Locality Constrained-lp Sparse Subspace Clustering for Image Clustering

In most sparse coding based image restoration and image classification problems, using the non-convex l(p)-norm minimization (0 <= p < 1) can often deliver better results than using the convex l(1)-norm minimization. Also, the high computational costs of l(1)-graph in Sparse Subspace Clustering prevent l(1)-graph from being used in large scale high-dimensional datasets. To address these problems, we in this paper propose an algorithm called Locality Constrained-l(p) Sparse Subspace Clustering (kappa NN-l(p)). The sparse graph constructed by locality constrained l(p)-norm minimization can remove most of the semantically unrelated links among data at lower computational cost. As a result, the discriminative performance is improved compared with the l(1)-graph. We also apply the k nearest neighbors to accelerate the sparse graph construction without losing its effectiveness. To demonstrate the improved performance of the proposed Locality Constrained-l(p) Sparse Subspace Clustering algorithm, comparative study was performed on benchmark problems of image clustering. Thoroughly experimental studies on real world datasets show that the Locality Constrained-l(p) Sparse Subspace Clustering algorithm can significantly outperform other state-of-the-art methods.(C) 2016 Published by Elsevier B.V.