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

2025-10-22

AI Summary

Existing tensor low-rank representation (TLRR) methods for image clustering suffer from poor robustness to noise and difficulty in jointly modeling global and local correlations. To address these issues, this paper proposes a data-adaptive bilateral TLRR framework. The method enhances global structure capture via learnable unitary transformations and simultaneously models local sample-wise and feature-wise correlations through a bilateral structural modeling mechanism. We further introduce a data-adaptive tensor nuclear norm, which jointly employs a non-convex ℓ₁/₂ norm and Frobenius norm regularization to significantly improve robustness against complex noise. A convergent non-convex optimization algorithm is developed based on the alternating direction method of multipliers (ADMM). Extensive experiments on multiple real-world image datasets demonstrate that our approach consistently outperforms state-of-the-art methods. The source code is publicly available.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Computer Vision: Representation Learning for Vision
• Natural Language Processing: Language Grounding & Multi-modal NLP

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

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.

Problem

• Develops data-adaptive tensor low-rank representation for clustering
• Exploits bilateral structure to capture local and global correlations
• Integrates robust regularization to handle complex real-world noise

Innovation

• Learns data-adaptive unitary transforms for tensor nuclear norm
• Exploits bilateral structure to capture local correlations
• Integrates mixed norms for robust noise handling