Matches in SemOpenAlex for { <https://semopenalex.org/work/W137000543> ?p ?o ?g. }
Showing items 1 to 83 of
83
with 100 items per page.
- W137000543 abstract "Statistical Latent Dirichlet Analysis produces mixture model data that are geometrically equivalent to points lying on a regular simplex in moderate to high dimensions. Numerous other statistical models and techniques also produce data in this geometric category, even though the meaning of the axes and coordinate values differs significantly. A distance function is used to further analyze these points, for example to cluster them. Several different distance functions are popular amongst statisticians; which distance function is chosen is usually driven by the historical preference of the application domain, information-theoretic considerations, or by the desirability of the clustering results. Relatively little consideration is usually given to how distance functions geometrically transform data, or the distances algebraic properties. Here we take a look at these issues, in the hope of providing complementary insight and inspiring further geometric thought. Several popular distances, χ, Jensen Shannon divergence, and the square of the Hellinger distance, are shown to be nearly equivalent; in terms of functional forms after transformations, factorizations, and series expansions; and in terms of the shape and proximity of constant-value contours. This is somewhat surprising given that their original functional forms look quite different. Cosine similarity is the square of the Euclidean distance, and a similar geometric relationship is shown with Hellinger and another cosine. We suggest a geodesic variation of Hellinger. The square-root projection that arises in Hellinger distance is briefly compared to standard normalization for Euclidean distance. We include detailed derivations of some ratio and difference bounds for illustrative purposes. We provide some constructions that nearly achieve the worst-case ratios, relevant for contours." @default.
- W137000543 created "2016-06-24" @default.
- W137000543 creator A5050840284 @default.
- W137000543 date "2010-12-01" @default.
- W137000543 modified "2023-09-23" @default.
- W137000543 title "Geometric Comparison of Popular Mixture-Model Distances." @default.
- W137000543 cites W1612003148 @default.
- W137000543 cites W1897321358 @default.
- W137000543 cites W1912497050 @default.
- W137000543 cites W1965555277 @default.
- W137000543 cites W1999528235 @default.
- W137000543 cites W2005797502 @default.
- W137000543 cites W2009435671 @default.
- W137000543 cites W2031648200 @default.
- W137000543 cites W2032916024 @default.
- W137000543 cites W2045656688 @default.
- W137000543 cites W2072773380 @default.
- W137000543 cites W2094963775 @default.
- W137000543 cites W2104648049 @default.
- W137000543 cites W2118783153 @default.
- W137000543 cites W2129070834 @default.
- W137000543 cites W2143668817 @default.
- W137000543 cites W2171235719 @default.
- W137000543 cites W3127518054 @default.
- W137000543 hasPublicationYear "2010" @default.
- W137000543 type Work @default.
- W137000543 sameAs 137000543 @default.
- W137000543 citedByCount "1" @default.
- W137000543 crossrefType "journal-article" @default.
- W137000543 hasAuthorship W137000543A5050840284 @default.
- W137000543 hasConcept C114614502 @default.
- W137000543 hasConcept C120174047 @default.
- W137000543 hasConcept C129782007 @default.
- W137000543 hasConcept C153024298 @default.
- W137000543 hasConcept C154945302 @default.
- W137000543 hasConcept C178009071 @default.
- W137000543 hasConcept C182964748 @default.
- W137000543 hasConcept C2524010 @default.
- W137000543 hasConcept C2639959 @default.
- W137000543 hasConcept C28826006 @default.
- W137000543 hasConcept C33923547 @default.
- W137000543 hasConcept C41008148 @default.
- W137000543 hasConcept C62438384 @default.
- W137000543 hasConceptScore W137000543C114614502 @default.
- W137000543 hasConceptScore W137000543C120174047 @default.
- W137000543 hasConceptScore W137000543C129782007 @default.
- W137000543 hasConceptScore W137000543C153024298 @default.
- W137000543 hasConceptScore W137000543C154945302 @default.
- W137000543 hasConceptScore W137000543C178009071 @default.
- W137000543 hasConceptScore W137000543C182964748 @default.
- W137000543 hasConceptScore W137000543C2524010 @default.
- W137000543 hasConceptScore W137000543C2639959 @default.
- W137000543 hasConceptScore W137000543C28826006 @default.
- W137000543 hasConceptScore W137000543C33923547 @default.
- W137000543 hasConceptScore W137000543C41008148 @default.
- W137000543 hasConceptScore W137000543C62438384 @default.
- W137000543 hasLocation W1370005431 @default.
- W137000543 hasOpenAccess W137000543 @default.
- W137000543 hasPrimaryLocation W1370005431 @default.
- W137000543 hasRelatedWork W1784689394 @default.
- W137000543 hasRelatedWork W1977834563 @default.
- W137000543 hasRelatedWork W2017203286 @default.
- W137000543 hasRelatedWork W2077398228 @default.
- W137000543 hasRelatedWork W2188368097 @default.
- W137000543 hasRelatedWork W220313 @default.
- W137000543 hasRelatedWork W2335152821 @default.
- W137000543 hasRelatedWork W2502372580 @default.
- W137000543 hasRelatedWork W2597525767 @default.
- W137000543 hasRelatedWork W2735010872 @default.
- W137000543 hasRelatedWork W2758535392 @default.
- W137000543 hasRelatedWork W2908275759 @default.
- W137000543 hasRelatedWork W2911933223 @default.
- W137000543 hasRelatedWork W2949470395 @default.
- W137000543 hasRelatedWork W2951422789 @default.
- W137000543 hasRelatedWork W2961969199 @default.
- W137000543 hasRelatedWork W2976725733 @default.
- W137000543 hasRelatedWork W3118441394 @default.
- W137000543 hasRelatedWork W3136732307 @default.
- W137000543 hasRelatedWork W3152483850 @default.
- W137000543 isParatext "false" @default.
- W137000543 isRetracted "false" @default.
- W137000543 magId "137000543" @default.
- W137000543 workType "article" @default.