Information-theoretic Bounds on Matrix Completion under Union of Subspaces Model

TL;DR

This paper extends matrix completion bounds to matrices with columns grouped into subspaces, impacting subspace clustering with incomplete data, and diverges from traditional big-data assumptions.

Contribution

It introduces new theoretical bounds for matrix completion under a union of subspaces model, relevant for clustering with missing information.

Findings

Extended matrix completion bounds for subspace models

Implications for subspace clustering with incomplete data

Diverges from traditional big-data assumptions

Abstract

In this short note we extend some of the recent results on matrix completion under the assumption that the columns of the matrix can be grouped (clustered) into subspaces (not necessarily disjoint or independent). This model deviates from the typical assumption prevalent in the literature dealing with compression and recovery for big-data applications. The results have a direct bearing on the problem of subspace clustering under missing or incomplete information.