Locality Constrained-ℓp Sparse Subspace Clustering for Image Clustering

In most sparse coding based image restoration and image classification problems, using the non-convex ℓp-norm minimization (0≤p<1) can often deliver better results than using the convex ℓ1-norm minimization. Also, the high computational costs of ℓ1-graph in Sparse Subspace Clustering prevent ℓ1-graph from being used in large scale high-dimensional datasets. To address these problems, we in this paper propose an algorithm called Locality Constrained-ℓp Sparse Subspace Clustering (kNN-ℓp). The sparse graph constructed by locality constrained ℓp-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 ℓ1-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-ℓp 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-ℓp Sparse Subspace Clustering algorithm can significantly outperform other state-of-the-art methods.