Tensorized Multi-View Subspace Clustering via Tensor Nuclear Norm and Block Diagonal Representation

Gan-Yi Tang, Gui-Fu Lu (), Yong Wang and Li-Li Fan
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Gan-Yi Tang: School of Computer Science and Information, Anhui Polytechnic University, Wuhu 241000, China
Gui-Fu Lu: School of Computer Science and Information, Anhui Polytechnic University, Wuhu 241000, China
Yong Wang: School of Computer Science and Information, Anhui Polytechnic University, Wuhu 241000, China
Li-Li Fan: School of Computer Science and Information, Anhui Polytechnic University, Wuhu 241000, China

Mathematics, 2025, vol. 13, issue 17, 1-18

Abstract: Recently, a growing number of researchers have focused on multi-view subspace clustering (MSC) due to its potential for integrating heterogeneous data. However, current MSC methods remain challenged by limited robustness and insufficient exploitation of cross-view high-order latent information for clustering advancement. To address these challenges, we develop a novel MSC framework termed TMSC-TNNBDR, a tensorized MSC framework that leverages t-SVD based tensor nuclear norm (TNN) regularization and block diagonal representation (BDR) learning to unify view consistency and structural sparsity. Specifically, each subspace representation matrix is constrained by a block diagonal regularizer to enforce cluster structure, while all matrices are aggregated into a tensor to capture high-order interactions. To efficiently optimize the model, we developed an optimization algorithm based on the inexact augmented Lagrange multiplier (ALM). The TMSC-TNNBDR exhibits both optimized block-diagonal structure and low-rank properties, thereby enabling enhanced mining of latent higher-order inter-view correlations while demonstrating greater resilience to noise. To investigate the capability of TMSC-TNNBDR, we conducted several experiments on certain datasets. Benchmarking on circumscribed datasets demonstrates our method’s superior clustering performance over comparative algorithms while maintaining competitive computational overhead.

Keywords: multi-view learning; tensor nuclear norm; subspace clustering; block diagonal matrix (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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