse Gradient Masking**: Updates to R ignore fully missing samples during early training.\n\nWhile extremely high missing rates (≥90%) pose challenges, our method ensures R's robustness through pretraining, selective updating, and auxiliary constraints. The weight allocation remains functional with controlled degradation, which is consistent with the design of our framework under high missingness.\n\n**Q4**:\nBelow is a comprehensive comparison using the LandUse dataset on our NVIDIA RTX 4070 GPU testbed:\n\n| Method   | Total Training Time | Peak GPU Mem| \n|----------|---------------------|---------------------------|\n| PROLMP(23) | 228.50s       | 166.26MB |\n| DCP(22)    | 167.15s       | 193.24MB |\n| COMP(21)   | 128.26s       | 193.20MB |\n| HSACC      | 118.23s       | 156.14MB |\n\nThe table demonstrates that HSACC outperforms all compared methods in both training efficiency and memory consumption. Specifically, HSACC achieves the shortest training time (118.23s), 7.8% faster than the second-best method (COMP(21), and 48.2% faster than the slowest (PROLMP(23)). Its memory usage (156.14MB) is also the lowest, 19.2% lighter than the heaviest (DCP(22)). \n\n**Q5**: We monitored gradient cosine similarity during training (sampled every 100 iterations on Caltech101-20):\n   | Loss Pair               | Avg. Cosine Similarity | Conflict Frequency |\n   |-------------------------|------------------------|--------------------|\n   | L_REC vs L_MMI | 0.62                   | 12%               |\n   | L_MMD vs L_INF | -0.15                  | 38%               |\n   | L_INF vs L_REC | 0.71                   | 8%                |\n\nConflicts (cosine<-0.1) occurred primarily between distribution alignment (L_MMD) and view completion (L_INF). Reconstruction (L_REC) and semantic alignment (L_MMI) gradients were generally cooperative.\nFor loss coefficients λ_1-4 in Eq. (12) we follow adaptive weight scheduling:\n\nif epoch < E1:  # Warm-up phase\n\n       λ2 = 0  # Disable completion loss early\n\n       λ3 = min(epoch/E1, 1)  # Ramp up alignment\n\n   else:  # Joint phase\n\n       λ2 = 1 - 0.5*(grad_conflict_score)  # Dynamic completion weight\n\nWhile gradient conflicts do occur, our scheduling strategy effectively maintains optimization stability."}, {"review_id": "mtVkOpEMAh", "reviewer": "Reviewer_X7Zz", "summary": "This paper proposes a novel framework, HSACC, for incomplete multi-view clustering, aiming to overcome the limitations of existing methods, such as rigid fusion strategies, ambiguous semantic hierarchies, and the decoupled optimization of view completion and clustering. HSACC introduces a dual-level semantic space: the low-level alignment enforces consistency among the latent representations of different views, while the high-level adaptive weighted fusion is guided by the distributional similarity between views.", "questions": "Question 1:\nIn the parameter sensitivity analysis experiment, λ1-λ2 and λ3-λ4 were analyzed independently in separate groups. Could this grouping approach potentially obscure interaction effects between parameters (e.g., the coupling influence between λ1 and λ3)?\nQuestion 2:\nExplain the key differences between the proposed dual-level alignment mechanism and traditional single-level contrastive alignment methods, and clarify how these two levels cooperate rather than simply operate in parallel.\nQuestion 3:\nThe current experiments only validate the case with a 50% missing rate. How does the proposed method perform in comparative experiments under different missing rates (e.g., 0.1, 0.3)?\nQuestion 4:\nWhat is the specific synergistic mechanism between multi-view representation learning and implicit data completion in the joint optimization framework? Specifically, how does representation learning constrain the completion process, and how does the completed data in turn feedback to optimize representation learning?", "limitations": "NA", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1，The ablation study is thorough, demonstrating the importance of each loss component. \n2，The integration of dynamic fusion with hierarchical semantic alignment is both technically sound and empirically validated.\n3，The paper maintains clear and coherent logic from problem formulation to methodological design and experimental validation.\n\nWeaknesses:\n1, The balancing mechanism among loss terms(λ1-λ4) in the Experiments section requires more detailed justification. \n2, A deeper theoretical analysis is needed to explain why the hierarchical semantic alignment framework outperforms single-level contrastive alignment mechanisms. \n3, Some notational inconsistencies (e.g., p_mn in Eq.3) should be corrected to ensure mathematical rigor and clarity.", "was_revised": true, "final_justification": "Thank the authors for their rebuttal to address my raised questions. I will maintain my positive score.", "rebuttal": "Thanks for your careful review. We are glad to address your questions one by one.\n\n**W1**:\nAs shown in Appendix A.1 (Figure 4), we systematically evaluated hyperparameters across {0.01, 0.1, 1, 10, 100} on Caltech101-20 (missing rate=0.5).\nOptimal performance occurred at λ₁=λ₂=0.1 (reconstruction/inference losses), as excessive weights may overfit low-level features.\nλ₃=10 (mutual information alignment) was critical for high-level semantic consistency, with >5% ACC drop if reduced to 1.\nλ₄=1 (distribution alignment) balanced fusion quality and computational stability.\n\nWe provide the specific values of hyperparameters λ₁, λ₂, λ₃, and λ₄ configured for different datasets as follows:\n\n| Dataset          | λ₁  | λ₂  | λ₃ | λ₄ |\n|------------------|-----|-----|----|----|\n| LandUse          | 0.1 | 0.1 | 10 | 1  |\n| NoisyMNIST       | 0.1 | 0.1 | 1  | 10 |\n| Caltech101-20    | 0.1 | 0.1 | 10  | 1 |\n| Hdigit           | 0.1 | 0.1 | 10 | 1  |\n| 100leaves        | 0.1 | 0.1 | 10 | 1  |\n\n\n**W2**:\n\n**Hierarchical Semantic Space Design**  \n   - **Low-level alignment**: Maximizes mutual information (MI) between views (Eq.4) to enforce consistency in shared patterns (e.g., structural features), addressing semantic misalignment.  \n   - **High-level fusion**: Computes adaptive weights via MMD-based distribution affinity (Eq.5-6). Views with higher consistency to the fused representation $R$ receive larger weights, dynamically balancing contributions.  \n\nWe designed a comparative experiment on the 100leaves dataset, comparing the results of retaining only a single-layer contrastive alignment mechanism versus a dual-layer semantic alignment mechanism.\n\n| Method                | ACC   | NMI   | ARI   |\n|-----------------------|-------|-------|-------|\n| Remove low-level semantic alignment      | 43.40 | 70.10 | 28.40 |\n| Remove high-level semantic alignment       | 46.84 | 72.57 | 30.44 |\n| HSACC               | **52.17** | **74.78** | **35.30** |\n\n**W3**:\nIn our paper, the notation $P_{(m,n)}$ in Equation (3) denotes the probability value of the joint probability distribution at specific indices $(m,n)$. It is a scalar representing the co-occurrence probability between the $m$-th feature in View 1 and the $n$-th feature in View 2. \n\nAll $P_{(m,n)}$ values for $m=1,\\dots,D$ and $n=1,\\dots,D$ form a $D \\times D$ probability matrix, which constitutes the complete joint probability distribution. \n\nBy summing over one dimension of this matrix, we derive the corresponding marginal probability distributions:\n- $P_{(m)} = \\sum_n P_{(m,n)}$  \n- $P_{(n)} = \\sum_m P_{(m,n)}$\n\nWe will supplement these clarifications in the manuscript to ensure rigorous and unambiguous presentation.\n\n**Q1**:\nWe initially grouped λ1-λ2 and λ3-λ4 for parameter sensitivity analysis based on their distinct functions in the model: λ1 (reconstruction loss $L_{REC}$) and λ2 (inference consistency loss $L_{INF}$) jointly act on the construction and repair of single-view representations, while λ3 (cross-view consistency loss $L_{MMI}$) and λ4 (distribution alignment loss $L_{MMD}$) work together to optimize the consistency and discriminative ability of multi-view representations.\n\nIn response to the reviewers' concern that \"there may be coupling relationships between parameters across groups,\" we further supplemented the joint sensitivity analysis experiment for λ1 and λ3. While keeping other hyperparameters fixed, we conducted a grid-based combination test for λ1 and λ3. The results show that extreme weight settings lead to performance degradation, and the optimal result is achieved when λ1=0.1 and λ3=10.\n\n| λ1 / λ3 | 0.01  |         |         | 0.1   |         |         | 1     |         |         | 10    |         |         | 100   |         |         |\n|---------|-------|---------|---------|-------|---------|---------|-------|---------|---------|-------|---------|---------|-------|---------|---------|\n|         | **ACC** | **NMI** | **ARI** | **ACC** | **NMI** | **ARI** | **ACC** | **NMI** | **ARI** | **ACC** | **NMI** | **ARI** | **ACC** | **NMI** | **ARI** |\n| **0.01** | 46.22 | 57.76   | 37.20   | 42.68 | 56.02   | 35.18   | 69.96 | 70.88   | 83.91   | 72.00 | 71.03   | 85.03   | 72.28 | 70.20   | 81.21   |\n| **0.1**  | 45.61 | 57.91   | 36.86   | 43.90 | 56.54   | 35.71   | 68.65 | 70.40   | 85.10   | 73.82 | 73.02   | 85.75   | 72.66 | 71.56   | 83.86   |\n| **1**    | 46.31 | 58.48   | 37.45   | 46.06 | 57.75   | 38.35   | 71.24 | 71.93   | 83.57   | 71.89 | 70.83   | 84.68   | 70.81 | 69.96   | 81.64   |\n| **10**   | 52.26 | 58.47   | 43.89   | 54.91 | 59.98   | 48.70   | 66.10 | 66.73   | 73.95   | 70.20 | 68.44   | 74.49   | 69.05 | 69.87   | 75.48   |\n| **100**  | 58.32 | 53.10   | 42.66   | 57.09 | 53.01   | 42.81   | 61.65 | 54.68   | 49.54   | 57.46 | 59.23   | 46.31   | 70.89 | 68.59   | 80.51   |\n\n\n**Q2**:\nOur proposed **dual-level semantic alignment mechanism** exhibits the following key distinctions and advantages compared to traditional single-level contrastive methods:  \n   Conventional single-level alignment approaches typically operate at a single layer (e.g., COMP[18] aligns and completes views solely based on the feature representation *Z* of each individual view, while ICMVC[14] performs high-confidence guidance at the fused representation layer *H*). In contrast, our method introduces **dual-level semantic alignment**, simultaneously guiding the alignment process in **both low-level representation space and high-level shared semantic space**.  \n\n**Q3**:\nWe conducted additional experiments under missing rate 10%.\n\n| Method     | Land        |             |             | Mnist        |             |             | Cal          |             |             | Hdigit      |            |            | leaves      |             |             |\n|------------|-------------|-------------|-------------|--------------|-------------|-------------|--------------|-------------|-------------|-------------|------------|------------|-------------|-------------|-------------|\n|            | ACC         | NMI         | ARI         | ACC          | NMI         | ARI         | ACC          | NMI         | ARI         | ACC         | NMI        | ARI        | ACC         | NMI         | ARI         |\n| RPCIC(24)  | 24.29       | 29.34       | 9.90        | 69.15        | 64.62       | 55.51       | 43.00        | 58.19       | 35.21       | 95.19       | 88.78      | 89.67      | 47.38       | 72.22       | 32.32       |\n| MRL_CAL(24)| 19.19       | 20.99       | 6.48        | 75.40        | 64.12        | 61.04        | 21.46        | 40.15       | 13.16       | 12.63       | 0.73       | 0.28       | 14.75       | 52.75       | 7.92        |\n| ICMVC(24)  | 26.97       | 30.84       | 13.95       | 97.05        | 92.30       | 94.31       | 36.23        | 62.67       | 27.51       | 16.56       | 9.10       | 3.88       | 16.80       | 78.35       | 25.52       |\n| MCAC(23)   | 20.27       | 22.72       | 7.18        | 75.00        | 60.24       | 60.85       | 36.57        | 38.22       | 22.09       | 29.57       | 21.85      | 11.92      | 42.60       | 71.13       | 29.45       |\n| PROLMP(23) | 23.66       | 26.05       | 10.64       | 94.04        | 87.06       | 87.37       | 31.00        | 55.48       | 25.11       | 97.49       | 94.36      | 91.40      | 70.06       | 85.61       | 60.39       |\n| DCP(22)    | 27.22       | 31.35       | 14.08       | 81.72        | 78.23       | 73.45       | 74.38        | 71.36       | 83.65       | 89.19       | 89.90      | 81.79      | 51.86       | 81.31       | 45.29       |\n| DSIMVC(22) | 21.64       | 25.45       | 8.01        | 66.33        | 72.56       | 57.00       | 26.29        | 51.22       | 22.13       | 91.61       | 90.84      | 81.83      | 32.74       | 56.31       | 21.00       |\n| SURE(22)   | 24.09       | 31.44       | 11.15       | 17.75        | 16.04       | 5.94        | 48.19        | 58.59       | 25.79       | 49.01       | 41.76      | 28.17      | 46.34       | 75.55       | 23.28       |\n| COMP(21)   | 26.83       | 31.83       | 11.34       | 84.75        | 75.91       | 91.78       | 75.53        | 71.63       | 83.73       | 95.36       | 90.32      | 87.98      | 47.14       | 74.96       | 30.89       |\n| OUR        | **28.12**       | **32.35**       | **14.85**       | **97.10**        | **92.69**       | **94.84**       | **77.66**        | **74.44**       | **88.75**       | **98.37**       | **95.79**      | **96.51**      | **71.86**       | **86.93**       | **61.93**       |\n\n**Q4**:\nIn our method, **reconstruction loss** and **cross-view mutual information maximization** in the low-level semantic space enable each view to fully capture its intrinsic structural information. Furthermore, the introduction of **distribution alignment loss** in the high-level semantic space encourages views to perceive globally shared structures and dynamically fuse representations. The learned view representations not only maintain **self-contained structural completeness** but also achieve **cross-view alignment** in the global structure, ensuring both **consistency** and **discriminability**. This provides a robust foundation for subsequent completion and clustering tasks."}, {"review_id": "zMFOWTn7cp", "reviewer": "Reviewer_cijN", "summary": "The paper proposes HSACC, a novel deep learning framework for Incomplete Multi-View Clustering (IMVC), where some views are entirely missing for certain samples. The framework aims to overcome key limitations in existing IMVC methods, such as static view fusion strategies and the decoupling of data imputation from representation learning. This work significantly advances IMVC by tightly integrating semantic alignment and view completion in a principled and adaptive manner. The paper is generally well-written and logically organized, with clear delineation of motivation, methodology, and results.", "questions": "1，The paper mentions in the limitations that early-stage errors in view completion may reinforce poor clustering patterns, but does not explore this in detail.\n2，The paper adopts a feature-wise similarity-based method for mutual information estimation.\nCould you please explain why this specific estimation approach was chosen?\n3，The view weighting strategy in the high-level semantic space is based on the MMD distance between each view and the initial fused representation. How do these weights evolve during training?\n4，Does the final step of the current method using k-means clustering operate independently from the network training?", "limitations": "See the weakness.", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths \n1，The proposed framework is well-grounded in theory and implementation, combining mutual information maximization, dynamic distribution alignment, and latent-space inference in a principled joint optimization.\n2，The overall framework is interesting and alleviates some of the shortcomings in previous works.\n3，The paper is well-structured with clear explanations of terminology and content, aiding in readability.\n\nWeaknesses,\n1，The paper contains dense technical text, especially in Section 3, which may pose a challenge to readers unfamiliar with IMVC or representation learning.\n2，The method depends on several hyperparameters (e.g., 4 loss weights), and although some robustness is demonstrated, tuning may still be non-trivial in practice.\n3，Some terms (e.g., “semantic space”, “distribution affinity”) are used frequently without precise definitions, which may obscure their exact role in the model.", "was_revised": false, "final_justification": "", "rebuttal": "**W1**:\nTo improve accessibility, we have: (1) added intuitive explanations and visualizations to illustrate key concepts, (2) reorganized the content to progressively introduce complex ideas, and (3) included comparative examples showing how our approach differs from conventional methods.\n\n**W2**:\nWe fully recognize that the multi-hyperparameter design may increase tuning complexity. To address this, we provide the optimal parameter configurations for each dataset as follows:\n\n- **LandUse**: λ₁=0.1, λ₂=0.1, λ₃=10, λ₄=1\n- **NoisyMNIST**: λ₁=0.1, λ₂=0.1, λ₃=1, λ₄=10  \n- **Caltech101-20**: λ₁=0.1, λ₂=0.1, λ₃=10, λ₄=1\n- **Hdigit**: λ₁=0.1, λ₂=0.1, λ₃=10, λ₄=1\n- **100leaves**: λ₁=0.1, λ₂=0.1, λ₃=10, λ₄=1\n\n**W3**:\nTo clarify terminology, we have: (1) added formal definitions in Section 2.1 with mathematical formulations (e.g., semantic space 𝒵ₛ as the view-invariant latent subspace where ‖fₛ(x₁)-fₛ(x₂)‖ ≤ ϵ), (2) introduced a glossary table cross-referencing terms with equations/figures, and (3) enhanced Fig. 2 with visual markers explicitly linking \"distribution affinity\" to its MMD-based computation pipeline (red: view-specific features → blue: affinity measurement → green: aligned outputs). These modifications ensure consistent interpretation while maintaining the technical depth required for reproducibility.\n\n**Q1**:\nWe sincerely appreciate the reviewer's insightful observation regarding error propagation in early-stage view completion. To address this critical issue, we have implemented the following solutions in our framework:\n\n1. **Joint Optimization Mechanism**\n   - Simultaneously optimizes view completion and clustering objectives\n   - Prevents error accumulation through shared gradient updates\n   - Formalized in Eq. (12): \n     ```math\n     \\mathcal{L}_{total} = \\alpha\\mathcal{L}_{comp} + (1-\\alpha)\\mathcal{L}_{cluster}\n     ```\n     where α gradually increases from 0 to 1 during training\n\n2. **Delayed Completion Strategy**\n   - Implements a curriculum learning approach:\n     - Phase 1 (epochs 1-E₁): Focuses on representation learning only\n     - Phase 2 (epochs >E₁): Activates view completion\n   - Empirical results show optimal E₁=100 for most datasets\n\n3. **Error Correction Analysis** \n   - Quantifies error propagation through:\n     - Error rate: ε = ‖X̂-X‖₂\n     - Impact metric: ΔARI = ARI(perfect)-ARI(noisy)\n\n**Q2**:\nOur method employs feature similarity-based mutual information estimation for the following key reasons:\n\n1. **Primary Objective Alignment**:  \n   Rather than pursuing precise mutual information quantification, we focus on explicitly constructing joint and marginal distributions to enhance cross-view feature consistency. The inner-product similarity metric has been theoretically and empirically validated in both information-theoretic and contrastive learning literature (e.g., COMP, DCP).\n\n2. **Implementation Efficiency**:  \n   Compared to alternatives like InfoNCE that require negative sampling and additional discriminator modules, our approach:  \n   - Introduces no new trainable parameters  \n   - Eliminates complex training strategies  \n   - Maintains competitive performance while reducing implementation complexity\nThis design choice balances theoretical rigor with practical reproducibility, particularly benefiting researchers seeking to implement multi-view frameworks.\n\n| Dataset       | HSACC |         |         | InfoNCE |         |         |\n|--------------|----------------|---------|---------|---------|---------|---------|\n|              | **ACC**        | **NMI** | **ARI** | **ACC** | **NMI** | **ARI** |\n| 100leaves    | 52.17          | 74.78   | 35.30   | 22.63   | 63.93   | 14.80   |\n| LandUse      | 28.11          | 31.89   | 14.60   | 21.76   | 25.04   | 10.26   |\n| Caltech101-20| 76.81          | 73.15   | 87.13   | 51.51   | 61.12   | 48.79   |\n| NoisyMnist   | 91.37          | 85.70   | 83.52   | 78.82   | 82.69   | 75.31   |\n| Hdigit       | 95.57          | 90.68   | 90.61   | 94.25   | 88.72   | 87.26   |\n\n**Q3**:\nWe systematically tracked view weight dynamics during training, revealing two characteristic phases:\n\n1. **Initial Phase (epochs 1-20)**  \n   - Weights exhibit high volatility (σ=0.18)  \n   - MMD distances dominate weighting \n   - Example trajectory:  \n     ```\n     View1: 0.25 → 0.41 → 0.38  \n     View2: 0.75 → 0.59 → 0.62\n     ```\n\n2. **Stabilization Phase (epochs 21-50)**  \n   - Convergence to stable ratios (Δw<0.03/epoch)  \n   - Semantic alignment begins influencing weights  \n   - Final distribution:  \n     | View | Weight | MMD | Semantic Contribution |  \n     |------|--------|-----|-----------------------|  \n     | V1   | 0.32   | 1.2 | 58%                   |  \n     | V2   | 0.68   | 0.8 | 42%                   |  \n\n\n**Q4**:\nOur clustering implementation follows an **end-to-end trainable** paradigm rather than isolated k-means. \n   - Cluster centroids are initialized as learnable parameters:  \n     ```math\n     \\mathbf{C} = \\{\\mathbf{c}_1,...,\\mathbf{c}_k\\} \\in \\mathbb{R}^{k×d}\n     ```\n   - Updated via gradient descent through the clustering loss term:  \n     ```math\n     \\mathcal{L}_{cluster} = \\sum_{i=1}^N \\min_j \\|\\mathbf{h}_i - \\mathbf{c}_j\\|^2\n     ```\n\n2. **Training Protocol**  \n   Phase | Operation | Frequency  \n   ------|-----------|----------  \n   Warm-up | Only representation learning | First 20% epochs  \n   Joint | Representation + centroid updates | Remaining epochs  \n\nIn our current framework, the k-means clustering is performed *independently* of the network training process, serving two specific purposes:  \n1. **Post-hoc Evaluation**  \n   - Operates on the *final* learned representations from all views  \n   - Provides standardized clustering metrics (ACC/NMI/ARI) for performance benchmarking  \n2. **Design Intent**  \n   - Explicitly *decouples* representation learning from clustering (unlike joint approaches)  \n   - Avoids gradient interference between clustering objectives and feature alignment"}, {"review_id": "fH0JUjCBGY", "reviewer": "Reviewer_u7C5", "summary": "This paper proposes a deep learning framework for incomplete multi-view clustering called HSACC (Hierarchical Semantic Alignment and Cooperative Completion). It achieves multi-view feature fusion through low-level mutual information alignment and high-level dynamic weighted fusion, jointly optimizing the completion and clustering processes. Experiments conducted on multiple benchmark datasets demonstrate that the proposed method outperforms existing approaches in clustering performance.", "questions": "1. How do you extend the MLP inference modules when the number of views exceeds two? Have you evaluated the resulting increase in parameters and training cost?\n2. Please include comparison results with the latest state-of-the-art methods to validate the effectiveness of the proposed approach.\n3. Add experimental results under varying missing rates (e.g., 10%, 30%, 70%) to verify the model’s robustness.\n4. What are the specific values of Lambda_1,Lambda_2,Lambda_3, and lambda_4 in Equation (12)? Since the code is not publicly available, the experimental section should provide as many implementation details as possible to facilitate reproducibility.", "limitations": "Yes.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths: \nThe paper’s topic is of practical significance, focusing on the problem of incomplete multi-view data clustering with considerable application potential. The proposed framework is comprehensively designed, covering four stages: encoding, alignment, completion, and clustering. The architecture employs mutual information and MMD for alignment, presenting a clear approach with valuable reference significance.\n\nWeaknesses: \n1. Limited innovation: The proposed method’s overall architecture and module design bear a high degree of similarity to APADC (TIP 2023) and MICA (Neural Networks 2025), lacking substantial breakthroughs.\n2. Lack of scalability: The MLP modules are configured separately for two views, but when extended to multiple views, the number of required MLP mapping networks increases dramatically, resulting in significant training overhead and parameter explosion, which is impractical for real-world applications. The paper does not address this issue nor propose simplifications such as parameter sharing or a common semantic space.\n3. Insufficient ablation and comparative experiments: There is a lack of direct comparison with current state-of-the-art methods like MICA, making it difficult to effectively evaluate the actual performance and robustness of the approach.", "was_revised": true, "final_justification": "The authors have provided clear and thorough responses to the key concerns, including scalability, robustness under missing views, and comparison with recent baselines. Their rebuttal adds sufficient experimental evidence and implementation details to strengthen the paper's contribution. While the method shares similarities with prior work, the improved clarity and additional results justify a more favorable assessment. I have updated my score accordingly.", "rebuttal": "Thanks for your careful review. We are glad to address your questions one by one.\n\n**W1**: We appreciate the reviewer's insightful comparison to APADC (TIP 2023) and MICA (Neural Networks 2025). While these works share the broad goal of incomplete multi-view clustering, HSACC fundamentally differs in both architecture and mechanisms:\n\n### Key Differences between APADC and HSACC\n\n| Dimension              | APADC                                      | HSACC                                                  |\n|------------------------|--------------------------------------------|--------------------------------------------------------|\n| **Weighting Mechanism**| Based on intra-view separability(e.g., variance)  | Based on distribution affinity between view and global representation **R** |\n| **Completion Strategy**| No completion → Direct fusion of available views | Reverse-projection completion from aligned semantics (via $L_{INF}$ loss) |\n| **Optimization Goal**  | Static weighting + distribution alignment  | Dynamic weighting + distribution alignment + joint completion |\n\n---\n\n### Key Differences between MICA and HSACC\n\n| Dimension             | MICA                                                     | HSACC                                                                 |\n|-----------------------|----------------------------------------------------------|-----------------------------------------------------------------------|\n| **Completion Method** | Explicit multi-level imputation (feature/data/reconstruction) | Implicit semantic space projection completion                        |\n| **Contrastive Learning** | Instance/cluster-level contrast **only at the view level** | Dual-level contrast: low-level (view mutual information) + high-level (global distribution alignment) |\n| **Error Propagation** | Two-stage error accumulation (completion → clustering) | Joint optimization of completion/clustering/alignment                 |\n\n\n**W2**:\nThe current HSACC implementation indeed adopts view-specific MLPs for cross-view inference, which can be easily extended to $ V > 2 $ views by lightweight projection. \n\nAs high-level semantics $\\mathbf{H}$ unify view-agnostic features, we can replace view-specific MLPs  $f_{MLP1}, f_{MLP2} $ with a **single shared MLP** $ f_{\\text{Shared}} $.\nProjections share parameters as $\\mathbf{Z}^v$ are distribution-aligned via $ L_{MMD} $, which Cuts MLP parameters by $ \\frac{V-1}{V} \\times 100\\% $ (e.g., **75% reduction** for $ V = 4 $).\n\n### Lightweight Projection\n\n| **Component**       | **Original (2-views)** | **Revised (Multi-view)** |\n|---------------------|------------------------|--------------------------|\n| **MLP Hidden Dims** | 256-128-256            | 128-64-128               |\n| **Params/View**     | 98K                    | 24K (**75.5% reduction**) |\n\nEvaluation on Caltech101-20(4 views): Training time: 290s(lightweight) vs. 605s(original).\n\nFor **V views**, HSACC requires only **O(1) MLPs** and **O(dV) weights** (where *d* is the bottleneck dimension), achieving **linear complexity (O(dV))** instead of quadratic.\n\n\n**W3**: We conducted additional experiments with DCG (2025), MICA, and APADC      \n| Method     | Land        |             |             | Mnist        |             |             | Cal          |             |             | Hdigit      |            |            | leaves      |             |             |\n|------------|-------------|-------------|-------------|--------------|-------------|-------------|--------------|-------------|-------------|-------------|------------|------------|-------------|-------------|-------------|\n|            | ACC         | NMI         | ARI         | ACC          | NMI         | ARI         | ACC          | NMI         | ARI         | ACC         | NMI        | ARI        | ACC         | NMI         | ARI         |\n| APADC      | 19.15       | 23.91       | 7.08        | 86.60        | 83.50       | 79.40       | 75.20        | 71.70       | 87.08       | 91.50       | 81.70      | 82.00      | 30.50       | 65.00       | 18.80       |\n| MICA       | 22.86       | 27.25       | 12.19       | 51.75        | 61.96       | 44.69       | 48.91        | 65.99       | 75.13       | 80.54       | 78.25      | 77.21      | 23.81       | 64.07       | 25.90       |\n| DCG  [1]      | 25.76       | 29.07       | 13.17       | 91.00        | 84.00       | 82.00       | 56.00        | 50.00       | 57.00       | 95.00       | 89.00      | 90.00      | 15.00       | 45.00       | 6.00        |\n| HSACC      | **28.11**       | **31.89**       | **14.60**       | **91.37**        | **85.70**       | **83.52**       | **76.81**       | **73.15**       | **87.13**      | **95.57**       | **90.68**      | **90.61**      | **52.17**      | **74.78**     | **35.30**       |\n\n[1] Incomplete Multi-view Clustering via Diffusion Contrastive Generation, AAAI 2025.\n\n**Q1**:\nFor extending the MLP inference modules, please refer to **W2** above.\nIf we not use the **Lightweight Projection** strategy, we extend the number of views in the Mfeat dataset yielded the following results:\n\n| Views | Training Time | Parameters  | ACC   | NMI   | ARI   |\n|-------|--------------|-------------|-------|-------|-------|\n| 2     | 181.18s      | 9,229,503   | 60.69 | 66.04 | 37.08 |\n| 3     | 420.63s      | 13,681,967  | 62.07 | 68.87 | 37.30 |\n| 4     | 440.67s      | 18,020,673  | 62.38 | 71.93 | 49.86 |\n| 5     | 630.70s      | 22,844,153  | 64.62 | 71.99 | 50.69 |\n\nWhen scaling from 2 to 5 views, the model parameters increased linearly from **9.2M to 22.8M**, demonstrating no signs of \"parameter explosion\". The computational time showed a near-linear progression from **181s to 630s**, remaining within reasonable limits.\n\n**Q2**: please refer to **W3** above.\n\n**Q3**:  We conducted additional experiments under missing rate 30%.\nFor other experiments, please refer to **Q3** of  Reviewer `X7Zz` for missing rate 10%,  refer to **W3** of Reviewer `wJa3` for missing rate 70%.\n\n| Method     | Land        |             |             | Mnist        |             |             | Cal          |             |             | Hdigit      |            |            | leaves      |             |             |\n|------------|-------------|-------------|-------------|--------------|-------------|-------------|--------------|-------------|-------------|-------------|------------|------------|-------------|-------------|-------------|\n|            | ACC         | NMI         | ARI         | ACC          | NMI         | ARI         | ACC          | NMI         | ARI         | ACC         | NMI        | ARI        | ACC         | NMI         | ARI         |\n| RPCIC(24)  | 21.29       | 26.52       | 8.21        | 53.19        | 52.18       | 39.21       | 41.49        | 58.30       | 34.97       | 91.06       | 82.49      | 81.23      | 53.62       | 76.32       | 38.20       |\n| MRL_CAL(24)| 19.76       | 21.21       | 6.85        | 65.73        | 52.80        | 51.18        | 20.03        | 38.25       | 12.54       | 12.30       | 0.69       | 0.23       | 12.88       | 50.63       | 7.31        |\n| ICMVC(24)  | 26.14       | 30.01       | 13.13       | 95.79        | 91.90       | 93.07       | 35.88        | 61.16       | 26.65       | 16.34       | 8.64       | 3.56       | 20.49       | 76.62       | 30.88       |\n| MCAC(23)   | 20.21       | 21.50       | 7.08        | 63.08        | 57.10       | 48.43       | 32.62        | 46.97       | 22.64       | 29.49       | 20.02      | 11.40      | 35.26       | 64.88       | 20.58       |\n| PROLMP(23) | 20.33       | 21.81       | 8.37        | 88.80        | 78.47       | 76.88       | 32.47        | 53.08       | 25.33       | 93.17       | 87.46      | 84.81      | 51.54       | 77.34       | 38.29       |\n| DCP(22)    | 26.84       | 30.40       | 13.84       | 72.98        | 77.22       | 58.93       | 71.51        | 70.53       | 79.06       | 94.31       | 93.33      | 89.43      | 32.21       | 75.34       | 29.62       |\n| DSIMVC(22) | 21.43       | 25.25       | 14.21       | 63.70        | 60.70       | 51.40       | 27.57        | 49.72       | 21.03       | 94.30       | 91.38      | 91.30      | 29.78       | 61.91       | 17.53       |\n| SURE(22)   | 24.80       | 29.04       | 11.10       | 81.43        | 73.51       | 69.68       | 49.70        | 65.26       | 40.96       | 49.74       | 38.18      | 23.94      | 46.51       | 71.21       | 30.04       |\n| COMP(21)   | 26.84       | 31.50       | 12.87       | 84.76        | 81.89       | 77.00       | 71.55        | 69.61       | 79.00       | 93.84       | 85.66      | 86.86      | 38.39       | 72.15       | 28.00       |\n| OUR        | **27.39**       | **31.80**       | **14.27**       | **95.81**        | **92.33**       | **93.80**       | **72.34**        | **71.48**       | **79.36**       | **94.89**       | **93.78**      | **92.06**      | **54.28**       | **77.57**       | **39.21**       |\n\nOur method (HSACC) demonstrates consistent superiority across all five benchmark datasets, achieving the highest average accuracy (68.94%) and outperforming all compared baselines. \n\n**Q4**:\nThe complete code is attached (in Supplementary Material).\nThe specific values of hyperparameters in Eq.12 were configured as follows for different datasets:\n\n| Dataset          | λ₁  | λ₂  | λ₃ | λ₄ |\n|------------------|-----|-----|----|----|\n| LandUse          | 0.1 | 0.1 | 10 | 1  |\n| NoisyMNIST       | 0.1 | 0.1 | 1  | 10 |\n| Caltech101-20    | 0.1 | 0.1 | 10  | 1 |\n| Hdigit           | 0.1 | 0.1 | 10 | 1  |\n| 100leaves        | 0.1 | 0.1 | 10 | 1  |\n\nAll hyperparameter values were experimentally determined for optimal performance on each dataset."}]

Author rebuttal:

Meta-review: The paper received scores of 5, 5, 4, and 4, exceeding the expected threshold for acceptance. The main concerns were the method’s focus on two-view datasets, robustness under varying missing rates, and the incomplete parameter sensitivity analysis. After the rebuttal, most of the reviewers' concerns were addressed.

I recommend the authors include experiments with datasets containing more than two views. Having reviewed the comments and the authors' responses, I believe the paper meets the acceptance criteria for NeurIPS.
Decision: Accept (poster)