Semi-Supervised Subspace Clustering via Tensor Low-Rank Representation

TL;DR

This paper introduces a semi-supervised subspace clustering method that leverages tensor low-rank representation to enhance affinity matrix construction and improve clustering accuracy, demonstrated through extensive experiments.

Contribution

The novel approach combines global low-rank tensor constraints with local geometry to simultaneously augment supervision and refine affinity matrices for better clustering.

Findings

Outperforms state-of-the-art methods on benchmark datasets

Effectively integrates limited supervision into clustering process

Demonstrates robustness across diverse data types

Abstract

In this letter, we propose a novel semi-supervised subspace clustering method, which is able to simultaneously augment the initial supervisory information and construct a discriminative affinity matrix. By representing the limited amount of supervisory information as a pairwise constraint matrix, we observe that the ideal affinity matrix for clustering shares the same low-rank structure as the ideal pairwise constraint matrix. Thus, we stack the two matrices into a 3-D tensor, where a global low-rank constraint is imposed to promote the affinity matrix construction and augment the initial pairwise constraints synchronously. Besides, we use the local geometry structure of input samples to complement the global low-rank prior to achieve better affinity matrix learning. The proposed model is formulated as a Laplacian graph regularized convex low-rank tensor representation problem, which is further solved with an alternative iterative algorithm. In addition, we propose to refine the affinity matrix with the augmented pairwise constraints. Comprehensive experimental results on eight commonly-used benchmark datasets demonstrate the superiority of our method over state-of-the-art methods. The code is publicly available at https://github.com/GuanxingLu/Subspace-Clustering.