Joint l_p- and l_2,p-norm minimization for subspace clustering with outlier pursuit

In most sparse coding based subspace clustering problems, using the non-convex l_p-norm minimization (0 < p < 1) can often deliver better results than using the convex l₁-norm minimization. In this paper, we propose a sparse subspace clustering via joint l_p-norm and l_2,p-norm minimization, where the l_p-norm imposed on sparse representations can achieve more sparsity for clustering while l_2,p-norm imposed on reconstructed error can handle outlier pursuit. We also propose an iterative solution to solve the proposed problem based on Iterative Shrinkage/Thresholding (IST) method. In addition, to the best knowledge, utilizing IST for solving l_2,p-norm minimization problem can be the first work in our paper and there is no such work before. Finally, to demonstrate the improved performance of the proposed method, comparative study was performed on benchmark problems of image clustering. Thoroughly experimental studies on real world datasets show that the method can significantly outperform other state-of-the-art methods.