Multi-view Low-rank Sparse Subspace Clustering

TL;DR

This paper introduces a novel multi-view subspace clustering method that learns a shared affinity matrix with low-rank and sparsity constraints, improving clustering performance on multiple datasets.

Contribution

It proposes a joint affinity matrix learning approach with low-rank and sparsity constraints, extending to nonlinear subspaces via kernel methods, outperforming existing algorithms.

Findings

Outperforms state-of-the-art methods on synthetic data

Achieves better clustering accuracy on real-world datasets

Effectively handles nonlinear subspace clustering

Abstract

Most existing approaches address multi-view subspace clustering problem by constructing the affinity matrix on each view separately and afterwards propose how to extend spectral clustering algorithm to handle multi-view data. This paper presents an approach to multi-view subspace clustering that learns a joint subspace representation by constructing affinity matrix shared among all views. Relying on the importance of both low-rank and sparsity constraints in the construction of the affinity matrix, we introduce the objective that balances between the agreement across different views, while at the same time encourages sparsity and low-rankness of the solution. Related low-rank and sparsity constrained optimization problem is for each view solved using the alternating direction method of multipliers. Furthermore, we extend our approach to cluster data drawn from nonlinear subspaces by solving the corresponding problem in a reproducing kernel Hilbert space. The proposed algorithm outperforms state-of-the-art multi-view subspace clustering algorithms on one synthetic and four real-world datasets.