2025/03/21 by Xianghan Meng, Meng, Xianghan, Zhiyuan Huang +9 · 2 citations
Computer Science · #Advanced Clustering Algorithms Research #Computer Vision and Pattern Recognition (cs.CV) #Domain Adaptation and Few-Shot Learning #FOS: Computer and information sciences #Face and Expression Recognition #Machine Learning (cs.LG)
paper · pdf · doi:10.48550/arxiv.2503.17288
openalex publication_date 2025/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 a catastrophic 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, prove that the regularized self-expressive model is able to prevent feature space collapse, and demonstrate that 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. The code is available at https://github.com/mengxianghan123/PRO-DSC.