Subspace Structure-Aware Spectral Clustering for Robust Subspace Clustering

Abstract

Subspace clustering is the problem of partitioning data drawn from a union of multiple subspaces. The most popular subspace clustering framework in recent years is the graph clustering-based approach, which performs subspace clustering in two steps: graph construction and graph clustering. Although both steps are equally important for accurate clustering, the vast majority of work has focused on improving the graph construction step rather than the graph clustering step. In this paper, we propose a novel graph clustering framework for robust subspace clustering. By incorporating a geometry-aware term with the spectral clustering objective, we encourage our framework to be robust to noise and outliers in given affinity matrices. We also develop an efficient expectation-maximization-based algorithm for optimization. Through extensive experiments on four real-world datasets, we demonstrate that the proposed method outperforms existing methods.