Shape Interaction Matrix Revisited and Robustified: Efficient Subspace Clustering with Corrupted and Incomplete Data

摘要

The Shape Interaction Matrix (SIM) is one of the earliest approaches toperforming subspace clustering (i.e., separating points drawn from a union ofsubspaces). In this paper, we revisit the SIM and reveal its connections toseveral recent subspace clustering methods. Our analysis lets us derive asimple, yet effective algorithm to robustify the SIM and make it applicable torealistic scenarios where the data is corrupted by noise. We justify our methodby intuitive examples and the matrix perturbation theory. We then show how thisapproach can be extended to handle missing data, thus yielding an efficient andgeneral subspace clustering algorithm. We demonstrate the benefits of ourapproach over state-of-the-art subspace clustering methods on severalchallenging motion segmentation and face clustering problems, where the dataincludes corrupted and missing measurements.