Exploring a Principled Framework for Deep Subspace Clustering

Xianghan Meng, Zhiyuan Huang, Wei He, Xianbiao Qi, Rong Xiao, Chun-Guang Li

Keywords: deep subspace clustering, self-expressive model, representation learning

TL;DR: We propose a principled framework for deep subspace clustering with theoretical justifications to avoid collapse and to form structured representations.

Abstract: Subspace clustering is a classical unsupervised learning task, built on a basic assumption that high-dimensional data can be approximated by a union of subspaces (UoS). Nevertheless, the real-world data are often deviating from the UoS assumption. To address this challenge, state-of-the-art deep subspace clustering algorithms attempt to jointly learn UoS representations and self-expressive coefficients. However, the general framework of the existing algorithms suffers from feature collapse and lacks a theoretical guarantee to learn desired UoS representation. In this paper, we present a Principled fRamewOrk for Deep Subspace Clustering (PRO-DSC), which is designed to learn structured representations and self-expressive coefficients in a unified manner. Specifically, in PRO-DSC, we incorporate an effective regularization on the learned representations into the self-expressive model, and prove that the regularized self-expressive model is able to prevent feature space collapse and the learned optimal representations under certain condition lie on a union of orthogonal subspaces. Moreover, we provide a scalable and efficient approach to implement our PRO-DSC and conduct extensive experiments to verify our theoretical findings and demonstrate the superior performance of our proposed deep subspace clustering approach.

Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning

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Submission Number: 3766