Subspace clustering by weighted correlation adaptive regression

Weiwei Wang, Cui-Ling Wu, Hua Huang, Xiang-Chu Feng

Abstract: Subspace clustering aims to reveal the latent subspace structure underlying high dimensional data by segmenting the data into corresponding subspaces. It has found wide applications in machine learning and computer vision. Most recent works on subspace segmentation focus on subspace representation based methods, which constructs the affinity matrix from the subspace representation of data points. In this work, we propose an explicit data-correlation-adaptive penalty on representation coefficients. Specifically, we define a data-correlation-adaptive penalty by a weighted combination of the l <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> -norm and l <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> -norm, and formulate the subspace representation as a weighted correlation adaptive regression (WCAR) problem. It can be regarded as a method which interpolates SSC and LSR adaptively depending on the correlation among data samples. It shows good subspace selection ability for uncorrelated data as well as grouping ability for highly correlated data. Experimental results on several commonly used clustering datasets show that our method performs better than the state-of-the-art methods.