Multi-view Clustering via Unified Multi-kernel Learning and Matrix Factorization

TL;DR

The paper addresses multi-view clustering by bridging matrix-factorization-based MVC with multi-kernel learning, proposing MVC-UMKLMF. It unifies the approach by mapping each view through kernels, removing nonnegativity constraints, and imposing orthogonality on the consensus embedding $\mathbf{H}$ rather than per-view factors, thereby reducing computational burden without sacrificing clustering quality. The method optimizes $\{\mathbf{G}_v\}$, $\mathbf{H}$, and $\boldsymbol{\omega}$ in a three-step alternating scheme, with convergence guarantees and favorable time complexity $O(n^2)$ per iteration. Empirical results on ten real-world datasets show competitive to superior performance across ACC, NMI, Purity, and ARI, with notably strong gains in NMI and robust convergence, supported by statistical tests and ablation studies.

Abstract

Multi-view clustering has become increasingly important due to the multi-source character of real-world data. Among existing multi-view clustering methods, multi-kernel clustering and matrix factorization-based multi-view clustering have gained widespread attention as mainstream approaches. However, multi-kernel clustering tends to learn an optimal kernel and then perform eigenvalue decomposition on it, which leads to high computational complexity. Matrix factorization-based multi-view clustering methods impose orthogonal constraints on individual views. This overly emphasizes the accuracy of clustering structures within single views and restricts the learning of individual views. Based on this analysis, we propose a multi-view clustering method that integrates multi-kernel learning with matrix factorization. This approach combines the advantages of both multi-kernel learning and matrix factorization. It removes the orthogonal constraints on individual views and imposes orthogonal constraints on the consensus matrix, resulting in an accurate final clustering structure. Ultimately, the method is unified into a simple form of multi-kernel clustering, but avoids learning an optimal kernel, thus reducing the time complexity. Furthermore, we propose an efficient three-step optimization algorithm to achieve a locally optimal solution. Experiments on widely-used real-world datasets demonstrate the effectiveness of our proposed method.

Figures (7)

• Figure 1: Comparison between existing kernel-based methods and the proposed method. Existing methods typically learn an optimal kernel from the kernel matrices of multiple views, followed by direct eigenvector decomposition to obtain $\mathbf{H}$. However, the introduction of the optimal kernel results in high computational complexity. In contrast, the proposed method directly performs matrix factorization on the kernel matrix of each view under constraints such as sparsity, thereby learning a consensus coefficient matrix $\mathbf{H}$.
• Figure 2: Comparison of nine clustering algorithms using Nemenyi’s test. (a) Statistical Results on the ACC Metric. (b) Statistical Results on the NMI Metric. (c) Statistical Results on the Purity Metric. (d) Statistical Results on the ARI Metric.
• Figure 3: Convergence of the proposed method on six datasets. (a) Convergence on BBC. (b) Convergence on BBCsports. (c) Convergence on Caltech101-7. (d) Convergence on Cornell. (e) Convergence on ProteinFold.
• Figure 4: Clustering Performance over Iteration on Two Datasets. (a) BBCsports. (b) ProteinFold.
• Figure 5: Visualization of different views in MSRA. (a) Visualization of $\mathbf{H}\mathbf{H}^T$. (b) Visualization of $\mathbf{G}_1\mathbf{G}_1^T$. (c) Visualization of $\mathbf{G}_2\mathbf{G}_2^T$. (d) Visualization of $\mathbf{G}_3\mathbf{G}_3^T$. (e) Visualization of $\mathbf{G}_4\mathbf{G}_4^T$. (f) Visualization of $\mathbf{G}_5\mathbf{G}_5^T$.