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 their corresponding subspaces. 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.
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