Multiview Clustering Integrating Biorthogonal Nonnegative Tensor Factorization and Anchor Graph Learning.

Abstract

Clustering aims to uncover heterogeneous features within data samples and partition them into meaningful groups. This article first establishes a theoretical connection between biorthogonal nonnegative matrix factorization (Bi-ONMF) and biorthogonal nonnegative tensor factorization (Bi-ONTF) under the t-product framework. Building on this foundation, we propose a novel Bi-ONTF model integrated with anchor graph learning (BNTF-AGL) for multiview clustering (MVC). The model employs sparse embedding learning to select anchor points, thereby eliminating redundant connections across multiview anchor graphs. To effectively capture complementary information among views, we introduce the tensor Schatten $p$ -norm as an approximation of the tensor tubal rank, which promotes consistency among cluster assignments across views. An adaptive augmented Lagrangian method (ALM) method is developed to optimize the proposed model, and we establish that every accumulation point of the resulting iterative sequence is a stationary Karush-Kuhn-Tucker (KKT) point under stated assumptions. Extensive experiments on nine real-world datasets demonstrate that the proposed method achieves competitive or superior clustering performance.