Latent temporal smoothness-induced Schatten-p norm factorization for sequential subspace clustering

Abstract

This paper presents an innovative latent temporal smoothness-induced Schatten-$p$ norm factorization (SpFLTS) method aimed at addressing challenges in sequential subspace clustering tasks. Globally, SpFLTS employs a low-rank subspace clustering framework based on Schatten-2/3 norm factorization to enhance the comprehensive capture of the original data features. Locally, a total variation smoothing term is induced to the temporal gradients of latent subspace matrices obtained from sub-orthogonal projections, thereby preserving smoothness in the sequential latent space. To efficiently solve the closed-form optimization problem, a fast Fourier transform is combined with the non-convex alternating direction method of multipliers to optimize latent subspace matrix, which greatly speeds up computation. Experimental results demonstrate that the proposed SpFLTS method surpasses existing techniques on multiple benchmark databases, highlighting its superior clustering performance and extensive application potential.