{"id":"https://openalex.org/W1506534972","doi":null,"title":"Stochastic Covariance Compression.","display_name":"Stochastic Covariance Compression.","publication_year":2014,"publication_date":"2014-12-04","ids":{"openalex":"https://openalex.org/W1506534972","mag":"1506534972"},"language":"en","primary_location":{"id":"mag:1506534972","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/1412.1740v1","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/abs/1412.1740v1","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5108523545","display_name":"Matt J. Kusner","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Matt J. Kusner","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084487169","display_name":"Nicholas Kolkin","orcid":"https://orcid.org/0000-0003-1233-1969","observed_orcids":["https://orcid.org/0000-0003-1233-1969"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nicholas Kolkin","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-1233-1969","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073763227","display_name":"Stephen Tyree","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Stephen Tyree","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5006380227","display_name":"Kilian Q. Weinberger","orcid":"https://orcid.org/0009-0008-9313-7239","observed_orcids":["https://orcid.org/0009-0008-9313-7239"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kilian Q. Weinberger","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10627","display_name":"Advanced Image and Video Retrieval Techniques","score":0.5038999915122986,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10627","display_name":"Advanced Image and Video Retrieval Techniques","score":0.5038999915122986,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10824","display_name":"Image Retrieval and Classification Techniques","score":0.4000999927520752,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.019999999552965164,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/symmetric-positive-definite-matrices","display_name":"symmetric positive definite matrices","score":0.8529999852180481},{"id":"https://openalex.org/keywords/riemannian-manifolds","display_name":"Riemannian manifolds","score":0.8190000057220459},{"id":"https://openalex.org/keywords/k-nearest-neighbors","display_name":"k-nearest neighbors","score":0.7419999837875366},{"id":"https://openalex.org/keywords/image-descriptors","display_name":"image descriptors","score":0.8140000104904175},{"id":"https://openalex.org/keywords/covariance-features","display_name":"covariance features","score":0.5450000166893005},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"dimensionality reduction","score":0.7680000066757202},{"id":"https://openalex.org/keywords/non-euclidean-metrics","display_name":"non-Euclidean metrics","score":0.5699999928474426}],"concepts":[{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.7381762862205505},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5647150874137878},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5232802033424377},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.5191444754600525},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5175975561141968},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.49434423446655273},{"id":"https://openalex.org/C148893098","wikidata":"https://www.wikidata.org/wiki/Q7295778","display_name":"Rational quadratic covariance function","level":5,"score":0.48370200395584106},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.48154857754707336},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.4690172076225281},{"id":"https://openalex.org/C113238511","wikidata":"https://www.wikidata.org/wiki/Q1071612","display_name":"k-nearest neighbors algorithm","level":2,"score":0.4689485728740692},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.467276930809021},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4665301442146301},{"id":"https://openalex.org/C58489278","wikidata":"https://www.wikidata.org/wiki/Q1172284","display_name":"Data set","level":2,"score":0.46171116828918457},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.4409993588924408},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.4296242594718933},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.42191046476364136},{"id":"https://openalex.org/C180877172","wikidata":"https://www.wikidata.org/wiki/Q5401390","display_name":"Estimation of covariance matrices","level":3,"score":0.4042947590351105},{"id":"https://openalex.org/C83042196","wikidata":"https://www.wikidata.org/wiki/Q5178898","display_name":"Covariance intersection","level":4,"score":0.32124853134155273},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.18091866374015808},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.12633097171783447},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:1506534972","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/1412.1740v1","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null}],"best_oa_location":{"id":"mag:1506534972","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/1412.1740v1","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W100531594","https://openalex.org/W202805564","https://openalex.org/W1484228140","https://openalex.org/W1490682695","https://openalex.org/W1566135517","https://openalex.org/W1571061365","https://openalex.org/W1629559917","https://openalex.org/W1862697533","https://openalex.org/W1928707779","https://openalex.org/W1969294188","https://openalex.org/W1979740015","https://openalex.org/W1983496390","https://openalex.org/W1983734765","https://openalex.org/W1990863955","https://openalex.org/W2017814585","https://openalex.org/W2057175746","https://openalex.org/W2093191240","https://openalex.org/W2096484739","https://openalex.org/W2099095260","https://openalex.org/W2106053110","https://openalex.org/W2107034620","https://openalex.org/W2117616929","https://openalex.org/W2133848164","https://openalex.org/W2137243801","https://openalex.org/W2138457014","https://openalex.org/W2143668817","https://openalex.org/W2144502914","https://openalex.org/W2144935315","https://openalex.org/W2145023731","https://openalex.org/W2151103935","https://openalex.org/W2153602280","https://openalex.org/W2156222070","https://openalex.org/W2157444450","https://openalex.org/W2158131535","https://openalex.org/W2161969291","https://openalex.org/W2162915993","https://openalex.org/W2163380389","https://openalex.org/W2165574896","https://openalex.org/W2165797462","https://openalex.org/W2166334548","https://openalex.org/W2168873314","https://openalex.org/W2171235719","https://openalex.org/W2172127734","https://openalex.org/W2177274842","https://openalex.org/W2187089797","https://openalex.org/W2294370754"],"related_works":["https://openalex.org/W1639285816","https://openalex.org/W2138457014","https://openalex.org/W2200039916","https://openalex.org/W2125959799","https://openalex.org/W2949246918","https://openalex.org/W2807878861","https://openalex.org/W2955137480","https://openalex.org/W3023245712","https://openalex.org/W2166334548","https://openalex.org/W2512601085"],"abstract_inverted_index":{"Covariance":[0,84],"matrices":[1,95],"are":[2,20,35,56],"an":[3,86],"effective":[4],"way":[5],"to":[6,52,58,96,114,122,146],"capture":[7],"global":[8],"spread":[9],"across":[10],"local":[11],"interest":[12],"points":[13],"in":[14,69,72,117],"images.":[15],"Often,":[16],"these":[17],"image":[18],"descriptors":[19],"more":[21],"compact,":[22],"robust":[23],"and":[24,37,41,60,116,168],"informative":[25],"than,":[26],"for":[27],"example,":[28],"bags":[29],"of":[30,65,93,124,134,165],"visual":[31],"words.":[32],"However,":[33],"they":[34],"symmetric":[36],"positive":[38],"definite":[39],"(SPD)":[40],"therefore":[42],"live":[43],"on":[44,149],"a":[45,90,97,163],"non-Euclidean":[46,53],"Riemannian":[47],"manifold,":[48],"which":[49],"gives":[50],"rise":[51],"metrics.":[54],"These":[55],"slow":[57],"compute":[59],"can":[61,109],"make":[62],"the":[63,111,131,141,156,166],"use":[64],"covariance":[66],"features":[67],"prohibitive":[68],"many":[70],"settings,":[71],"particular":[73],"k-nearest":[74],"neighbors":[75],"(kNN)":[76],"classification.":[77,137],"In":[78,138],"this":[79],"paper":[80],"we":[81,108],"present":[82],"Stochastic":[83],"Compression,":[85],"algorithm":[87],"that":[88,107],"compresses":[89],"data":[91,112,158],"set":[92,100,143],"SPD":[94],"much":[98],"smaller":[99],"with":[101],"similar":[102],"kNN":[103,136,150],"characteristics.":[104],"We":[105],"show":[106],"reduce":[110],"sets":[113],"1/6":[115],"some":[118],"cases":[119],"even":[120,154],"up":[121],"1/50":[123],"their":[125],"original":[126,157],"size,":[127],"while":[128,160],"approximately":[129],"matching":[130],"test":[132],"error":[133],"full":[135],"fact,":[139],"because":[140],"compressed":[142],"is":[144],"learned":[145],"perform":[147],"well":[148],"tasks,":[151],"it":[152],"sometimes":[153],"outperforms":[155],"set,":[159],"requiring":[161],"only":[162],"fraction":[164],"space":[167],"drastically":[169],"reduced":[170],"test-time":[171],"computation.":[172]},"counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2026-09-21T07:43:02.447757","created_date":"2016-06-24T00:00:00"}