To lie or not to lie in a subspace

Abstract

Give deterministic necessary and sufficient conditions to guarantee that if a subspace fits certain partially observed data from a union of subspaces, it is because such data really lies in a subspace. Furthermore, Give deterministic necessary and sufficient conditions to guarantee that if a subspace fits certain partially observed data, such subspace is unique. Do this by characterizing when and only when a set of incomplete vectors behaves as a single but complete one.

First author mistakenly listed advisors as co-authors in his research proposal. This is corrected in the current version. 59 pages, 19 figures. Subspace clustering, missing data, converse of matrix completion