Orderly Subspace Clustering

Abstract Semi-supervised representation-based subspace clustering is to partition data into their underlying subspaces by finding effective data representations with partial supervisions. Essentially, an effective and accurate representation should be able to uncover and preserve the true data structure. Meanwhile, a reliable and easy-to-obtain supervision is desirable for practical learning. To meet these two objectives, in this paper we make the first attempt towards utilizing the orderly relationship, such as the data a is closer to b than to c, as a novel supervision. We propose an orderly subspace clustering approach with a novel regularization term. OSC enforces the learned representations to simultaneously capture the intrinsic subspace structure and reveal orderly structure that is faithful to true data relationship. Experimental results with several benchmarks have demonstrated that aside from more accurate clustering against state-of-the-arts, OSC interprets orderly data structure which is beyond what current approaches can offer.