Non-convex tensorial multi-view clustering by integrating [formula omitted]-based sliced-Laplacian regularization and [formula omitted]-sparsity

Abstract

Consider the recent upswing in interest around multi-view clustering procedures. Such methods aim to boost clustering efficiency by leveraging information from numerous perspectives. Much research has been devoted to tensorial representation to exploit high-order correlations underlying disparate views while preserving the local geometric structure inside each view. Our research introduces a novel multi-view clustering approach. This approach creates a 3rd-order tensor, assimilating features from all perspectives. We use the t-product in the tensor space to generate the self-representation tensor from the tensorial data. We incorporate the ℓ1-based sliced-Laplacian regularization to increase our model’s resilience and introduce a fresh column-wise sparse norm: the ℓ2,p-norm with 0<p<1. This norm displays attributes of invariance, continuity, and differentiability. We present a closed-form answer to the ℓ2,p-regularized shrinkage problem, broadening its relevance to other generalized problems. Simultaneously, we propose a tensorial arctan-function as an improved surrogate for the tensor rank. This function has proven more proficient at assessing consistency across multiple viewpoints. By integrating these two components, we formulate an effective algorithm that refines our suggested model, ensuring that the constructed sequence gravitates toward the stationary KKT point. Our team conducts extensive experiments on various datasets to evaluate our model’s effectiveness, spanning diverse situations and scales. Results from these experiments emphasize that our approach establishes a novel performance standard.