Classifying and Comparing Approaches to Subspace Clustering with Missing Data

Abstract

In recent years, many methods have been proposed for the task of subspace clustering with missing data (SCMD), and its complementary problem, high-rank matrix completion (HRMC). Given incomplete data drawn from a union of subspaces, these methods aim to simultaneously cluster each data point and recover the unobserved entries. In this work, we review the current state of this literature. We organize the existing methods into five distinct families and discuss their relative strengths and weaknesses. This classification exposes some gaps in the current literature, which we fill by introducing a few natural extensions of prior methods. Finally, we provide a thorough and unbiased evaluation of representative methods on synthetic data. Our experiments demonstrate a clear advantage for alternating between projected zero-filled sparse subspace clustering, and per-group matrix completion. Understanding why this intuitive but heuristic method performs well is an open problem for future theoretical study.