Title: Incomplete Multi-view Clustering via Hierarchical Semantic Alignment and Cooperative Completion
Venue: NeurIPS 2025
Accepted: yes
Keywords: incomplete multi-view clustering

unsupervised learning

joint representation 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

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 https://github.com/XiaojianDing/2025-NeurIPS-HSACC .

1 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-based approaches. Traditional IMVC methods usually infer the missing parts based on the available information [2, 3], and subsequently employ specific machine learning techniques for multi-view clustering, such as non-negative matrix factorization methods [4, 5], kernel methods [6, 7], subspace learning methods [8, 9], and graph methods [10, 11]. These shallow IMVC methods commonly suffer from limited linear modeling capacity and sensitivity to complex missing patterns,

hindering their ability to fully exploit latent correlations and complementary information in incomplete multi-view data [7]. 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-based approaches [12], (2) GAN-based methods [13], (3) GCN-based techniques [14], and (4) contrastive learning-based 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 (e.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 on variance [16] or sharing weights across all views [17]), they lack a 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-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 a single framework for joint optimization [18, 19], they overlook the varying significance of different views in the fused representation within specific tasks or distributions. As a 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 a 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 an 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 highdimensional semantic spaces, leveraging learned discriminative features to guide completion. Finally, the completed views and latent representations are jointly optimized through reconstruction and clustering objectives. In summary, our contributions can be summarized as follows:

We propose a novel hierarchical semantic alignment and dynamic weighted fusion mechanism that, through dual-level semantic space design and adaptive weight allocation, significantly enhances the robustness and discriminability of cross-view fusion.

We propose a 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 on 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-based methods. These methods employ shared latent spaces and cross-reconstruction 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

strategy preserves the completeness of multi-view representations, with representative works including [13, 22, 23, 24]. (3) Graph Convolutional Network-based 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-based methods. By incorporating contrastive loss to maximize agreement between positive pairs across different views, these approaches leverage complementary inter-view information to infer representations for missing views [15, 18, 27].

2.2 Contrastive Learning

The core principle of contrastive learning [28, 29, 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 crossview alignment. For instance, PVC-SSN [15] addresses incomplete multi-view clustering via selfsupervised contrastive learning, where a self-supervised module enhances the discriminative capacity of the learned representations. Similarly, COMP [18] achieves both cross-view consistency and missing view recovery by maximizing mutual information across views while minimizing conditional entropy. Prolmp [27] introduces a 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 [31] proposes a 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 instanceand cluster-level contrastive learning, further improving representation integrity under incomplete settings.

Backprop

Backprop

一

LMMI

LINF

Local consistencylearning:

ClusteringResult

￥.

K-means

Different samples

z1

Encoder

X1

Z1

push

pull

(Z,2²)

LRECX1

Z1

…★

iBackprop

Decoder

iBackprop

Backprop

infer

infer

LMMD

LREC&2

Global contrastalignment:

weightfusion

x2

Decoder

H

Z1

minimize

MLP1

MLP2

Dynamic

weights

Z1

Encoder

minimize

NW

: incomplete data

(a)viewreconstruction

(b)multi-viewrepresentation learning

(c)datarecovery and clustering

3 Method

As shown in Figure 1, given two views X 1 and X 2 , we first map them to Z 1 and Z 2 via autoencoders, and then extract semantic information at two levels. In the low-level semantic space, the model maximizes the mutual information between views to ensure consistency alignment. In the high-level semantic space, Z 1 and Z 2 are concatenated to form the initial fused representation R , and cross-view distribution alignment is introduced to measure the matching degree between each view representation

Z v 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 to obtain a unified high-level shared representation H , and an alignment objective is further designed to minimize the distribution discrepancy between H and each view. Furthermore, based on the current learned latent representations Z 1 and Z 2 , the model maps them to a high-dimensional semantic space through an MLP to obtain Q 1 and Q 2 , 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

In this paper, { X v ∈ R N × d v } V v =1 represents a multi-view data set with V views, where X v = { x v 1 , ..., x v l , ..., x v N } , d v represents the feature dimension of the v -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 v i indicates the i -th sample in the v -th view. Additionally, we define an indicator matrix A ∈ { 0 , 1 } N × V , whose elements are defined as follows:

In this matrix, each column represents the availability status of all instances in a specific view.

3.2 The Loss Function

View Reconstruction Loss We construct view-specific autoencoders, where E v and D v denote the encoder and decoder for the v -th view, respectively. Given the input X v , the encoder extracts the latent representation Z v = E v ( X v ) ∈ R N × D , which is then reconstructed through the decoder as ˆ X v = D v ( Z v ) . 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:

Cross-view Consistency Loss In deep multi-view learning, maximizing the mutual information between features of different views is crucial for improve representation consistency [18]. To this end, we estimate mutual information via feature-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 1 and view 2 be z 1 i and z 2 i , respectively, where z 1 i,m and z 2 i,n represent the m -th and n -th scalar features. The similarity between the features of this sample across the two views is defined as p ( i ) m,n = z 1 i,m · z 2 i,n . By aggregating the similarities across all samples, we obtain the joint probability distribution P ∈ R D × D between view 1 and view 2. The ( m,n ) -th element of the matrix is defined as:

By summing over the rows and columns of the joint probability distribution P ∈ R D × D , we obtain the marginal probability distributions P (1) , P (2) ∈ R D for each view, with elements defined as P ( m ) = ∑ D n =1 P ( m,n ) and P ( n ) = ∑ D m =1 P ( m,n ) . Based on the above distributions, we define the mutual information loss between views as:

where I ( Z 1 ; Z 2 ) measures the information correlation between Z 1 and Z 2 . Minimizing this loss is equivalent to maximizing their mutual information.

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 to obtain a higher-level common representation and minimize its discrepancy with each view, thereby enhancing the consistency and complementarity of cross-view representations.

Step 1 : Estimating View Weights

For the given two view representations Z 1 and Z 2 , we first calculate their initial fusion representation R as R = Z 1 + Z 2 2 . 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 a linear kernel (i.e., k ( x, y ) = x T 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 us to quantify the discrepancy between the view-specific representation and the initial fused representation, as follows:

where N is the number of samples, z v i and r i 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 representation should contribute more to the final decision, we assign it a higher weight. Conversely, a view exhibiting a greater discrepancy is assigned a lower weight. This design enables the dynamic adjustment of each view's contribution. Accordingly, we define a weight function W v = f ( D ( Z v , R )) to calculate the weights, where f ( D ) is defined as:

In multi-view learning tasks, since each view Z v may carry complementary information, we perform weighted fusion of all view-specific representations using the learned weights W v , in order to integrate diverse perspectives into the high-level common representation H , where H = ∑ V v =1 W v · Z v .

Step 2 : Distribution alignment between H and Z v

Motivated by domain adaptation [33], to further enhance the information interaction between views and promote the completion of missing views, we aim to align the distribution of single-view representations Z v with the high-level common representation H . Specifically, let P denote the distribution of the view-specific representations Z v = { z v 1 , z v 2 , . . . , z v i } N i =1 , and let Q denote the distribution of the high-level common representations H = { h 1 , h 2 , . . . , h j } N j =1 . We measure their discrepancy in the high-level semantic space by computing the distance between P and Q :

Here, L MMD denotes the overall discrepancy loss between all views and the high-level common representation H , where H is the Reproducing Kernel Hilbert Space (RKHS). The terms E x ∼P Z v [ ϕ ( x )] and E y ∼Q H [ ϕ ( y )] represent the mean embeddings of the v -th view and the common representation H in the RKHS, respectively. Here, ϕ ( · ) is a feature mapping function that projects samples into the RKHS. Since it is difficult to compute the expectations directly, we approximate them using sample means. Taking E x ∼P Z v [ ϕ ( x )] as an example:

where Φ( Z v ) = [ ϕ ( z v 1 ) T , ϕ ( z v 2 ) T , . . . , ϕ ( z v N ) T ] T denote the feature mapping of all samples in view Z v , where 1 N is a vector of length N with all elements equal to 1. Similarly, the expectation E y ∼Q H [ ϕ ( y )] can be approximated. In RKHS, the inner product of feature mappings can be computed using the kernel function k ( x, y ) = ⟨ ϕ ( x ) , ϕ ( y ) ⟩ H . To simplify the computation, we construct kernel matrices K Z v Z v , K HH , and K Z v H , each of size N × N , representing the internal similarities of

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 it using kernel matrices, we obtain the final distribution alignment loss:

Inference Consistency Loss In incomplete multi-view clustering, we design cross-view inference modules f MLP1 and f MLP2 to learn nonlinear mappings in the latent space for implicitly completing missing views. Specifically, the latent representations Z 1 and Z 2 are projected into a high-dimensional semantic space, yielding Q 1 = f MLP1 ( Z 1 ) = f MLP1 ( E 1 ( X 1 )) and Q 2 = f MLP2 ( Z 2 ) = f MLP2 ( E 2 ( X 2 )) , 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 L INF to supervise the accuracy of the cross-view mapping:

Here, z v i is the true latent representation of the i -th sample in the v -th view, and q v i is 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 ( v 1 , v 2 ) as L MMI = 2 V ( V -1) ∑ v 1 <v 2 L MMI ( Z v 1 , Z v 2 ) , after which the latent representations are fused to obtain the global representation H , followed by distribution alignment with each view through the loss L MMD . Finally, in cross-view inference, the latent representation of view v 1 is projected by an MLP to infer the semantics of view v 2 , and the inference consistency loss is defined as L INF = 1 N ∑ N i =1 1 V ( V -1) ∑ v 1 = v 2 ∥ z v 2 i -q v 1 → v 2 i ∥ 2 2 , to ensure consistency between the inferred results and the true latent representations.

3.3 Objective Function and Optimization Algorithm

Thus, our overall objective function can be expressed as:

The λ 1 , λ 2 , λ 3 , and λ 4 are trade-off parameters in the loss function. Ultimately, we optimize Eq. (11) 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 1.

Algorithm 1: Incomplete Multi-View Clustering via Hierarchical Semantic Alignment and Cooperative Completion

Obtain all Q 1 2 via cross-view inference MLP to complete the views;

Input: Incomplete multi-view dataset { X v } V v =1 with indicator matrix A , epoch E , E 1 ; Parameters: Trade-off coefficients λ 1 , λ 2 , λ 3 , λ 4 Output: Clustering results for epoch = 1 to E do Learn view-specific representations via Eqs. (2) and (4); Concatenate the learned Z v to obtain R ; Calculate the view weight W v using Eq. (6); Fuse based on the weight W v to obtain H ; Calculate the distribution discrepancy between H and Z v via Eq. (9); if epoch ≥ E 1 then v → v

Update representations via joint optimization using Eq. (11);

Perform k -means clustering algorithm on the concatenated views;

4 Experiments

4.1 Experimental Setting

Datasets To evaluate the effectiveness of the proposed method, we selected five representative datasets. LandUse_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 1 and Gaussiannoised 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 [38] contains 1,600 samples from 100 categories.

Comparing Methods We conducted comparative experiments with nine state-of-the-art 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 to 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 information-theoretic 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 [18] simultaneously achieves data recovery and view-consistency learning by integrating contrastive learning and a dual-prediction mechanism.

Experimental Configuration All experiments were conducted on an NVIDIA RTX 4070 GPU using PyTorch 2.3.1. Our method employs a unified fully connected autoencoder, with the encoder structured as Input-1024-1024-1024-Output and the decoder mirrored accordingly. During the data recovery phase, a multilayer perceptron (MLP) with hidden layer dimensions of 256-128-256 is used for cross-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 1 -th epoch (e.g., E 1 = 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 1 presents the clustering results of various IMVC methods under different missing rates, where the best and second-best results are highlighted in bold and underline, respectively. It 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-art imputation-based IMVC methods. However, the experimental results demonstrate that our method still achieves superior performance compared to both. In particular, on the Caltech101-20 dataset with a missing rate of 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.

Ablation Study To evaluate the effectiveness of each loss component, we conducted ablation experiments on the Caltech101-20 dataset, focusing on four modules: L REC , L MMI , L MMD , and L INF . 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 L REC , achieves an ACC, NMI, and ARI of 42.07%, 41.06%, and 28.38%, respectively. By introducing the cross-view consistency loss L MMI , model M-9 shows substantial improvements

across all three metrics, with an ACC of 68.69%, NMI of 67.63%, and ARI of 73.68%. By further incorporating the distribution alignment loss L MMD 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 a 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 λ 1 , λ 2 , λ 3 , and λ 4 in the total loss function of our proposed method. Experiments are conducted on the Caltech101-20 dataset with a missing rate of 0.5, and each hyperparameter is evaluated over the range { 0 . 01 , 0 . 1 , 1 , 10 , 100 } . As shown in Figure 2, smaller values of λ 1 and λ 2 lead to better performance, with the optimal value being 0.1, while the best values for λ 3 and λ 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 Caltech101-20 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.

Convergence Analysis 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 4, the corresponding curves on the Caltech101-20 and Noisy MNIST and LandUse_21 datasets indicate that as the number of training epochs increases, the loss values decrease

(a) Analysis of parameters

λ

1

and

λ

2

80

08

90

75

75

80

ACC70

NMI70

ARI

70

65

65

60

100101

1

10

100

60

1001010.10.01

1

10

100

60

10010

1

10

100

0.1 0.01

0.01

0.1

0.01

0.1

0.1 0.01

0.01

0.1

A2

A2

A2

80

80

90

75

75

80

ACC70

NMI70

AR1

70

65

65

60

10

100

60

10

100

60

10

100

10010

1

1

100

1

N4

0.1 0.01

0.01

0.1

>3

N4

0.1

0.01

0.01

0.1

N3

N4

1

0.1

0.01

0.01

0.1

3

(b) Analysis of parameters

λ

3

and

λ

4

Model

M-1

M-2

M-3

M-4

M-5

M-6

M-7

M-9 M-10 M-11 M-12 M-13 M-14 M-15

L

REC

✓

✓

✓

✓

✓

✓

✓

✓

L

MMI

✓

✓

✓

✓

✓

✓

✓

✓

L

MMD

✓

✓

✓

✓

✓

✓

✓

✓

L

INF

✓

✓

✓

✓

✓

✓

✓

✓

ACC

42.07 54.92 36.90 43.96 42.45 51.52 55.97 67.40 68.69 71.60 50.80 71.29 72.31 73.15 76.81

NMI

41.06 54.70 44.70 31.71 28.38 53.68 57.85 67.97 67.63 71.12 53.12 68.48 71.65 71.25 73.15

ARI

28.38 51.66 23.50 29.61 31.05 38.05 51.22 71.08 73.68 80.30 34.68 78.27 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.

(a) Caltech101-20

(b) Noisy MNIST

Performance

0.8

ACC

NMI

ARI

-2620

0.6

Loss

-2640

S507

Clustering

0.4

-2660

-2680

0.2

-2700

0

Epoch

0.30

ACC

NMI

=4000

0.25

0.20

ARI

Loss

=4050

SS07

0.15

-4100

0.10

0.05

4150

0

100 200 300 400 500 600 700 800 9001000

Epoch

Performance

0.9

0.8

Loss

ACC

NMI

ARI

-19400

-19500

0.7

SSOT

Clustering

-19600

0.6

-19700

0.5

0.4

00861-

0

100

200

300

400

500

600

700

Epoch

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) of 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 2 views to 186.99 seconds for 5 views, while the clustering performance steadily improves, achieving the highest ACC (88.64), NMI (88.14), and ARI (81.09) with 5 views.

(a) 50 epoch

(b) 150 epoch

(c) 250 epoch

(d) 600 epoch

(e) 50 epoch

(f) 100 epoch

(g) 350 epoch

(h) 500 epoch

12.0

0.0

11.0

1.0

5 Conclusion

In this paper, we propose a novel framework, HSACC, based on hierarchical semantic alignment and cooperative completion. By designing a dual-level semantic space and employing a joint optimization strategy, the proposed method maps the learned latent representations into high-dimensional semantic spaces to 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 across multiple datasets, verifying its effectiveness and superiority. In future work, we plan to extend this framework to more complex multi-modal incomplete data scenarios, and further enhance its generalization ability and computational efficiency in real-world large-scale applications.

References

H. Gao, Y. Peng, and S. Jian, 'Incomplete multi-view clustering,' in Intelligent Information Processing VIII: 9th IFIP TC 12 International Conference, IIP 2016, Melbourne, VIC, Australia, November 18-21, 2016, Proceedings 9 . Springer, 2016, pp. 245-255.

J. Yin and S. Sun, 'Incomplete multi-view clustering with reconstructed views,' IEEE Transactions on Knowledge and Data Engineering , vol. 35, no. 3, pp. 2671-2682, 2023.

X. Liu, M. Li, C. Tang, J. Xia, J. Xiong, L. Liu, M. Kloft, and E. Zhu, 'Efficient and effective regularized incomplete multi-view clustering,' IEEE Transactions on Pattern Analysis and Machine Intelligence , vol. 43, no. 8, pp. 2634-2646, 2021.

H. Zhao, Z. Ding, and Y. Fu, 'Multi-view clustering via deep matrix factorization,' in Proceedings of the AAAI conference on artificial intelligence , vol. 31, no. 1, 2017.

J. Wen, G. Xu, Z. Tang, W. Wang, L. Fei, and Y. Xu, 'Graph regularized and feature aware matrix factorization for robust incomplete multi-view clustering,' IEEE Transactions on Circuits and Systems for Video Technology , vol. 34, no. 5, pp. 3728-3741, 2024.

X. Liu, X. Zhu, M. Li, C. Tang, E. Zhu, J. Yin, and W. Gao, 'Efficient and effective incomplete multi-view clustering,' in Proceedings of the AAAI conference on artificial intelligence , vol. 33, no. 01, 2019, pp. 4392-4399.

J. Guo and J. Ye, 'Anchors bring ease: An embarrassingly simple approach to partial multi-view clustering,' in Proceedings of the AAAI conference on artificial intelligence , vol. 33, no. 01, 2019, pp. 118-125.

S. Deng, J. Wen, C. Liu, K. Yan, G. Xu, and Y. Xu, 'Projective incomplete multi-view clustering,' IEEE Transactions on Neural Networks and Learning Systems , vol. 35, no. 8, pp. 10 539-10 551, 2024.

N. Xu, Y. Guo, X. Zheng, Q. Wang, and X. Luo, 'Partial multi-view subspace clustering,' in Proceedings of the 26th ACM International conference on multimedia , 2018, pp. 1794-1801.

J. Wen, Y. Xu, and H. Liu, 'Incomplete multiview spectral clustering with adaptive graph learning,' IEEE Transactions on Cybernetics , vol. 50, no. 4, pp. 1418-1429, 2020.

N. Rai, S. Negi, S. Chaudhury, and O. Deshmukh, 'Partial multi-view clustering using graph regularized nmf,' in 2016 23rd International Conference on Pattern Recognition (ICPR) . IEEE, 2016, pp. 2192-2197.

J. Xu, C. Li, Y. Ren, L. Peng, Y. Mo, X. Shi, and X. Zhu, 'Deep incomplete multi-view clustering via mining cluster complementarity,' in Proceedings of the AAAI conference on artificial intelligence , vol. 36, no. 8, 2022, pp. 8761-8769.

R. Lin, S. Du, S. Wang, and W. Guo, 'Consistent graph embedding network with optimal transport for incomplete multi-view clustering,' Information Sciences , vol. 647, p. 119418, 2023.

G. Chao, Y. Jiang, and D. Chu, 'Incomplete contrastive multi-view clustering with highconfidence guiding,' in Proceedings of the AAAI conference on artificial intelligence , vol. 38, no. 10, 2024, pp. 11 221-11 229.

W. Feng, G. Sheng, Q. Wang, Q. Gao, Z. Tao, and B. Dong, 'Partial multi-view clustering via self-supervised network,' in Proceedings of the AAAI Conference on Artificial Intelligence , vol. 38, no. 11, 2024, pp. 11 988-11 995.

J. Xu, C. Li, L. Peng, Y. Ren, X. Shi, H. T. Shen, and X. Zhu, 'Adaptive feature projection with distribution alignment for deep incomplete multi-view clustering,' IEEE Transactions on Image Processing , vol. 32, pp. 1354-1366, 2023.

Z. Zhu, C. Pu, X. Zhang, J. Wang, and X. Zhou, 'Dual-dimensional contrastive learning for incomplete multi-view clustering,' Neurocomputing , vol. 615, p. 128892, 2025.

Y. Lin, Y. Gou, Z. Liu, B. Li, J. Lv, and X. Peng, 'Completer: Incomplete multi-view clustering via contrastive prediction,' in Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , 2021, pp. 11 174-11 183.

H. Wang, W. Zhang, and X. Ma, 'Contrastive and adversarial regularized multi-level representation learning for incomplete multi-view clustering,' Neural Networks , vol. 172, p. 106102, 2024.

S. Wei, J. Wang, G. Yu, C. Domeniconi, and X. Zhang, 'Deep incomplete multi-view multiple clusterings,' in 2020 IEEE International Conference on Data Mining (ICDM) , 2020, pp. 651660.

C. Zhang, Z. Han, H. Fu, J. T. Zhou, Q. Hu et al. , 'Cpm-nets: Cross partial multi-view networks,' Advances in Neural Information Processing Systems , vol. 32, 2019.

J. Wang, Z. Xu, X. Yang, D. Guo, and L. Liu, 'Self-supervised image clustering from multiple incomplete views via constrastive complementary generation,' IET Computer Vision , vol. 17, no. 2, pp. 189-202, 2023.

J. Gui, Z. Sun, Y. Wen, D. Tao, and J. Ye, 'A review on generative adversarial networks: Algorithms, theory, and applications,' IEEE Transactions on Knowledge and Data Engineering , vol. 35, no. 4, pp. 3313-3332, 2023.

Q. Wang, Z. Ding, Z. Tao, Q. Gao, and Y. Fu, 'Generative partial multi-view clustering,' arXiv preprint arXiv:2003.13088 , 2020.

Y. Wang, D. Chang, Z. Fu, J. Wen, and Y. Zhao, 'Incomplete multiview clustering via cross-view relation transfer,' IEEE Transactions on Circuits and Systems for Video Technology , vol. 33, no. 1, pp. 367-378, 2023.

J. Wen, Z. Wu, Z. Zhang, L. Fei, B. Zhang, and Y. Xu, 'Structural deep incomplete multi-view clustering network,' in Proceedings of the 30th ACM international conference on information &knowledge management , 2021, pp. 3538-3542.

H. Li, Y. Li, M. Yang, P. Hu, D. Peng, and X. Peng, 'Incomplete multi-view clustering via prototype-based imputation,' arXiv preprint arXiv:2301.11045 , 2023.

A. v. d. Oord, Y . Li, and O. Vinyals, 'Representation learning with contrastive predictive coding,' arXiv preprint arXiv:1807.03748 , 2018.

T. Chen, S. Kornblith, M. Norouzi, and G. Hinton, 'A simple framework for contrastive learning of visual representations,' in International conference on machine learning . PmLR, 2020, pp. 1597-1607.

Y.-H. H. Tsai, Y. Wu, R. Salakhutdinov, and L.-P. Morency, 'Self-supervised learning from a multi-view perspective,' arXiv preprint arXiv:2006.05576 , 2020.

K. Zhang, S. Du, Y. Wang, and T. Deng, 'Deep incomplete multi-view clustering via attentionbased direct contrastive learning,' Expert Systems with Applications , vol. 255, p. 124745, 2024.

Z. Wang, Y. Du, Y. Wang, R. Ning, and L. Li, 'Deep incomplete multi-view clustering via multi-level imputation and contrastive alignment,' Neural Networks , vol. 181, p. 106851, 2025.

Y. Ganin and V. Lempitsky, 'Unsupervised domain adaptation by backpropagation,' in International conference on machine learning . PMLR, 2015, pp. 1180-1189.

Y. Yang and S. Newsam, 'Bag-of-visual-words and spatial extensions for land-use classification,' in Proceedings of the 18th SIGSPATIAL international conference on advances in geographic information systems , 2010, pp. 270-279.

W. Wang, R. Arora, K. Livescu, and J. Bilmes, 'On deep multi-view representation learning,' in International conference on machine learning . PMLR, 2015, pp. 1083-1092.

Y. Li, F. Nie, H. Huang, and J. Huang, 'Large-scale multi-view spectral clustering via bipartite graph,' in Proceedings of the AAAI conference on artificial intelligence , vol. 29, no. 1, 2015.

Z. Yang, N. Liang, W. Yan, Z. Li, and S. Xie, 'Uniform distribution non-negative matrix factorization for multiview clustering,' IEEE Transactions on Cybernetics , vol. 51, no. 6, pp. 3249-3262, 2021.

Q. Zheng, J. Zhu, and Z. Li, 'Collaborative unsupervised multi-view representation learning,' IEEE Transactions on Circuits and Systems for Video Technology , vol. 32, no. 7, pp. 4202-4210, 2021.

H. Yuan, S. Lai, X. Li, J. Dai, Y. Sun, and Z. Ren, 'Robust prototype completion for incomplete multi-view clustering,' in Proceedings of the 32nd ACM International Conference on Multimedia , 2024, pp. 10 402-10 411.

Y. Zhang and C. Zhu, 'Incomplete multi-view clustering via attention-based contrast learning,' International Journal of Machine Learning and Cybernetics , vol. 14, no. 12, pp. 4101-4117, 2023.

Y. Lin, Y. Gou, X. Liu, J. Bai, J. Lv, and X. Peng, 'Dual contrastive prediction for incomplete multi-view representation learning,' IEEE Transactions on Pattern Analysis and Machine Intelligence , vol. 45, no. 4, pp. 4447-4461, 2023.

H. Tang and Y. Liu, 'Deep safe incomplete multi-view clustering: Theorem and algorithm,' in International conference on machine learning . PMLR, 2022, pp. 21 090-21 110.

M. Yang, Y. Li, P. Hu, J. Bai, J. Lv, and X. Peng, 'Robust multi-view clustering with incomplete information,' IEEE Transactions on Pattern Analysis and Machine Intelligence , vol. 45, no. 1, pp. 1055-1069, 2023.

NeurIPS Paper Checklist

The checklist is designed to encourage best practices for responsible machine learning research, addressing issues of reproducibility, transparency, research ethics, and societal impact. Do not remove the checklist: The papers not including the checklist will be desk rejected. The checklist should follow the references and follow the (optional) supplemental material. The checklist does NOT count towards the page limit.

Please read the checklist guidelines carefully for information on how to answer these questions. For each question in the checklist:

You should answer [Yes] , [No] , or [NA] .

[NA] means either that the question is Not Applicable for that particular paper or the relevant information is Not Available.

Please provide a short (1-2 sentence) justification right after your answer (even for NA).

The checklist answers are an integral part of your paper submission. They are visible to the reviewers, area chairs, senior area chairs, and ethics reviewers. You will be asked to also include it (after eventual revisions) with the final version of your paper, and its final version will be published with the paper.

The reviewers of your paper will be asked to use the checklist as one of the factors in their evaluation. While "[Yes] " is generally preferable to "[No] ", it is perfectly acceptable to answer "[No] " provided a proper justification is given (e.g., "error bars are not reported because it would be too computationally expensive" or "we were unable to find the license for the dataset we used"). In general, answering "[No] " or "[NA] " is not grounds for rejection. While the questions are phrased in a binary way, we acknowledge that the true answer is often more nuanced, so please just use your best judgment and write a justification to elaborate. All supporting evidence can appear either in the main paper or the supplemental material, provided in appendix. If you answer [Yes] to a question, in the justification please point to the section(s) where related material for the question can be found.

IMPORTANT, please:

Delete this instruction block, but keep the section heading 'NeurIPS Paper Checklist" ,

Keep the checklist subsection headings, questions/answers and guidelines below.

Do not modify the questions and only use the provided macros for your answers .

1. Claims

Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?

Answer: [Yes]

Justification: The scope and contributions of this paper are clearly stated in the abstract and introduction.

Guidelines:

The answer NA means that the abstract and introduction do not include the claims made in the paper.

The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No or NA answer to this question will not be perceived well by the reviewers.

The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings.

It is fine to include aspirational goals as motivation as long as it is clear that these goals are not attained by the paper.

2. Limitations

Question: Does the paper discuss the limitations of the work performed by the authors?

Answer: [Yes]

Justification: The limitations are discussed in the Conclusion section.

Guidelines:

The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.

The authors are encouraged to create a separate "Limitations" section in their paper.

The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g., independence assumptions, noiseless settings, model well-specification, asymptotic approximations only holding locally). The authors should reflect on how these assumptions might be violated in practice and what the implications would be.

The authors should reflect on the scope of the claims made, e.g., if the approach was only tested on a few datasets or with a few runs. In general, empirical results often depend on implicit assumptions, which should be articulated.

The authors should reflect on the factors that influence the performance of the approach. For example, a facial recognition algorithm may perform poorly when image resolution is low or images are taken in low lighting. Or a speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon.

The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size.

If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness.

While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, a worse outcome might be that reviewers discover limitations that aren't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an important role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed to not penalize honesty concerning limitations.

3. Theory assumptions and proofs

Question: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof?

Answer: [NA]

Justification: Our work is empirical in nature and does not contain formal theoretical results or proofs.

Guidelines:

The answer NA means that the paper does not include theoretical results.

All the theorems, formulas, and proofs in the paper should be numbered and crossreferenced.

All assumptions should be clearly stated or referenced in the statement of any theorems.

The proofs can either appear in the main paper or the supplemental material, but if they appear in the supplemental material, the authors are encouraged to provide a short proof sketch to provide intuition.

Inversely, any informal proof provided in the core of the paper should be complemented by formal proofs provided in appendix or supplemental material.

Theorems and Lemmas that the proof relies upon should be properly referenced.

4. Experimental result reproducibility

Question: Does the paper fully disclose all the information needed to reproduce the main experimental results of the paper to the extent that it affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided or not)?

Answer: [Yes]

Justification: The paper provides sufficient details on the algorithm, datasets, and experimental setup to support reproducibility of the main results.

Guidelines:

The answer NA means that the paper does not include experiments.

If the paper includes experiments, a No answer to this question will not be perceived well by the reviewers: Making the paper reproducible is important, regardless of whether the code and data are provided or not.

If the contribution is a dataset and/or model, the authors should describe the steps taken to make their results reproducible or verifiable.

Depending on the contribution, reproducibility can be accomplished in various ways. For example, if the contribution is a novel architecture, describing the architecture fully might suffice, or if the contribution is a specific model and empirical evaluation, it may be necessary to either make it possible for others to replicate the model with the same dataset, or provide access to the model. In general. releasing code and data is often one good way to accomplish this, but reproducibility can also be provided via detailed instructions for how to replicate the results, access to a hosted model (e.g., in the case of a large language model), releasing of a model checkpoint, or other means that are appropriate to the research performed.

While NeurIPS does not require releasing code, the conference does require all submissions to provide some reasonable avenue for reproducibility, which may depend on the nature of the contribution. For example

(a) If the contribution is primarily a new algorithm, the paper should make it clear how to reproduce that algorithm.

(b) If the contribution is primarily a new model architecture, the paper should describe the architecture clearly and fully.

(c) If the contribution is a new model (e.g., a large language model), then there should either be a way to access this model for reproducing the results or a way to reproduce the model (e.g., with an open-source dataset or instructions for how to construct the dataset).

(d) We recognize that reproducibility may be tricky in some cases, in which case authors are welcome to describe the particular way they provide for reproducibility. In the case of closed-source models, it may be that access to the model is limited in some way (e.g., to registered users), but it should be possible for other researchers to have some path to reproducing or verifying the results.

5. Open access to data and code

Question: Does the paper provide open access to the data and code, with sufficient instructions to faithfully reproduce the main experimental results, as described in supplemental material?

Answer: [Yes]

Justification: We will upload the code package as supplementary material, and the latest GitHub link will be provided upon paper acceptance.

Guidelines:

The answer NA means that paper does not include experiments requiring code.

Please see the NeurIPS code and data submission guidelines ( https://nips.cc/ public/guides/CodeSubmissionPolicy ) for more details.

While we encourage the release of code and data, we understand that this might not be possible, so 'No' is an acceptable answer. Papers cannot be rejected simply for not including code, unless this is central to the contribution (e.g., for a new open-source benchmark).

The instructions should contain the exact command and environment needed to run to reproduce the results. See the NeurIPS code and data submission guidelines ( https: //nips.cc/public/guides/CodeSubmissionPolicy ) for more details.

The authors should provide instructions on data access and preparation, including how to access the raw data, preprocessed data, intermediate data, and generated data, etc.

The authors should provide scripts to reproduce all experimental results for the new proposed method and baselines. If only a subset of experiments are reproducible, they should state which ones are omitted from the script and why.

At submission time, to preserve anonymity, the authors should release anonymized versions (if applicable).

Providing as much information as possible in supplemental material (appended to the paper) is recommended, but including URLs to data and code is permitted.

6. Experimental setting/details

Question: Does the paper specify all the training and test details (e.g., data splits, hyperparameters, how they were chosen, type of optimizer, etc.) necessary to understand the results?

Answer: [Yes]

Justification: The paper provides the details of data preprocessing and hyperparameter settings in the Experiments section, while the optimization process is included in the appendix.**

Guidelines:

The answer NA means that the paper does not include experiments.

The experimental setting should be presented in the core of the paper to a level of detail that is necessary to appreciate the results and make sense of them.

The full details can be provided either with the code, in appendix, or as supplemental material.

7. Experiment statistical significance

Question: Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?

Answer: [No]

Justification: Most compared baseline methods do not include statistical significance in their experiments; therefore, we follow the same practice and do not report it in our work.

Guidelines:

The answer NA means that the paper does not include experiments.

The authors should answer "Yes" if the results are accompanied by error bars, confidence intervals, or statistical significance tests, at least for the experiments that support the main claims of the paper.

The factors of variability that the error bars are capturing should be clearly stated (for example, train/test split, initialization, random drawing of some parameter, or overall run with given experimental conditions).

The method for calculating the error bars should be explained (closed form formula, call to a library function, bootstrap, etc.)

The assumptions made should be given (e.g., Normally distributed errors).

It should be clear whether the error bar is the standard deviation or the standard error of the mean.

It is OK to report 1-sigma error bars, but one should state it. The authors should preferably report a 2-sigma error bar than state that they have a 96% CI, if the hypothesis of Normality of errors is not verified.

For asymmetric distributions, the authors should be careful not to show in tables or figures symmetric error bars that would yield results that are out of range (e.g. negative error rates).

If error bars are reported in tables or plots, The authors should explain in the text how they were calculated and reference the corresponding figures or tables in the text.

8. Experiments compute resources

Question: For each experiment, does the paper provide sufficient information on the computer resources (type of compute workers, memory, time of execution) needed to reproduce the experiments?

Answer: [Yes]

Justification: The computer resources is stated in the Experiments section.

Guidelines:

The answer NA means that the paper does not include experiments.

The paper should indicate the type of compute workers CPU or GPU, internal cluster, or cloud provider, including relevant memory and storage.

The paper should provide the amount of compute required for each of the individual experimental runs as well as estimate the total compute.

The paper should disclose whether the full research project required more compute than the experiments reported in the paper (e.g., preliminary or failed experiments that didn't make it into the paper).

9. Code of ethics

Question: Does the research conducted in the paper conform, in every respect, with the NeurIPS Code of Ethics https://neurips.cc/public/EthicsGuidelines ?

Answer: [Yes]

Justification: This paper conforms with the NeurIPS Code of Ethics.

Guidelines:

The answer NA means that the authors have not reviewed the NeurIPS Code of Ethics.

If the authors answer No, they should explain the special circumstances that require a deviation from the Code of Ethics.

The authors should make sure to preserve anonymity (e.g., if there is a special consideration due to laws or regulations in their jurisdiction).

10. Broader impacts

Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?

Answer: [NA]

Justification: The proposed algorithm has no direct societal impact. All datasets used in this paper are publicly available, and the algorithm is solely focused on producing clustering assignments.

Guidelines:

The answer NA means that there is no societal impact of the work performed.

If the authors answer NA or No, they should explain why their work has no societal impact or why the paper does not address societal impact.

Examples of negative societal impacts include potential malicious or unintended uses (e.g., disinformation, generating fake profiles, surveillance), fairness considerations (e.g., deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations.

The conference expects that many papers will be foundational research and not tied to particular applications, let alone deployments. However, if there is a direct path to any negative applications, the authors should point it out. For example, it is legitimate to point out that an improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster.

The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology is being used as intended but gives incorrect results, and harms following from (intentional or unintentional) misuse of the technology.

If there are negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms to monitor how a system learns from feedback over time, improving the efficiency and accessibility of ML).

11. Safeguards

Question: Does the paper describe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?

Answer: [NA]

Justification: All datasets used in this paper are publicly available, so no specific safeguards are required.

Guidelines:

The answer NA means that the paper poses no such risks.

Released models that have a high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere to usage guidelines or restrictions to access the model or implementing safety filters.

Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images.

We recognize that providing effective safeguards is challenging, and many papers do not require this, but we encourage authors to take this into account and make a best faith effort.

12. Licenses for existing assets

Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?

Answer: [Yes]

Justification: Original papers and datasets are properly cited.

Guidelines:

The answer NA means that the paper does not use existing assets.

The authors should cite the original paper that produced the code package or dataset.

The authors should state which version of the asset is used and, if possible, include a URL.

The name of the license (e.g., CC-BY 4.0) should be included for each asset.

For scraped data from a particular source (e.g., website), the copyright and terms of service of that source should be provided.

If assets are released, the license, copyright information, and terms of use in the package should be provided. For popular datasets, paperswithcode.com/datasets has curated licenses for some datasets. Their licensing guide can help determine the license of a dataset.

For existing datasets that are re-packaged, both the original license and the license of the derived asset (if it has changed) should be provided.

If this information is not available online, the authors are encouraged to reach out to the asset's creators.

13. New assets

Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?

Answer: [NA]

Justification: No new assets are introduced in the paper.

Guidelines:

The answer NA means that the paper does not release new assets.

Researchers should communicate the details of the dataset/code/model as part of their submissions via structured templates. This includes details about training, license, limitations, etc.

The paper should discuss whether and how consent was obtained from people whose asset is used.

At submission time, remember to anonymize your assets (if applicable). You can either create an anonymized URL or include an anonymized zip file.

14. Crowdsourcing and research with human subjects

Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well as details about compensation (if any)?

Answer: [NA]

Justification: No crowdsourcing or human subjects were involved in this work.

Guidelines:

The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.

Including this information in the supplemental material is fine, but if the main contribution of the paper involves human subjects, then as much detail as possible should be included in the main paper.

According to the NeurIPS Code of Ethics, workers involved in data collection, curation, or other labor should be paid at least the minimum wage in the country of the data collector.

15. Institutional review board (IRB) approvals or equivalent for research with human subjects

Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or an equivalent approval/review based on the requirements of your country or institution) were obtained?

Answer: [NA]

Justification: The paper does not involve any research with human subjects or crowdsourcing, and therefore does not require IRB or equivalent ethical approval.

Guidelines:

The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.

Depending on the country in which research is conducted, IRB approval (or equivalent) may be required for any human subjects research. If you obtained IRB approval, you should clearly state this in the paper.

We recognize that the procedures for this may vary significantly between institutions and locations, and we expect authors to adhere to the NeurIPS Code of Ethics and the guidelines for their institution.

For initial submissions, do not include any information that would break anonymity (if applicable), such as the institution conducting the review.

16. Declaration of LLM usage

Question: Does the paper describe the usage of LLMs if it is an important, original, or non-standard component of the core methods in this research? Note that if the LLM is used only for writing, editing, or formatting purposes and does not impact the core methodology, scientific rigorousness, or originality of the research, declaration is not required.

Answer: [NA]

Justification: The core methodology does not involve the use of large language models (LLMs).

Guidelines:

The answer NA means that the core method development in this research does not involve LLMs as any important, original, or non-standard components.

Please refer to our LLM policy ( https://neurips.cc/Conferences/2025/LLM ) for what should or should not be described.

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_21 dataset at different training epochs, Figures (e)-(h) present the clustering results of the Hdigit dataset at different training epochs, while Figures (i)-(l) 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) 50 epoch

(b) 100 epoch

(c) 200 epoch

(d) 500 epoch

(e) 50 epoch

(f) 100 epoch

(g) 150 epoch

(h) 200 epoch

(i) 50 epoch

(j) 100 epoch

(k) 150 epoch

(l) 450 epoch

20.0

100

D.0

Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis 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.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths: \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.\n\nQUESTIONS:\n1. 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.\n\nLIMITATIONS:\nYes.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-06-23"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe 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.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths \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.\n\nQUESTIONS:\n1，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?\n\nLIMITATIONS:\nSee the weakness.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 5, "CLARITY": 4, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-24"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis 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.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\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.\n\nQUESTIONS:\nQuestion 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?\n\nLIMITATIONS:\nNA", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-30"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis 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.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths：\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%).\n\nQUESTIONS:\n1.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 ?\n\nLIMITATIONS:\nWhile 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.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-06-30"}