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Many clustering problems in computer vision and other contexts are alsoclassification problems, where each cluster shares a meaningful label. Subspaceclustering algorithms in particular are often applied to problems that fit thisdescription, for example with face images or handwritten digits. While it isstraightforward to request human input on these datasets, our goal is to reducethis input as much as possible. We present a pairwise-constrained clusteringalgorithm that actively selects queries based on the union-of-subspaces model.The central step of the algorithm is in querying points of minimum marginbetween estimated subspaces; analogous to classifier margin, these lie near thedecision boundary. We prove that points lying near the intersection ofsubspaces are points with low margin. Our procedure can be used after anysubspace clustering algorithm that outputs an affinity matrix. We demonstrateon several datasets that our algorithm drives the clustering error downconsiderably faster than the state-of-the-art active query algorithms ondatasets with subspace structure and is competitive on other datasets.

Leveraging Union of Subspace Structure to Improve Constrained Clustering