One-step Low-Rank Representation for Clustering

Existing low-rank representation-based methods adopt a two-step framework, which must employ an extra clustering method to gain labels after representation learning. In this paper, a novel one-step representation-based method, i.e., One-step Low-Rank Representation (OLRR), is proposed to capture multi-subspace structures for clustering. OLRR integrates the low-rank representation model and clustering into a unified framework. Thus it can jointly learn the low-rank subspace structure embedded in the database and gain the clustering results. In particular, by approximating the representation matrix with two same clustering indicator matrices, OLRR can directly show the probability of samples belonging to each cluster. Further, a probability penalty is introduced to ensure that the samples with smaller distances are more inclined to be in the same cluster, thus enhancing the discrimination of the clustering indicator matrix and resulting in a more favorable clustering performance. Moreover, to enhance the robustness against noise, OLRR uses the probability to guide denoising and then performs representation learning and clustering in a recovered clean space. Extensive experiments well demonstrate the robustness and effectiveness of OLRR. Our code is publicly available at: https://github.com/fuzhiqiang1230/OLRR.