Deterministic Conditions for Subspace Identifiability from Incomplete Sampling
arXiv:1410.0633v329 citations
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This addresses a theoretical problem in linear algebra and signal processing, with potential applications in data recovery and compressed sensing, but it appears incremental as it builds on existing subspace identification frameworks.
The paper tackles the problem of identifying a subspace from incomplete coordinate projections, establishing necessary and sufficient deterministic conditions for identifiability.
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.