Matches in SemOpenAlex for { <https://semopenalex.org/work/W4313447753> ?p ?o ?g. }
Showing items 1 to 69 of
69
with 100 items per page.
- W4313447753 abstract "The Johnson--Lindenstrauss (JL) lemma is a powerful tool for dimensionality reduction in modern algorithm design. The lemma states that any set of high-dimensional points in a Euclidean space can be flattened to lower dimensions while approximately preserving pairwise Euclidean distances. Random matrices satisfying this lemma are called JL transforms (JLTs). Inspired by existing $s$-hashing JLTs with exactly $s$ nonzero elements on each column, the present work introduces an ensemble of sparse matrices encompassing so-called $s$-hashing-like matrices whose expected number of nonzero elements on each column is~$s$. The independence of the sub-Gaussian entries of these matrices and the knowledge of their exact distribution play an important role in their analyses. Using properties of independent sub-Gaussian random variables, these matrices are demonstrated to be JLTs, and their smallest and largest singular values are estimated non-asymptotically using a technique from geometric functional analysis. As the dimensions of the matrix grow to infinity, these singular values are proved to converge almost surely to fixed quantities (by using the universal Bai--Yin law), and in distribution to the Gaussian orthogonal ensemble (GOE) Tracy--Widom law after proper rescalings. Understanding the behaviors of extreme singular values is important in general because they are often used to define a measure of stability of matrix algorithms. For example, JLTs were recently used in derivative-free optimization algorithmic frameworks to select random subspaces in which are constructed random models or poll directions to achieve scalability, whence estimating their smallest singular value in particular helps determine the dimension of these subspaces." @default.
- W4313447753 created "2023-01-06" @default.
- W4313447753 creator A5044878102 @default.
- W4313447753 creator A5083426306 @default.
- W4313447753 date "2022-12-30" @default.
- W4313447753 modified "2023-09-27" @default.
- W4313447753 title "Sparse Johnson--Lindenstrauss transforms and analysis of their extreme singular values" @default.
- W4313447753 doi "https://doi.org/10.48550/arxiv.2212.14858" @default.
- W4313447753 hasPublicationYear "2022" @default.
- W4313447753 type Work @default.
- W4313447753 citedByCount "0" @default.
- W4313447753 crossrefType "posted-content" @default.
- W4313447753 hasAuthorship W4313447753A5044878102 @default.
- W4313447753 hasAuthorship W4313447753A5083426306 @default.
- W4313447753 hasBestOaLocation W43134477531 @default.
- W4313447753 hasConcept C105795698 @default.
- W4313447753 hasConcept C106487976 @default.
- W4313447753 hasConcept C109282560 @default.
- W4313447753 hasConcept C111030470 @default.
- W4313447753 hasConcept C114614502 @default.
- W4313447753 hasConcept C118615104 @default.
- W4313447753 hasConcept C121332964 @default.
- W4313447753 hasConcept C158693339 @default.
- W4313447753 hasConcept C159985019 @default.
- W4313447753 hasConcept C163716315 @default.
- W4313447753 hasConcept C18903297 @default.
- W4313447753 hasConcept C192562407 @default.
- W4313447753 hasConcept C2777759810 @default.
- W4313447753 hasConcept C28826006 @default.
- W4313447753 hasConcept C33923547 @default.
- W4313447753 hasConcept C46757340 @default.
- W4313447753 hasConcept C62520636 @default.
- W4313447753 hasConcept C64812099 @default.
- W4313447753 hasConcept C86803240 @default.
- W4313447753 hasConceptScore W4313447753C105795698 @default.
- W4313447753 hasConceptScore W4313447753C106487976 @default.
- W4313447753 hasConceptScore W4313447753C109282560 @default.
- W4313447753 hasConceptScore W4313447753C111030470 @default.
- W4313447753 hasConceptScore W4313447753C114614502 @default.
- W4313447753 hasConceptScore W4313447753C118615104 @default.
- W4313447753 hasConceptScore W4313447753C121332964 @default.
- W4313447753 hasConceptScore W4313447753C158693339 @default.
- W4313447753 hasConceptScore W4313447753C159985019 @default.
- W4313447753 hasConceptScore W4313447753C163716315 @default.
- W4313447753 hasConceptScore W4313447753C18903297 @default.
- W4313447753 hasConceptScore W4313447753C192562407 @default.
- W4313447753 hasConceptScore W4313447753C2777759810 @default.
- W4313447753 hasConceptScore W4313447753C28826006 @default.
- W4313447753 hasConceptScore W4313447753C33923547 @default.
- W4313447753 hasConceptScore W4313447753C46757340 @default.
- W4313447753 hasConceptScore W4313447753C62520636 @default.
- W4313447753 hasConceptScore W4313447753C64812099 @default.
- W4313447753 hasConceptScore W4313447753C86803240 @default.
- W4313447753 hasLocation W43134477531 @default.
- W4313447753 hasOpenAccess W4313447753 @default.
- W4313447753 hasPrimaryLocation W43134477531 @default.
- W4313447753 hasRelatedWork W1561511259 @default.
- W4313447753 hasRelatedWork W1633562754 @default.
- W4313447753 hasRelatedWork W1656221318 @default.
- W4313447753 hasRelatedWork W1993734719 @default.
- W4313447753 hasRelatedWork W2016308609 @default.
- W4313447753 hasRelatedWork W2061057735 @default.
- W4313447753 hasRelatedWork W2089618463 @default.
- W4313447753 hasRelatedWork W2560350525 @default.
- W4313447753 hasRelatedWork W2952498887 @default.
- W4313447753 hasRelatedWork W4308670116 @default.
- W4313447753 isParatext "false" @default.
- W4313447753 isRetracted "false" @default.
- W4313447753 workType "article" @default.