Matches in SemOpenAlex for { <https://semopenalex.org/work/W4286908084> ?p ?o ?g. }
Showing items 1 to 68 of
68
with 100 items per page.
- W4286908084 abstract "Let $mathcal{M}$ be a smooth $d$-dimensional submanifold of $mathbb{R}^N$ with boundary that's equipped with the Euclidean (chordal) metric, and choose $m leq N$. In this paper we consider the probability that a random matrix $A in mathbb{R}^{m times N}$ will serve as a bi-Lipschitz function $A: mathcal{M} rightarrow mathbb{R}^m$ with bi-Lipschitz constants close to one for three different types of distributions on the $m times N$ matrices $A$, including two whose realizations are guaranteed to have fast matrix-vector multiplies. In doing so we generalize prior randomized metric space embedding results of this type for submanifolds of $mathbb{R}^N$ by allowing for the presence of boundary while also retaining, and in some cases improving, prior lower bounds on the achievable embedding dimensions $m$ for which one can expect small distortion with high probability. In particular, motivated by recent modewise embedding constructions for tensor data, herein we present a new class of highly structured distributions on matrices which outperform prior structured matrix distributions for embedding sufficiently low-dimensional submanifolds of $mathbb{R}^N$ (with $d lesssim sqrt{N}$) with respect to both achievable embedding dimension, and computationally efficient realizations. As a consequence we are able to present, for example, a general new class of Johnson-Lindenstrauss embedding matrices for $mathcal{O}(log^c N)$-dimensional submanifolds of $mathbb{R}^N$ which enjoy $mathcal{O}(N log (log N))$-time matrix vector multiplications." @default.
- W4286908084 created "2022-07-25" @default.
- W4286908084 creator A5004103671 @default.
- W4286908084 creator A5045093139 @default.
- W4286908084 creator A5076518821 @default.
- W4286908084 date "2021-10-08" @default.
- W4286908084 modified "2023-09-28" @default.
- W4286908084 title "On Fast Johnson-Lindenstrauss Embeddings of Compact Submanifolds of $mathbb{R}^N$ with Boundary" @default.
- W4286908084 doi "https://doi.org/10.48550/arxiv.2110.04193" @default.
- W4286908084 hasPublicationYear "2021" @default.
- W4286908084 type Work @default.
- W4286908084 citedByCount "0" @default.
- W4286908084 crossrefType "posted-content" @default.
- W4286908084 hasAuthorship W4286908084A5004103671 @default.
- W4286908084 hasAuthorship W4286908084A5045093139 @default.
- W4286908084 hasAuthorship W4286908084A5076518821 @default.
- W4286908084 hasBestOaLocation W42869080841 @default.
- W4286908084 hasConcept C106487976 @default.
- W4286908084 hasConcept C110121322 @default.
- W4286908084 hasConcept C114614502 @default.
- W4286908084 hasConcept C118615104 @default.
- W4286908084 hasConcept C134306372 @default.
- W4286908084 hasConcept C151300846 @default.
- W4286908084 hasConcept C154945302 @default.
- W4286908084 hasConcept C159985019 @default.
- W4286908084 hasConcept C192562407 @default.
- W4286908084 hasConcept C198043062 @default.
- W4286908084 hasConcept C202444582 @default.
- W4286908084 hasConcept C22324862 @default.
- W4286908084 hasConcept C33676613 @default.
- W4286908084 hasConcept C33923547 @default.
- W4286908084 hasConcept C41008148 @default.
- W4286908084 hasConcept C41608201 @default.
- W4286908084 hasConcept C62354387 @default.
- W4286908084 hasConceptScore W4286908084C106487976 @default.
- W4286908084 hasConceptScore W4286908084C110121322 @default.
- W4286908084 hasConceptScore W4286908084C114614502 @default.
- W4286908084 hasConceptScore W4286908084C118615104 @default.
- W4286908084 hasConceptScore W4286908084C134306372 @default.
- W4286908084 hasConceptScore W4286908084C151300846 @default.
- W4286908084 hasConceptScore W4286908084C154945302 @default.
- W4286908084 hasConceptScore W4286908084C159985019 @default.
- W4286908084 hasConceptScore W4286908084C192562407 @default.
- W4286908084 hasConceptScore W4286908084C198043062 @default.
- W4286908084 hasConceptScore W4286908084C202444582 @default.
- W4286908084 hasConceptScore W4286908084C22324862 @default.
- W4286908084 hasConceptScore W4286908084C33676613 @default.
- W4286908084 hasConceptScore W4286908084C33923547 @default.
- W4286908084 hasConceptScore W4286908084C41008148 @default.
- W4286908084 hasConceptScore W4286908084C41608201 @default.
- W4286908084 hasConceptScore W4286908084C62354387 @default.
- W4286908084 hasLocation W42869080841 @default.
- W4286908084 hasLocation W42869080842 @default.
- W4286908084 hasOpenAccess W4286908084 @default.
- W4286908084 hasPrimaryLocation W42869080841 @default.
- W4286908084 hasRelatedWork W128603258 @default.
- W4286908084 hasRelatedWork W1966053345 @default.
- W4286908084 hasRelatedWork W1970861445 @default.
- W4286908084 hasRelatedWork W1994464108 @default.
- W4286908084 hasRelatedWork W2055993960 @default.
- W4286908084 hasRelatedWork W2063696182 @default.
- W4286908084 hasRelatedWork W2313739945 @default.
- W4286908084 hasRelatedWork W2774791677 @default.
- W4286908084 hasRelatedWork W2964052968 @default.
- W4286908084 hasRelatedWork W3159266028 @default.
- W4286908084 isParatext "false" @default.
- W4286908084 isRetracted "false" @default.
- W4286908084 workType "article" @default.