  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 often 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 pairwise-constrained 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
subspaces 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 clustering error down
considerably faster than the state-of-the-art active query algorithms on
datasets with subspace structure and is competitive on other datasets.
