Subspace Clustering Through Parametric Representation and Sparse Optimization

We consider the problem of recovering a finite number of linear subspaces from a collection of unlabeled data points that lie in the union of the subspaces. The data are such that it is not known which data point originates from which subspace. To address this challenge, we show that the clustering problem is amenable to a sparse optimization problem. Considering a candidate subspace and the distances of the data points to that subspace, the foundation of the proposed method lies in the maximization of the number of zero distances. This can be relaxed into a convex optimization. Efficiency of the relaxation can be significantly increased by solving a sequence of reweighted convex optimization problems.