Matches in SemOpenAlex for { <https://semopenalex.org/work/W1966596927> ?p ?o ?g. }
Showing items 1 to 82 of
82
with 100 items per page.
- W1966596927 endingPage "1912" @default.
- W1966596927 startingPage "1904" @default.
- W1966596927 abstract "The Nystrom method approximates eigenvectors of a given kernel matrix by randomly sampling subset of data. Previous researches focus on good kernel approximation while the quality of eigenvector approximation is rarely explored. In online eigenvector approximation method, one can minimize the kernel approximation error to guarantee a good eigenvector approximation. However in this work, we paradoxically prove that for batch approximation methods like Nystrom, it is no longer true. This unexpected discovery opens a question: What criterion should we use in Nystrom to generate a decent eigenvector approximation? To address this problem, we propose a novel criterion named Hilbert Space Embedding (HSE) Nystrom criterion which directly minimizes the eigenvector approximation error. The proposed HSE criterion provides a general framework to approximate eigenvectors within linear time and space complexity. We then show that we can rediscover many successful Nystrom methods with the proposed criterion, including K-means Nystrom and Density Nystrom. To further demonstrate the power of our criterion, we actually design a novel algorithm to approximate eigenvectors of Laplacian matrices based on the proposed criterion with better accuracy among existing linear complexity methods. We demonstrate the efficiency and efficacy of our proposal in numerical experiments. HighlightsA new criterion for Nystrom method to find accurate eigenvector approximation.The conventional criterion does not work well in eigenvector approximation.We need to adjust kernel width together with average weight adaptively.Propose a new criterion to adaptively optimize the parameters efficiently." @default.
- W1966596927 created "2016-06-24" @default.
- W1966596927 creator A5041008852 @default.
- W1966596927 creator A5065063835 @default.
- W1966596927 creator A5086529957 @default.
- W1966596927 date "2015-05-01" @default.
- W1966596927 modified "2023-10-17" @default.
- W1966596927 title "Large-scale eigenvector approximation via Hilbert Space Embedding Nyström" @default.
- W1966596927 cites W1946137962 @default.
- W1966596927 cites W1967934524 @default.
- W1966596927 cites W2023871431 @default.
- W1966596927 cites W2053186076 @default.
- W1966596927 cites W2082624758 @default.
- W1966596927 cites W2097308346 @default.
- W1966596927 cites W2109025268 @default.
- W1966596927 cites W2116810533 @default.
- W1966596927 cites W2125525099 @default.
- W1966596927 doi "https://doi.org/10.1016/j.patcog.2014.11.017" @default.
- W1966596927 hasPublicationYear "2015" @default.
- W1966596927 type Work @default.
- W1966596927 sameAs 1966596927 @default.
- W1966596927 citedByCount "7" @default.
- W1966596927 countsByYear W19665969272016 @default.
- W1966596927 countsByYear W19665969272017 @default.
- W1966596927 countsByYear W19665969272018 @default.
- W1966596927 countsByYear W19665969272023 @default.
- W1966596927 crossrefType "journal-article" @default.
- W1966596927 hasAuthorship W1966596927A5041008852 @default.
- W1966596927 hasAuthorship W1966596927A5065063835 @default.
- W1966596927 hasAuthorship W1966596927A5086529957 @default.
- W1966596927 hasConcept C111919701 @default.
- W1966596927 hasConcept C11413529 @default.
- W1966596927 hasConcept C121332964 @default.
- W1966596927 hasConcept C134306372 @default.
- W1966596927 hasConcept C154945302 @default.
- W1966596927 hasConcept C158693339 @default.
- W1966596927 hasConcept C2778572836 @default.
- W1966596927 hasConcept C2778755073 @default.
- W1966596927 hasConcept C28826006 @default.
- W1966596927 hasConcept C33923547 @default.
- W1966596927 hasConcept C41008148 @default.
- W1966596927 hasConcept C41608201 @default.
- W1966596927 hasConcept C62520636 @default.
- W1966596927 hasConcept C62799726 @default.
- W1966596927 hasConcept C80884492 @default.
- W1966596927 hasConceptScore W1966596927C111919701 @default.
- W1966596927 hasConceptScore W1966596927C11413529 @default.
- W1966596927 hasConceptScore W1966596927C121332964 @default.
- W1966596927 hasConceptScore W1966596927C134306372 @default.
- W1966596927 hasConceptScore W1966596927C154945302 @default.
- W1966596927 hasConceptScore W1966596927C158693339 @default.
- W1966596927 hasConceptScore W1966596927C2778572836 @default.
- W1966596927 hasConceptScore W1966596927C2778755073 @default.
- W1966596927 hasConceptScore W1966596927C28826006 @default.
- W1966596927 hasConceptScore W1966596927C33923547 @default.
- W1966596927 hasConceptScore W1966596927C41008148 @default.
- W1966596927 hasConceptScore W1966596927C41608201 @default.
- W1966596927 hasConceptScore W1966596927C62520636 @default.
- W1966596927 hasConceptScore W1966596927C62799726 @default.
- W1966596927 hasConceptScore W1966596927C80884492 @default.
- W1966596927 hasFunder F4320321001 @default.
- W1966596927 hasIssue "5" @default.
- W1966596927 hasLocation W19665969271 @default.
- W1966596927 hasOpenAccess W1966596927 @default.
- W1966596927 hasPrimaryLocation W19665969271 @default.
- W1966596927 hasRelatedWork W1482902903 @default.
- W1966596927 hasRelatedWork W2014857453 @default.
- W1966596927 hasRelatedWork W2024527795 @default.
- W1966596927 hasRelatedWork W2728580971 @default.
- W1966596927 hasRelatedWork W2949326632 @default.
- W1966596927 hasRelatedWork W2977833117 @default.
- W1966596927 hasRelatedWork W3046145628 @default.
- W1966596927 hasRelatedWork W3084216571 @default.
- W1966596927 hasRelatedWork W3092798325 @default.
- W1966596927 hasRelatedWork W4234882900 @default.
- W1966596927 hasVolume "48" @default.
- W1966596927 isParatext "false" @default.
- W1966596927 isRetracted "false" @default.
- W1966596927 magId "1966596927" @default.
- W1966596927 workType "article" @default.