Data Representation and Clustering with Double Low-Rank Constraints

Abstract

High-dimensional data are usually drawn from an union of multiple low-dimensional subspaces. Low-rank representation (LRR), as a multi-subspace structure learning method, uses low rank constraints to extract the low-rank subspace structure of high-dimensional data. However, LRR is highly dependent on the multi-subspace property of the data itself, which is easily disturbed by some higher intensity global noise. Thus, a data representation learning method (UV-LRR) capable of handling both sparse global noise and locally structured sparse noise with dual low-rank constraints on the input data and the representation coefficients is proposed in this paper. The sparse global noise and the local structured noise are constrained by using $$l_1$$ and $$l_{2,1}$$ norm, respectively, to separate a large amount of noise latent in the data. The UV decomposition and nuclear norm minimization is also used to compress the rank of input data and representation coefficients to extract the multi-subspace structure underlying the observed data. The experimental results show that the proposed method has superior performance in the clustering experiments for each dataset.