Balanced and Discrete Regression for Image Clustering

Abstract

The minimization of <inline-formula> <tex-math notation="LaTeX">$\ell _{2,p}$ </tex-math></inline-formula> norm is a powerful regularization for robustness feature extraction, sparse representation and data denoising. However, its potential for clusters distribution modeling remains largely unexplored. In this paper, we present theoretical evidence that the <inline-formula> <tex-math notation="LaTeX">$\ell _{2,p}$ </tex-math></inline-formula> norm can effectively promote clusters balance with the maximization (<inline-formula> <tex-math notation="LaTeX">$0 \lt p \lt 2$ </tex-math></inline-formula>). Based on this theoretical foundation, we present a discrete regression clustering framework which incorporates the proposed regularization. Compared with existed anchor-graph multi-view clustering methods, our proposed method explicitly leverages the probabilistic nature of anchor graphs and realizes collaborative clustering for anchor points and sample points. It is important that our method can guarantee the balanced anchor points distribution which helps improve the robustness. Experimental results validate the effectiveness and superiority of the proposed approach.