Deterministic Conditions for Subspace Identifiability from Incomplete Sampling

TL;DR

This paper establishes precise deterministic conditions under which a low-dimensional subspace can be uniquely identified from incomplete coordinate projections, advancing understanding in subspace recovery.

Contribution

It provides necessary and sufficient deterministic conditions for subspace identifiability from partial coordinate projections, a novel theoretical result.

Findings

Derived deterministic conditions for subspace identifiability

Characterized when incomplete sampling suffices for unique recovery

Enhanced theoretical understanding of subspace sampling limitations

Abstract

Consider a generic $r$-dimensional subspace of $\mathbb{R}^d$, $r<d$, and suppose that we are only given projections of this subspace onto small subsets of the canonical coordinates. The paper establishes necessary and sufficient deterministic conditions on the subsets for subspace identifiability.