Dual Representation Learning for One-Step Clustering of Multi-View Data

In real-world applications, multi-view data is widely available. Multi-view data refers to data collected from multiple sources or through multiple representations, such as different language versions of the same news story or disease data obtained through different medical tests. Multi-view learning is an effective method for mining multi-view data, and multi-view clustering, as an important part of multi-view learning, has been receiving increasing attention in recent years. However, designing an effective multi-view data mining method and making it more pertinent remains a challenging task.

Traditional multi-view clustering methods are mainly divided into two categories: original views-based methods and common latent view-based methods. The former typically extends traditional clustering algorithms (such as K-means, fuzzy clustering, or spectral clustering) to handle multi-view data, while the latter explores the common latent representation between views through representation learning techniques (such as self-representation, matrix factorization, and canonical correlation analysis). However, existing methods face two key challenges: First, multi-view data contains both consistent knowledge between views and unique knowledge of each view, but existing methods often fail to fully explore both types of knowledge simultaneously. Second, most common latent view-based methods separate representation learning from clustering partition, which limits the interaction between representation learning and clustering tasks, thereby affecting clustering performance.

To address these issues, this paper proposes a new one-step multi-view clustering method based on dual representation learning, aiming to simultaneously explore the consistent knowledge between views and the unique knowledge of each view, and unify representation learning with clustering partition into a single framework to achieve more efficient clustering performance.

Source of the Paper

This paper is co-authored by Wei Zhang, Zhaohong Deng, Kup-Sze Choi, Jun Wang, and Shitong Wang. The authors are affiliated with Nantong University, Jiangnan University, The Hong Kong Polytechnic University, and Shanghai University. The paper was accepted on February 28, 2025, and published in the journal Artificial Intelligence Review, with the DOI 10.1007/s10462-025-11183-0.

Research Content and Process

1. Dual Representation Learning Mechanism

This paper proposes a dual representation learning mechanism based on matrix factorization to simultaneously explore the consistent knowledge and unique knowledge in multi-view data. Specifically, for a given multi-view dataset, assuming that consistent knowledge and unique knowledge are linearly separable, this paper learns the common representation and specific representation by optimizing the following objective function:

[ \min_{h, w_k, s_k, pk} \sum{k=1}^{K} |X_k - h^T w_k - s_k^T p_k|_F^2 + \gamma (|h^T|_F^2 + |s_k^T|_F^2) ]

Here, (h) is the common latent representation between views, (s_k) is the specific representation of the (k)-th view, (w_k) and (p_k) are mapping matrices, and (\gamma) is a regularization parameter. Through this mechanism, the paper is able to simultaneously learn the consistent representation between views and the specific representation of each view.

2. One-Step Multi-View Clustering Framework

To enhance the relevance between representation learning and clustering tasks, this paper proposes a novel one-step multi-view clustering framework that unifies dual representation learning and clustering partition into a single optimization framework. Specifically, a maximum entropy mechanism and an orthogonal constraint are introduced to further optimize clustering performance. The final objective function is as follows:

[ \min_{h, w_k, s_k, p_k, u, v_k, \alphak} \sum{k=1}^{K} |X_k - h^T w_k - s_k^T p_k|_F^2 + \gamma (|h^T|_F^2 + |s_k^T|F^2) + \sum{k=1}^{K} \alpha_k |s_k - v_k u|F^2 + \alpha{K+1} |h - v_{K+1} u|F^2 + \beta \sum{k=1}^{K+1} |v_k^T v_k - I|F^2 - \delta \sum{k=1}^{K+1} \alpha_k \ln \alpha_k ]

Here, (u) is the cluster indicator matrix, (v_k) is the cluster center matrix, (\alpha_k) is the view weight, and (\beta) and (\delta) are balancing parameters. Through this framework, the paper achieves mutual enhancement between representation learning and clustering partition, thereby improving clustering performance.

3. Optimization Process

This paper adopts an alternating optimization approach to solve the above objective function. Specifically, the optimization process consists of seven steps, updating (h), (s_k), (w_k), (p_k), (\alpha_k), (v_k), and (u) iteratively. By updating these variables iteratively, the paper gradually optimizes the clustering results.

4. Experimental Results and Analysis

Extensive experiments were conducted on seven real-world multi-view datasets to validate the effectiveness of the proposed method. The results show that the proposed method achieves the best clustering performance on most datasets compared to existing multi-view clustering methods. Specifically, the proposed method outperforms other comparison methods in terms of normalized mutual information (NMI), accuracy (ACC), purity, and adjusted Rand index (ARI).

Additionally, ablation studies were conducted to verify the contributions of the dual representation learning mechanism, the one-step learning mechanism, and the regularization terms to clustering performance. The results show that simultaneously exploring consistent knowledge and unique knowledge, unifying representation learning and clustering partition into a single framework, and introducing regularization terms can significantly improve clustering performance.

Conclusion and Significance

This paper proposes a one-step multi-view clustering method based on dual representation learning, aiming to simultaneously explore the consistent knowledge and unique knowledge in multi-view data and unify representation learning with clustering partition into a single framework. By introducing a maximum entropy mechanism and an orthogonal constraint, the paper further optimizes clustering performance. Experimental results demonstrate that the proposed method achieves excellent clustering performance on multiple real-world datasets, proving its effectiveness in practical applications.

The main contributions of this paper include: 1. Proposing a new dual representation learning mechanism that can simultaneously explore the consistent knowledge between views and the unique knowledge of each view. 2. Designing a novel one-step multi-view clustering framework that unifies dual representation learning and clustering partition into an adaptive framework. 3. Conducting extensive experiments on multiple real-world datasets to validate the efficiency and effectiveness of the proposed method.

This research provides new ideas and methods for the field of multi-view clustering, with significant scientific value and application prospects. Future research can further explore how to apply the proposed method to more complex multi-view data scenarios, such as high-dimensional data or nonlinear data.

Research Highlights

1. Dual Representation Learning Mechanism: This paper proposes, for the first time, a dual representation learning mechanism based on matrix factorization, which can simultaneously explore the consistent knowledge and unique knowledge in multi-view data.
2. One-Step Clustering Framework: A novel one-step multi-view clustering framework is designed, unifying representation learning and clustering partition into a single optimization framework, enabling mutual enhancement between the two processes.
3. Maximum Entropy and Orthogonal Constraint: The introduction of a maximum entropy mechanism and an orthogonal constraint further optimizes clustering performance and enhances the robustness of the model.
4. Extensive Experimental Validation: Extensive experiments were conducted on multiple real-world datasets, validating the efficiency and effectiveness of the proposed method, providing new research directions for the field of multi-view clustering.

Through this research, the field of multi-view clustering has been advanced both theoretically and practically, offering important references for future related studies.