Adaptive weighted least squares regression for subspace clustering

Abstract

In this research paper, we consider the subspace clustering problem which aims at finding a low-dimensional representation of a high-dimensional data set. In particular, our central focus is upon the least squares regression based on which we elaborate an adaptive weighted least squares regression for subspace clustering. Compared to the least squares regression, we consider the data locality to adaptively select relevant and close samples and discard irrelevant and faraway ones. Additionally, we impose a weight matrix on the representation errors to adaptively highlight the meaningful features and minimize the effect of redundant/noisy ones. Finally, we also add a non-negativity constraint on the representation coefficients to enhance the graph interpretability. These interesting properties allow to build up a more informative and quality graph, thereby yielding very promising clustering results. Extensive experiments on synthetic and real databases demonstrated that our clustering method achieves consistently optimal results, compared to multiple clustering methods.