Multi-View Spectral Clustering via Structured Low-Rank Matrix Factorization (1709.01212v3)

Abstract: Multi-view data clustering attracts more attention than their single view counterparts due to the fact that leveraging multiple independent and complementary information from multi-view feature spaces outperforms the single one. Multi-view Spectral Clustering aims at yielding the data partition agreement over their local manifold structures by seeking eigenvalue-eigenvector decompositions. However, as we observed, such classical paradigm still suffers from (1) overlooking the flexible local manifold structure, caused by (2) enforcing the low-rank data correlation agreement among all views; worse still, (3) LRR is not intuitively flexible to capture the latent data clustering structures. In this paper, we present the structured LRR by factorizing into the latent low-dimensional data-cluster representations, which characterize the data clustering structure for each view. Upon such representation, (b) the laplacian regularizer is imposed to be capable of preserving the flexible local manifold structure for each view. (c) We present an iterative multi-view agreement strategy by minimizing the divergence objective among all factorized latent data-cluster representations during each iteration of optimization process, where such latent representation from each view serves to regulate those from other views, such intuitive process iteratively coordinates all views to be agreeable. (d) We remark that such data-cluster representation can flexibly encode the data clustering structure from any view with adaptive input cluster number. To this end, (e) a novel non-convex objective function is proposed via the efficient alternating minimization strategy. The complexity analysis are also presented. The extensive experiments conducted against the real-world multi-view datasets demonstrate the superiority over state-of-the-arts.

• The paper introduces a structured low-rank matrix factorization that captures latent cluster representations for improved multi-view spectral clustering.
• It leverages Laplacian regularization to preserve local manifold structures in each view for enhanced clustering performance.
• An iterative agreement strategy refines inter-view consensus, outperforming traditional methods in clustering accuracy and normalized mutual information.

Multi-View Spectral Clustering via Structured Low-Rank Matrix Factorization

Yang Wang and Lin Wu's paper proposes a novel approach to multi-view spectral clustering by introducing a structured low-rank matrix factorization methodology. The focus of this research is on effectively leveraging the complementary information from multiple data views to enhance clustering performance, addressing limitations observed in traditional methods like Low-Rank Representation (LRR).

Overview and Contributions

The paper critiques existing multi-view spectral clustering approaches for inadequacies in capturing flexible local manifold structures and enforcing rigid agreements across different views. Traditional methods often impose a singular low-rank data correlation agreement, which can lead to suboptimal inter-view consensus and inadequate representation of latent clustering structures.

To counter these deficiencies, the authors propose a structured LRR technique that factorizes data into latent low-dimensional cluster representations. This approach offers several key benefits:

1. Latent Representation Factorization: The factorization into a symmetric data-cluster indicator matrix enables capturing the ideal clusters beyond basic correlation matrices.
2. Laplacian Regularization: It enhances the model's capability to retain the local manifold structure for each view, crucial for effective spectral clustering.
3. Iterative Agreement Strategy: The method iteratively minimizes divergence among latent representations, refining inter-view consensus throughout the optimization process.

Theoretical Framework

The framework relies on reformulating the classical LRR to focus on structured matrix factorization. This is achieved by representing the data-cluster relationship within each view with the assumption that these latent structures can implicitly guide the clustering process across views. The work further employs a non-convex objective function, optimized via an efficient alternating minimization approach, which integrates the regularized structure and agrees with the shared data-cluster representations across views.

Experimental Findings

Extensive experiments performed on real-world datasets demonstrated the superiority of the proposed method over existing approaches, including state-of-the-art methods such as LRRGL. The findings reveal improved clustering accuracy (ACC) and normalized mutual information (NMI), supporting the efficacy of leveraging structured low-rank matrix factorization to better harness multi-view data complementarities.

Discussion on Implications

The implications of this research are twofold. Practically, the proposed model could enhance data clustering applications in various domains like image analysis, bioinformatics, and social network analytics, where multi-view data is prevalent. Theoretically, it underscores the importance of combining structural regularization with latent factorization to encapsulate both shared and view-specific data structures more holistically. This nuanced approach could stimulate further studies into flexible, adaptive models for multi-modal data harmonization in clustering tasks.

Future Directions

Potential future developments might focus on enhancing the out-of-sample extension of this framework, employing adaptive weight-learning strategies for different views, and reducing parameter sensitivity. The integration of dynamic graph learning into the clustering paradigm, which has shown promising results in single-view cases, could also enrich multi-view clustering efficacy.

In summary, this work lays a robust foundation for advancing multi-view clustering methodologies, promising more aligned and flexible clustering results in applications dependent on multi-modal data analysis.