Smooth Representation Clustering

Subspace clustering is a powerful technology for clustering data according to the underlying subspaces. Representation based methods are the most popular subspace clustering approach in recent years. In this paper, we analyze the grouping effect of representation based methods in depth. In particular, we introduce the enforced grouping effect conditions, which greatly facilitate the analysis of grouping effect. We further find that grouping effect is important for subspace clustering, which should be explicitly enforced in the data self-representation model, rather than implicitly implied by the model as in some prior work. Based on our analysis, we propose the SMooth Representation (SMR) model. We also propose a new affinity measure based on the grouping effect, which proves to be much more effective than the commonly used one. As a result, our SMR significantly outperforms the state-of-the-art ones on benchmark datasets.