Subspace Clustering using Ensembles of $K$-Subspaces

We present a novel approach to the subspace clustering problem that leverages ensembles of the K-subspaces (KSS) algorithm via the evidence accumulation clustering framework. Our algorithm forms a co-association matrix whose (i, j)th entry is the number of times points i and j are clustered together by several runs of KSS with random initializations. We analyze the entries of this co-association matrix and show that a naïve version of our algorithm can recover subspaces for points drawn from the same conditions as the Thresholded Subspace Clustering algorithm. We show on synthetic data that our method performs well under subspaces with large intersection, subspaces with small principal angles, and noisy data. Finally, we provide a variant of our algorithm that achieves state-of-the-art performance across several benchmark datasets, including a resulting error for the COIL-20 database that is less than half that achieved by existing algorithms.