Learning with $\ell^{0}$-Graph: $\ell^{0}$-Induced Sparse Subspace Clustering

ℓ 1-graph [19, 4], a sparse graph built by reconstructing each datum with all the other data using sparse representation , has been demonstrated to be effective in clustering high dimensional data and recovering independent subspaces from which the data are drawn. It is well known that ℓ 1-norm used in ℓ 1-graph is a convex relaxation of ℓ 0-norm for enforcing the sparsity. In order to handle general cases when the subspaces are not independent and follow the original principle of sparse representation, we propose a novel ℓ 0-graph that employs ℓ 0-norm to encourage the sparsity of the constructed graph, and develop a proximal method to solve the associated optimization problem with the proved guarantee of convergence. Extensive experimental results on various data sets demonstrate the superiority of ℓ 0-graph compared to other competing clustering methods including ℓ 1-graph.