1 code implementation • 28 Jun 2022 • Karan Srivastava, Daniel L. Pimentel-Alarcón
This paper derives a perturbation bound on the optimal subspace estimator obtained from a subset of its canonical projections contaminated by noise.
no code implementations • ICLR 2021 • Alejandro Pimentel-Alarcón, Daniel L. Pimentel-Alarcón
Motivated by metagenomics, recommender systems, dictionary learning, and related problems, this paper introduces subspace splitting(SS): the task of clustering the entries of what we call amixed-features vector, that is, a vector whose subsets of coordinates agree with a collection of subspaces.
no code implementations • 2 Aug 2018 • Daniel L. Pimentel-Alarcón, Usman Mahmood
Subspace clustering achieves this through a union of linear subspaces.
no code implementations • NeurIPS 2018 • Daniel L. Pimentel-Alarcón
A more general model assumes that each column of X corresponds to one of several low-rank matrices.
no code implementations • 9 Mar 2015 • Daniel L. Pimentel-Alarcón, Nigel Boston, Robert D. Nowak
Finite completability is the tipping point in LRMC, as a few additional samples of a finitely completable matrix guarantee its unique completability.
no code implementations • 2 Oct 2014 • Daniel L. Pimentel-Alarcón, Robert D. Nowak, Nigel Boston
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.
no code implementations • 24 Aug 2014 • Daniel L. Pimentel-Alarcón
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.