FLoSS: Facility location for subspace segmentation

Subspace segmentation is the task of segmenting data lying on multiple linear subspaces. Its applications in computer vision include motion segmentation in video, structure-from-motion, and image clustering. In this work, we describe a novel approach for subspace segmentation that uses probabilistic inference via a message-passing algorithm. We cast the subspace segmentation problem as that of choosing the best subset of linear subspaces from a set of candidate subspaces constructed from the data. Under this formulation, subspace segmentation corresponds to facility location, a well studied operational research problem. Approximate solutions to this NP-hard optimization problem can be found by performing maximum-a-posteriori (MAP) inference in a probabilistic graphical model. We describe the graphical model and a message-passing inference algorithm. We demonstrate the performance of Facility Location for Subspace Segmentation, or FLoSS, on synthetic data as well as on 3D multi-body video motion segmentation from point correspondences.