To lie or not to lie in a subspace
This addresses a foundational issue in subspace clustering and data analysis for researchers, offering theoretical guarantees rather than incremental improvements.
The paper tackles the problem of determining when partially observed data from a union of subspaces genuinely lies in a single subspace, providing deterministic necessary and sufficient conditions to guarantee this and ensure uniqueness of the subspace.
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.