Matches in SemOpenAlex for { <https://semopenalex.org/work/W2950248432> ?p ?o ?g. }
- W2950248432 abstract "We show how to approximate a data matrix $mathbf{A}$ with a much smaller sketch $mathbf{tilde A}$ that can be used to solve a general class of constrained k-rank approximation problems to within $(1+epsilon)$ error. Importantly, this class of problems includes $k$-means clustering and unconstrained low rank approximation (i.e. principal component analysis). By reducing data points to just $O(k)$ dimensions, our methods generically accelerate any exact, approximate, or heuristic algorithm for these ubiquitous problems. For $k$-means dimensionality reduction, we provide $(1+epsilon)$ relative error results for many common sketching techniques, including random row projection, column selection, and approximate SVD. For approximate principal component analysis, we give a simple alternative to known algorithms that has applications in the streaming setting. Additionally, we extend recent work on column-based matrix reconstruction, giving column subsets that not only `cover' a good subspace for $bv{A}$, but can be used directly to compute this subspace. Finally, for $k$-means clustering, we show how to achieve a $(9+epsilon)$ approximation by Johnson-Lindenstrauss projecting data points to just $O(log k/epsilon^2)$ dimensions. This gives the first result that leverages the specific structure of $k$-means to achieve dimension independent of input size and sublinear in $k$." @default.
- W2950248432 created "2019-06-27" @default.
- W2950248432 creator A5018420180 @default.
- W2950248432 creator A5023229845 @default.
- W2950248432 creator A5047346803 @default.
- W2950248432 creator A5059735243 @default.
- W2950248432 creator A5091524323 @default.
- W2950248432 date "2014-10-24" @default.
- W2950248432 modified "2023-09-27" @default.
- W2950248432 title "Dimensionality Reduction for k-Means Clustering and Low Rank Approximation" @default.
- W2950248432 cites W1578468649 @default.
- W2950248432 cites W1937322722 @default.
- W2950248432 cites W1945899805 @default.
- W2950248432 cites W1970576574 @default.
- W2950248432 cites W1981773323 @default.
- W2950248432 cites W1988638201 @default.
- W2950248432 cites W2003690406 @default.
- W2950248432 cites W2004791924 @default.
- W2950248432 cites W2042465463 @default.
- W2950248432 cites W2045390367 @default.
- W2950248432 cites W2059867647 @default.
- W2950248432 cites W2064980127 @default.
- W2950248432 cites W2065060195 @default.
- W2950248432 cites W2088424151 @default.
- W2950248432 cites W2096908304 @default.
- W2950248432 cites W2101043704 @default.
- W2950248432 cites W2104469471 @default.
- W2950248432 cites W2110105238 @default.
- W2950248432 cites W2117756735 @default.
- W2950248432 cites W2121689290 @default.
- W2950248432 cites W2122695681 @default.
- W2950248432 cites W2134342155 @default.
- W2950248432 cites W2135940344 @default.
- W2950248432 cites W2140477921 @default.
- W2950248432 cites W2142827986 @default.
- W2950248432 cites W2144335278 @default.
- W2950248432 cites W2150593711 @default.
- W2950248432 cites W2157988812 @default.
- W2950248432 cites W2164899006 @default.
- W2950248432 cites W2199495299 @default.
- W2950248432 cites W2229238337 @default.
- W2950248432 cites W2547648546 @default.
- W2950248432 cites W2949412345 @default.
- W2950248432 cites W2949789485 @default.
- W2950248432 cites W2951863880 @default.
- W2950248432 cites W2962984690 @default.
- W2950248432 cites W2963098024 @default.
- W2950248432 cites W2963879412 @default.
- W2950248432 cites W3037079313 @default.
- W2950248432 cites W37129894 @default.
- W2950248432 cites W826455576 @default.
- W2950248432 hasPublicationYear "2014" @default.
- W2950248432 type Work @default.
- W2950248432 sameAs 2950248432 @default.
- W2950248432 citedByCount "14" @default.
- W2950248432 countsByYear W29502484322013 @default.
- W2950248432 countsByYear W29502484322014 @default.
- W2950248432 countsByYear W29502484322015 @default.
- W2950248432 countsByYear W29502484322017 @default.
- W2950248432 countsByYear W29502484322018 @default.
- W2950248432 countsByYear W29502484322019 @default.
- W2950248432 countsByYear W29502484322020 @default.
- W2950248432 crossrefType "posted-content" @default.
- W2950248432 hasAuthorship W2950248432A5018420180 @default.
- W2950248432 hasAuthorship W2950248432A5023229845 @default.
- W2950248432 hasAuthorship W2950248432A5047346803 @default.
- W2950248432 hasAuthorship W2950248432A5059735243 @default.
- W2950248432 hasAuthorship W2950248432A5091524323 @default.
- W2950248432 hasConcept C105795698 @default.
- W2950248432 hasConcept C106487976 @default.
- W2950248432 hasConcept C111030470 @default.
- W2950248432 hasConcept C111335779 @default.
- W2950248432 hasConcept C11413529 @default.
- W2950248432 hasConcept C114614502 @default.
- W2950248432 hasConcept C117160843 @default.
- W2950248432 hasConcept C126255220 @default.
- W2950248432 hasConcept C13355873 @default.
- W2950248432 hasConcept C134306372 @default.
- W2950248432 hasConcept C148764684 @default.
- W2950248432 hasConcept C154945302 @default.
- W2950248432 hasConcept C159985019 @default.
- W2950248432 hasConcept C164226766 @default.
- W2950248432 hasConcept C173801870 @default.
- W2950248432 hasConcept C192562407 @default.
- W2950248432 hasConcept C21080849 @default.
- W2950248432 hasConcept C22789450 @default.
- W2950248432 hasConcept C25023664 @default.
- W2950248432 hasConcept C2524010 @default.
- W2950248432 hasConcept C27438332 @default.
- W2950248432 hasConcept C2780551164 @default.
- W2950248432 hasConcept C32834561 @default.
- W2950248432 hasConcept C33676613 @default.
- W2950248432 hasConcept C33923547 @default.
- W2950248432 hasConcept C41008148 @default.
- W2950248432 hasConcept C57493831 @default.
- W2950248432 hasConcept C70518039 @default.
- W2950248432 hasConcept C73555534 @default.
- W2950248432 hasConcept C90199385 @default.
- W2950248432 hasConceptScore W2950248432C105795698 @default.
- W2950248432 hasConceptScore W2950248432C106487976 @default.