Margin-based active subspace clustering

Subspace clustering has typically been approached as an unsupervised machine learning problem. However in several applications where the union of subspaces model is useful, it is also reasonable to assume you have access to a small number of labels. In this paper we investigate the benefit labeled data brings to the subspace clustering problem. We focus on incorporating labels into the k-subspaces algorithm, a simple and computationally efficient alternating estimation algorithm. We find that even a very small number of randomly selected labels can greatly improve accuracy over the unsupervised approach. We demonstrate that with enough labels, we get a significant improvement by using actively selected labels chosen for points that are nearly equidistant to more than one estimated subspace. We show this improvement on simulated data and face images.