Robust Kernelized Multi-View Self-Representations for Clustering by Tensor Multi-Rank Minimization

TL;DR

This paper introduces a kernelized tensor multi-view clustering method that effectively handles non-linear subspaces, providing an optimal solution with state-of-the-art results on real-world datasets.

Contribution

It proposes a novel kernelization approach for tensor multi-view clustering and develops an efficient algorithm with guaranteed optimality.

Findings

Achieves state-of-the-art clustering performance on real-world datasets.

Effectively handles non-linear subspace clustering problems.

Provides a closed-form solution with guaranteed optimality.

Abstract

Most recently, tensor-SVD is implemented on multi-view self-representation clustering and has achieved the promising results in many real-world applications such as face clustering, scene clustering and generic object clustering. However, tensor-SVD based multi-view self-representation clustering is proposed originally to solve the clustering problem in the multiple linear subspaces, leading to unsatisfactory results when dealing with the case of non-linear subspaces. To handle data clustering from the non-linear subspaces, a kernelization method is designed by mapping the data from the original input space to a new feature space in which the transformed data can be clustered by a multiple linear clustering method. In this paper, we make an optimization model for the kernelized multi-view self-representation clustering problem. We also develop a new efficient algorithm based on the alternation direction method and infer a closed-form solution. Since all the subproblems can be solved exactly, the proposed optimization algorithm is guaranteed to obtain the optimal solution. In particular, the original tensor-based multi-view self-representation clustering problem is a special case of our approach and can be solved by our algorithm. Experimental results on several popular real-world clustering datasets demonstrate that our approach achieves the state-of-the-art performance.