Abstract

Many clustering problems in computer vision and other contexts are also classification problems, where each cluster shares a meaningful label. Subspace clustering algorithms in particular are ofte applied to problems that fit this description, for example with face images or handwritten digits. While it is straightforward to request human input on these datasets, our goal is to reduce this input as much as possible. We present a pairwiseconstrained clustering algorithm that actively selects queries based on the union-of-subspaces model. The central step of the algorithm is in querying points of minimum margin between estimated subspaces; analogous to classifier margin, these lie near the decision boundary. We prove that points lying near the intersection of subspac are points with low margin. Our procedure can be used after any subspace clustering algorithm that outputs an affinity matrix. We demonstrate on several datasets that our algorithm drives the cluste ing error down considerably faster than the stateof-the-art active query algorithms on datasets wit subspace structure and is competitive on other datasets.