Data-Adaptive Transformed Bilateral Tensor Low-Rank Representation for Clustering

TL;DR

This paper introduces TBTLRR, a novel tensor low-rank representation model that adaptively learns transforms and exploits bilateral structure, improving image clustering robustness and accuracy in noisy scenarios.

Contribution

The paper proposes a data-adaptive tensor nuclear norm and an efficient optimization algorithm for tensor low-rank representation, enhancing robustness and effectiveness in image clustering.

Findings

Outperforms state-of-the-art clustering methods

Effectively handles complex noise in real-world data

Demonstrates superior global and local correlation capture

Abstract

Tensor low-rank representation (TLRR) has demonstrated significant success in image clustering. However, most existing methods rely on fixed transformations and suffer from poor robustness to noise. In this paper, we propose a novel transformed bilateral tensor low-rank representation model called TBTLRR, which introduces a data-adaptive tensor nuclear norm by learning arbitrary unitary transforms, allowing for more effective capture of global correlations. In addition, by leveraging the bilateral structure of latent tensor data, TBTLRR is able to exploit local correlations between image samples and features. Furthermore, TBTLRR integrates the $\ell_{1/2}$-norm and Frobenius norm regularization terms for better dealing with complex noise in real-world scenarios. To solve the proposed nonconvex model, we develop an efficient optimization algorithm inspired by the alternating direction method of multipliers (ADMM) and provide theoretical convergence. Extensive experiments validate its superiority over the state-of-the-art methods in clustering. The code will be available at https://github.com/xianchaoxiu/TBTLRR.