{"id":"https://openalex.org/W1983334819","doi":"https://doi.org/10.1109/cvpr.2010.5539962","title":"Modeling pixel means and covariances using factorized third-order boltzmann machines","display_name":"Modeling pixel means and covariances using factorized third-order boltzmann machines","publication_year":2010,"publication_date":"2010-06-01","ids":{"openalex":"https://openalex.org/W1983334819","doi":"https://doi.org/10.1109/cvpr.2010.5539962","mag":"1983334819"},"language":"en","primary_location":{"id":"doi:10.1109/cvpr.2010.5539962","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cvpr.2010.5539962","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111465122","display_name":"Marc\u2019Aurelio Ranzato","orcid":null},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Marc'Aurelio Ranzato","raw_affiliation_strings":["Department of Computer Science, University of Toronto, Toronto, Canada","Department of Computer Science - University of Toronto, 10 King's College Road, Toronto, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Toronto, Toronto, Canada","institution_ids":["https://openalex.org/I185261750"]},{"raw_affiliation_string":"Department of Computer Science - University of Toronto, 10 King's College Road, Toronto, Canada","institution_ids":["https://openalex.org/I185261750"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108093963","display_name":"Geoffrey E. Hinton","orcid":null},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Geoffrey E. Hinton","raw_affiliation_strings":["Department of Computer Science, University of Toronto, Toronto, Canada","Department of Computer Science - University of Toronto, 10 King's College Road, Toronto, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Toronto, Toronto, Canada","institution_ids":["https://openalex.org/I185261750"]},{"raw_affiliation_string":"Department of Computer Science - University of Toronto, 10 King's College Road, Toronto, Canada","institution_ids":["https://openalex.org/I185261750"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5111465122"],"corresponding_institution_ids":["https://openalex.org/I185261750"],"apc_list":null,"apc_paid":null,"fwci":39.9468,"has_fulltext":false,"cited_by_count":224,"citation_normalized_percentile":{"value":0.99843176,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"2551","last_page":"2558"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10320","display_name":"Neural Networks and Applications","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T12859","display_name":"Cell Image Analysis Techniques","score":0.9890999794006348,"subfield":{"id":"https://openalex.org/subfields/1304","display_name":"Biophysics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.9819999933242798,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6754640340805054},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.6263964772224426},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.6087523698806763},{"id":"https://openalex.org/keywords/pixel","display_name":"Pixel","score":0.5642009377479553},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.53938889503479},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.5208216905593872},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.4872421324253082},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.4688606858253479},{"id":"https://openalex.org/keywords/boltzmann-machine","display_name":"Boltzmann machine","score":0.46000009775161743},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4389953911304474},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.43710723519325256},{"id":"https://openalex.org/keywords/generative-model","display_name":"Generative model","score":0.43537187576293945},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.42305296659469604},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.4138030707836151},{"id":"https://openalex.org/keywords/mixture-model","display_name":"Mixture model","score":0.410395085811615},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2831944227218628},{"id":"https://openalex.org/keywords/generative-grammar","display_name":"Generative grammar","score":0.26804104447364807},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.258347749710083},{"id":"https://openalex.org/keywords/deep-learning","display_name":"Deep learning","score":0.2292511761188507},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.14876538515090942}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6754640340805054},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.6263964772224426},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.6087523698806763},{"id":"https://openalex.org/C160633673","wikidata":"https://www.wikidata.org/wiki/Q355198","display_name":"Pixel","level":2,"score":0.5642009377479553},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.53938889503479},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.5208216905593872},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.4872421324253082},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.4688606858253479},{"id":"https://openalex.org/C192576344","wikidata":"https://www.wikidata.org/wiki/Q194706","display_name":"Boltzmann machine","level":3,"score":0.46000009775161743},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4389953911304474},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.43710723519325256},{"id":"https://openalex.org/C167966045","wikidata":"https://www.wikidata.org/wiki/Q5532625","display_name":"Generative model","level":3,"score":0.43537187576293945},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.42305296659469604},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.4138030707836151},{"id":"https://openalex.org/C61224824","wikidata":"https://www.wikidata.org/wiki/Q2260434","display_name":"Mixture model","level":2,"score":0.410395085811615},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2831944227218628},{"id":"https://openalex.org/C39890363","wikidata":"https://www.wikidata.org/wiki/Q36108","display_name":"Generative grammar","level":2,"score":0.26804104447364807},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.258347749710083},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.2292511761188507},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.14876538515090942},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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":2,"locations":[{"id":"doi:10.1109/cvpr.2010.5539962","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cvpr.2010.5539962","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.165.2794","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.165.2794","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://learning.cs.toronto.edu/%7Ehinton/absps/ranzato_cvpr2010.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.4000000059604645}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W1566135517","https://openalex.org/W1567512734","https://openalex.org/W1578197944","https://openalex.org/W1641020902","https://openalex.org/W2020604100","https://openalex.org/W2025768430","https://openalex.org/W2100495367","https://openalex.org/W2105464873","https://openalex.org/W2108581046","https://openalex.org/W2110163763","https://openalex.org/W2110176223","https://openalex.org/W2110798204","https://openalex.org/W2111842831","https://openalex.org/W2116064496","https://openalex.org/W2119938170","https://openalex.org/W2122922389","https://openalex.org/W2125027820","https://openalex.org/W2130325614","https://openalex.org/W2131686571","https://openalex.org/W2134653808","https://openalex.org/W2136163184","https://openalex.org/W2136922672","https://openalex.org/W2139427956","https://openalex.org/W2140262144","https://openalex.org/W2142615865","https://openalex.org/W2145607950","https://openalex.org/W2151103935","https://openalex.org/W2154956324","https://openalex.org/W2161000554","https://openalex.org/W2161969291","https://openalex.org/W2165225968","https://openalex.org/W2546302380","https://openalex.org/W3070706509","https://openalex.org/W3118608800","https://openalex.org/W4285719527","https://openalex.org/W6634886587","https://openalex.org/W6676481782","https://openalex.org/W6676581180","https://openalex.org/W6677760137","https://openalex.org/W6680246460","https://openalex.org/W6683775911","https://openalex.org/W6684349851","https://openalex.org/W6787972765"],"related_works":["https://openalex.org/W2916681395","https://openalex.org/W2529583158","https://openalex.org/W1575733688","https://openalex.org/W2963348254","https://openalex.org/W1489099099","https://openalex.org/W2886934452","https://openalex.org/W1974955043","https://openalex.org/W2171145682","https://openalex.org/W4360831753","https://openalex.org/W2808857225"],"abstract_inverted_index":{"Learning":[0],"a":[1,8,58,67,76,96,109],"generative":[2],"model":[3,69,91,100],"of":[4,11,41,57,86,124],"natural":[5,125],"images":[6,126],"is":[7],"useful":[9],"way":[10],"extracting":[12],"features":[13,32,89,130],"that":[14,70,90,99,105,131],"capture":[15],"interesting":[16],"regularities.":[17],"Previous":[18],"work":[19],"on":[20,26,46,136],"learning":[21],"such":[22],"models":[23],"has":[24],"focused":[25],"methods":[27,47],"in":[28,48],"which":[29,49],"the":[30,37,50,54,92,101,113,137],"latent":[31,88],"are":[33],"used":[34,115],"to":[35],"determine":[36,53],"mean":[38],"and":[39,95,127],"variance":[40],"each":[42,81],"pixel":[43],"independently,":[44],"or":[45],"hidden":[51],"units":[52],"covariance":[55,94],"matrix":[56],"zero-mean":[59],"Gaussian":[60],"distribution.":[61],"In":[62],"this":[63,106],"work,":[64],"we":[65],"propose":[66],"probabilistic":[68,110],"combines":[71],"these":[72],"two":[73],"approaches":[74],"into":[75],"single":[77],"framework.":[78],"We":[79,103],"represent":[80],"image":[82],"using":[83],"one":[84],"set":[85,98],"binary":[87],"image-specific":[93],"separate":[97],"mean.":[102],"show":[104],"approach":[107],"provides":[108],"framework":[111],"for":[112],"widely":[114],"simple-cell":[116],"complex-cell":[117],"architecture,":[118],"it":[119,128],"produces":[120],"very":[121],"realistic":[122],"samples":[123],"extracts":[129],"yield":[132],"state-of-the-art":[133],"recognition":[134],"accuracy":[135],"challenging":[138],"CIFAR":[139],"10":[140],"dataset.":[141]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":16},{"year":2018,"cited_by_count":16},{"year":2017,"cited_by_count":22},{"year":2016,"cited_by_count":23},{"year":2015,"cited_by_count":18},{"year":2014,"cited_by_count":27},{"year":2013,"cited_by_count":20},{"year":2012,"cited_by_count":27}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
