Subspace Segmentation by Correlation Adaptive Regression

Abstract

Subspace segmentation aims to segment a given data set into clusters with each cluster corresponding to a subspace. Most recent works focus on subspace representation-based methods, which construct the affinity matrix based on the subspace representation of the data points. Ideally, the affinity matrix should be inter-cluster sparse and intra-cluster uniform. The inter-cluster sparsity guarantees segmenting data into different subspaces from which they are originally drawn and the intra-cluster uniformity encourages clustering highly correlated data together. Most previous methods partly satisfy these properties and cannot obtain ideal results. To satisfy both properties, we propose an explicit data correlation adaptive regression model for the subspace representation. The proposed model essentially uses l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -norm on the coefficients of highly correlated data points while l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm on that of less correlated data points. The l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -norm tends to enforce the coefficients corresponding to highly correlated data have the grouping effect, while the l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm tends to enforce the coefficients corresponding to uncorrelated data to be zero. So, the proposed model can ensure the affinity matrix have two attractive properties: inter-subspace sparsity and intra-cluster uniformity. Experimental results on several commonly used clustering data sets show that our method performs better than the state-of-the-art methods.