A proximal framework for fuzzy subspace clustering

This paper proposes a fuzzy partitioning subspace clustering algorithm that minimizes a variant of the FCM cost function with a weighted Euclidean distance and a non-differentiable penalty term. The form of the cost function suggests to split the optimization problem, taking advantage of the framework of proximal optimization. The expression of the proximal operator for the penalty term is derived and implemented in a new algorithm, PFSCM, which combines proximal descent and alternate optimization. A discussion on the extension of this work to produce sparse estimations of the subspaces is conducted. Experimental results show the relevance of the proposed approach.