Multi-view Spectral Clustering on the Grassmannian Manifold With Hypergraph Representation

2025-03-08

AI Summary

Traditional multi-view spectral clustering suffers from oversimplified pairwise graph modeling, inefficient spectral decomposition in Euclidean space, and inadequate consistency modeling across views. To address these issues, this paper proposes a sparse representation learning-based multi-view hypergraph spectral clustering method. First, high-order relational structures are preserved by constructing hypergraphs via sparse coding. Second, inter-view orthogonality constraints are explicitly modeled on the Grassmann manifold to avoid local optima and approximation errors. Third, an alternating Riemannian gradient descent algorithm is designed to enable efficient, unconstrained optimization intrinsically on the manifold. Extensive experiments on four real-world multi-view benchmark datasets demonstrate that the proposed method significantly outperforms seven state-of-the-art approaches in both clustering accuracy and robustness. These results validate the effectiveness of low-dimensional manifold representation and high-order structural modeling for multi-view clustering.

Technology Category

• Machine Learning: Multi-instance/Multi-view Learning
• Computer Vision: Representation Learning for Vision
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Web Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

Graph-based multi-view spectral clustering methods have achieved notable progress recently, yet they often fall short in either oversimplifying pairwise relationships or struggling with inefficient spectral decompositions in high-dimensional Euclidean spaces. In this paper, we introduce a novel approach that begins to generate hypergraphs by leveraging sparse representation learning from data points. Based on the generated hypergraph, we propose an optimization function with orthogonality constraints for multi-view hypergraph spectral clustering, which incorporates spectral clustering for each view and ensures consistency across different views. In Euclidean space, solving the orthogonality-constrained optimization problem may yield local maxima and approximation errors. Innovately, we transform this problem into an unconstrained form on the Grassmannian manifold. Finally, we devise an alternating iterative Riemannian optimization algorithm to solve the problem. To validate the effectiveness of the proposed algorithm, we test it on four real-world multi-view datasets and compare its performance with seven state-of-the-art multi-view clustering algorithms. The experimental results demonstrate that our method outperforms the baselines in terms of clustering performance due to its superior low-dimensional and resilient feature representation.

Problem

• Improves multi-view spectral clustering by addressing oversimplified pairwise relationships.
• Transforms orthogonality-constrained optimization into unconstrained form on Grassmannian manifold.
• Validates algorithm effectiveness on real-world datasets, outperforming existing methods.

Innovation

• Hypergraph generation via sparse representation learning
• Orthogonality-constrained optimization on Grassmannian manifold
• Alternating iterative Riemannian optimization algorithm