Fast Low-Rank Subspace Segmentation

Subspace segmentation is the problem of segmenting (or grouping) a set of n data points into a number of clusters, with each cluster being a (linear) subspace. The recently established algorithms such as Sparse Subspace Clustering (SSC), Low-Rank Representation (LRR) and Low-Rank Subspace Segmentation (LRSS) are effective in terms of segmentation accuracy, but computationally inefficient as they possess a complexity of O (n^3), which is too high to afford for the case where n is very large. In this paper we devise a fast subspace segmentation algorithm with complexity of O (n (n) ). This is achieved by firstly using partial Singular Value Decomposition (SVD) to approximate the solution of LRSS, secondly utilizing Locality Sensitive Hashing (LSH) to build a sparse affinity graph that encodes the subspace memberships, and finally adopting a fast Normalized Cut (NCut) algorithm to produce the final segmentation results. Besides of high efficiency, our algorithm also has comparable effectiveness as the original LRSS method.