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A low-rank non-convex norm method for multiview graph clustering

Alaeddine Zahir, Khalide Jbilou, Ahmed Ratnani

TL;DR

This work tackles multi-view clustering by learning a consensus graph from multiple views using a low-rank, non-convex tensor norm (t-Gamma) within a spectral-embedding framework. The method, CGMVC-NC, alternates between optimizing view-specific spectral factors on the Stiefel manifold, updating a sparse tensor representation, and refining a fused graph via Ky Fan-based principles, enabling a robust capture of high-order view correlations. Empirical results on three real-world datasets show CGMVC-NC achieves higher clustering accuracy and competitive other metrics compared to strong baselines, highlighting the practical value of non-convex tensor norms for fusion. The approach provides a scalable, flexible tool for integrated analysis of multi-view data with potential extensions to broader data types and tasks in areas like computer vision, neuroscience, and social networks.

Abstract

This study introduces a novel technique for multi-view clustering known as the "Consensus Graph-Based Multi-View Clustering Method Using Low-Rank Non-Convex Norm" (CGMVC-NC). Multi-view clustering is a challenging task in machine learning as it requires the integration of information from multiple data sources or views to cluster data points accurately. The suggested approach makes use of the structural characteristics of multi-view data tensors, introducing a non-convex tensor norm to identify correlations between these views. In contrast to conventional methods, this approach demonstrates superior clustering accuracy across several benchmark datasets. Despite the non-convex nature of the tensor norm used, the proposed method remains amenable to efficient optimization using existing algorithms. The approach provides a valuable tool for multi-view data analysis and has the potential to enhance our understanding of complex systems in various fields. Further research can explore the application of this method to other types of data and extend it to other machine-learning tasks.

A low-rank non-convex norm method for multiview graph clustering

TL;DR

This work tackles multi-view clustering by learning a consensus graph from multiple views using a low-rank, non-convex tensor norm (t-Gamma) within a spectral-embedding framework. The method, CGMVC-NC, alternates between optimizing view-specific spectral factors on the Stiefel manifold, updating a sparse tensor representation, and refining a fused graph via Ky Fan-based principles, enabling a robust capture of high-order view correlations. Empirical results on three real-world datasets show CGMVC-NC achieves higher clustering accuracy and competitive other metrics compared to strong baselines, highlighting the practical value of non-convex tensor norms for fusion. The approach provides a scalable, flexible tool for integrated analysis of multi-view data with potential extensions to broader data types and tasks in areas like computer vision, neuroscience, and social networks.

Abstract

This study introduces a novel technique for multi-view clustering known as the "Consensus Graph-Based Multi-View Clustering Method Using Low-Rank Non-Convex Norm" (CGMVC-NC). Multi-view clustering is a challenging task in machine learning as it requires the integration of information from multiple data sources or views to cluster data points accurately. The suggested approach makes use of the structural characteristics of multi-view data tensors, introducing a non-convex tensor norm to identify correlations between these views. In contrast to conventional methods, this approach demonstrates superior clustering accuracy across several benchmark datasets. Despite the non-convex nature of the tensor norm used, the proposed method remains amenable to efficient optimization using existing algorithms. The approach provides a valuable tool for multi-view data analysis and has the potential to enhance our understanding of complex systems in various fields. Further research can explore the application of this method to other types of data and extend it to other machine-learning tasks.
Paper Structure (17 sections, 1 theorem, 26 equations, 2 figures, 4 tables, 2 algorithms)

This paper contains 17 sections, 1 theorem, 26 equations, 2 figures, 4 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Related work
  4. Proposed method
  5. Data
  6. Graph construction
  7. Problem formulation
  8. Solution
  9. Algorithm
  10. Experiments
  11. Data sets
  12. Compared methods
  13. Evaluation metrics
  14. Computation complexity
  15. Parameter setting
  16. ...and 2 more sections

Key Result

Theorem 4.1

mohar1991laplacianchung1997spectral The number of connected components in the non-negative similarity matrix of a graph is the same as the multiplicity of the eigenvalue 0 of its corresponding Laplacian matrix.

Figures (2)

  • Figure 4.1: The proposed method framework
  • Figure 5.1: Time cost of different methods per second.

Theorems & Definitions (1)

  • Theorem 4.1