We propose an active learning framework that is especially designed to be beneficial in the setting of subspace clustering, and in particular, K-Subspace Clustering (KSC). KSC is a K-means like algorithm that alternates between fitting subspaces and allocating data objects to their closest subspace. The simplicity and low computational cost of this algorithm have helped it gain much popularity in the family of subspace clustering algorithms. However, it is well-known that KSC is very sensitive to the initialisation of cluster memberships and is prone to get stuck in local minima.
Several approaches have been proposed in the literature to tackle its shortcomings: for example through better initialisation schemes, or through consensus clustering. Although these schemes help with improving the cluster performance to some extent, they add much extra computational burden and rarely achieve perfect performance. We instead introduce active learning to subspace clustering that queries true classes sequentially and intelligently. We propose a novel active learning strategy that queries the true classes of those data objects that are likely to be misclassified, and subsequently recovers the correct subspace structure which then helps to uncover the true classes for the remaining data objects.
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