Discriminative and coherent subspace clustering

The ubiquitous large, complex and high dimensional datasets in computer vision and machine learning generate the problem of subspace clustering, which aims to partition the data into several low dimensional subspaces. Most state-of-the-art methods divide the problem into two stages: first learn the affinity from the data and then infer the cluster labels based on the affinity. The Structured Sparse Subspace Clustering (SSSC) model combines the affinity learning and the label inferring into one unified framework and empirically outperforms the two-stage methods. However, the SSSC method does not fully utilize the affinity and the labels to guide each other. In this work, we present a new regularity which combines the labels and the affinity to enforce the coherence of the affinity for data points from the same cluster and the discrimination of the labels for data points from different clusters. Based on this, we give a new unified optimization framework for subspace clustering. It enforces the coherence and discrimination of the affinity matrix as well as the labels, thus we call it Discriminative and Coherent Subspace Clustering (DCSC). Extended experiments on commonly used datasets demonstrate that our method performs better than some two stage state-of-the-art methods and the unified method SSSC in revealing the subspace structure of high-dimensional data.