  Subspace clustering is a growing field of unsupervised learning that has
gained much popularity in the computer vision community. Applications can be
found in areas such as motion segmentation and face clustering. It assumes that
data originate from a union of subspaces, and clusters the data depending on
the corresponding subspace. In practice, it is reasonable to assume that a
limited amount of labels can be obtained, potentially at a cost. Therefore,
algorithms that can effectively and efficiently incorporate this information to
improve the clustering model are desirable. In this paper, we propose an active
learning framework for subspace clustering that sequentially queries
informative points and updates the subspace model. The query stage of the
proposed framework relies on results from the perturbation theory of principal
component analysis, to identify influential and potentially misclassified
points. A constrained subspace clustering algorithm is proposed that
monotonically decreases the objective function subject to the constraints
imposed by the labelled data. We show that our proposed framework is suitable
for subspace clustering algorithms including iterative methods and spectral
methods. Experiments on synthetic data sets, motion segmentation data sets, and
Yale Faces data sets demonstrate the advantage of our proposed active strategy
over state-of-the-art.
