RPCA-induced self-representation for subspace clustering

Abstract

The self-expressiveness property of the data, i.e., each sample is linearly represented as a combination of other samples, has recently aroused much attention in the community of data mining and machine learning and shown great promising for subspace clustering. However, real-world data are usually contaminated by noise and outliers. The true similarity between samples directly learned from the original data may deviate from the intrinsic structure of the data, and subsequent clustering results will be severely affected. Hence naively taking a corrupted dictionary, i.e., data itself, will not always obtain the desired clustering performance. To address the above issues, this paper proposes a robust principal component analysis induced self-representation clustering method via adaptively learning the similarity graph from the clean data in the self-representation framework, where the original data are recovered, and the representation coefficients are obtained simultaneously in a unified framework. Specifically, we jointly integrate a nonnegative constraint and a distance regularization into the proposed framework, which guarantees the learned affinity matrix can simultaneously capture the global and local structure of data. Experimental results on both synthetic data and several famous multimedia datasets demonstrate that the proposed method performs much better against state-of-the-arts.