Deterministic Conditions for Subspace Identifiability from Incomplete   Sampling
  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. 
Daniel L. Pimentel-Alarc\'on, Robert D. Nowak, Nigel Boston
stat.ML cs.LG math.CO