Learning idempotent representation for subspace clustering

TL;DR

This paper introduces the IDR algorithm that produces reconstruction matrices for subspace clustering, ensuring they are block diagonal and fully connected, thereby improving clustering accuracy and efficiency.

Contribution

The paper proposes a novel idempotent representation method with a new constraint, enhancing subspace clustering by directly approximating normalized membership matrices.

Findings

IDR outperforms related algorithms in experiments.

IDR produces block diagonal, fully connected matrices.

IDR is computationally efficient and converges reliably.

Abstract

The critical point for the successes of spectral-type subspace clustering algorithms is to seek reconstruction coefficient matrices which can faithfully reveal the subspace structures of data sets. An ideal reconstruction coefficient matrix should have two properties: 1) it is block diagonal with each block indicating a subspace; 2) each block is fully connected. Though there are various spectral-type subspace clustering algorithms have been proposed, some defects still exist in the reconstruction coefficient matrices constructed by these algorithms. We find that a normalized membership matrix naturally satisfies the above two conditions. Therefore, in this paper, we devise an idempotent representation (IDR) algorithm to pursue reconstruction coefficient matrices approximating normalized membership matrices. IDR designs a new idempotent constraint for reconstruction coefficient matrices. And by combining the doubly stochastic constraints, the coefficient matrices which are closed to normalized membership matrices could be directly achieved. We present the optimization algorithm for solving IDR problem and analyze its computation burden as well as convergence. The comparisons between IDR and related algorithms show the superiority of IDR. Plentiful experiments conducted on both synthetic and real world datasets prove that IDR is an effective and efficient subspace clustering algorithm.