Self-Supervised Convolutional Subspace Clustering Network with the Block Diagonal Regularizer

The practical visual data do not necessarily lie in linear subspaces, so deep convolutional subspace clustering network is proposed to segment the practical visual data into multiple categories accurately. The original convolutional subspace clustering network contains the stacked convolutional encoder module, the stacked convolutional decoder module and the self-expression module. We firstly alter the self-expression module, i.e., add a new k-block diagonal regularizer to the weights of the self-expression module. It means that the ℓ1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell _1$$\end{document} or ℓ2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell _2$$\end{document} regularizer is abandoned. The k-block diagonal regularizer is proposed to directly pursue the block diagonal matrix, so introducing this regularizer to the self-expression module will make the learned representation matrix conform with the block diagonal matrix better. Secondly, we add a new spectral clustering module to this convolutional subspace clustering network, in which the spectral clustering result is used to supervise the learning of the representation matrix. This subspace structured regularizer is introduced to the spectral clustering module, which further refines the learned representation matrix. Experimental results on three challenging datasets have demonstrated that the proposed deep learning based subspace clustering method achieves the better clustering effect over the state-of-the-arts.