Robust Subspace Clustering by Bi-Sparsity Pursuit: Guarantees and Sequential Algorithm

We consider subspace clustering under sparse noise, for which a non-convex optimization framework based on sparse data representations has been recently developed. This setup is suitable for a large variety of applications with high dimensional data, such as image processing, which is naturally decomposed into a sparse unstructured foreground and a background residing in a union of low-dimensional subspaces. In this framework, we further discuss both performance and implementation of the key optimization problem. We provide an analysis of this optimization problem demonstrating that our approach is capable of recovering linear subspaces as a local optimal solution for sufficiently large data sets and sparse noise vectors. We also propose a sequential algorithmic solution, which is particularly useful for extremely large data sets and online vision applications such as video processing.