{"id":"https://openalex.org/W2218916852","doi":"https://doi.org/10.1109/tnnls.2016.2601307","title":"Riemannian Dictionary Learning and Sparse Coding for Positive Definite Matrices","display_name":"Riemannian Dictionary Learning and Sparse Coding for Positive Definite Matrices","publication_year":2016,"publication_date":"2016-09-13","ids":{"openalex":"https://openalex.org/W2218916852","doi":"https://doi.org/10.1109/tnnls.2016.2601307","mag":"2218916852","pmid":"https://pubmed.ncbi.nlm.nih.gov/28113681"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2016.2601307","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2016.2601307","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Neural Networks and Learning Systems","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1507.02772","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024613828","display_name":"Anoop Cherian","orcid":"https://orcid.org/0000-0002-5566-0351"},"institutions":[{"id":"https://openalex.org/I118347636","display_name":"Australian National University","ror":"https://ror.org/019wvm592","country_code":"AU","type":"education","lineage":["https://openalex.org/I118347636"]},{"id":"https://openalex.org/I2802348851","display_name":"Vision Australia","ror":"https://ror.org/05vje5x10","country_code":"AU","type":"nonprofit","lineage":["https://openalex.org/I2802348851"]},{"id":"https://openalex.org/I4210127558","display_name":"Australian Centre for Robotic Vision","ror":"https://ror.org/02zv9xv82","country_code":"AU","type":"facility","lineage":["https://openalex.org/I4210127558"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Anoop Cherian","raw_affiliation_strings":["Australian Centre for Robotic Vision, Australian National University, Canberra, ANU, Australia","[Australian Centre for Robotic Vision, Australian National University, Canberra, ANU, Australia]"],"affiliations":[{"raw_affiliation_string":"Australian Centre for Robotic Vision, Australian National University, Canberra, ANU, Australia","institution_ids":["https://openalex.org/I4210127558","https://openalex.org/I2802348851","https://openalex.org/I118347636"]},{"raw_affiliation_string":"[Australian Centre for Robotic Vision, Australian National University, Canberra, ANU, Australia]","institution_ids":["https://openalex.org/I4210127558","https://openalex.org/I2802348851","https://openalex.org/I118347636"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058767558","display_name":"Suvrit Sra","orcid":"https://orcid.org/0000-0001-8516-4925"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Suvrit Sra","raw_affiliation_strings":["Laboratory of Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, MIT, USA","[Laboratory of Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, MIT, USA]"],"affiliations":[{"raw_affiliation_string":"Laboratory of Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, MIT, USA","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"[Laboratory of Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, MIT, USA]","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5024613828"],"corresponding_institution_ids":["https://openalex.org/I118347636","https://openalex.org/I2802348851","https://openalex.org/I4210127558"],"apc_list":null,"apc_paid":null,"fwci":1.1825,"has_fulltext":true,"cited_by_count":11,"citation_normalized_percentile":{"value":0.84558751,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"28","issue":"12","first_page":"2859","last_page":"2871"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9984999895095825,"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/T10057","display_name":"Face and Expression Recognition","score":0.9984999895095825,"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/T10627","display_name":"Advanced Image and Video Retrieval Techniques","score":0.9976000189781189,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/neural-coding","display_name":"Neural coding","score":0.5964898467063904},{"id":"https://openalex.org/keywords/riemannian-geometry","display_name":"Riemannian geometry","score":0.5716925859451294},{"id":"https://openalex.org/keywords/conic-section","display_name":"Conic section","score":0.5006632804870605},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.494655579328537},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.48419955372810364},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.4795365333557129},{"id":"https://openalex.org/keywords/k-svd","display_name":"K-SVD","score":0.4715440571308136},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.47147348523139954},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.4616900682449341},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.45040684938430786},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4239116609096527},{"id":"https://openalex.org/keywords/sparse-approximation","display_name":"Sparse approximation","score":0.42108193039894104},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.392220675945282},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.3395228385925293},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.23182591795921326},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13031312823295593}],"concepts":[{"id":"https://openalex.org/C77637269","wikidata":"https://www.wikidata.org/wiki/Q7002051","display_name":"Neural coding","level":2,"score":0.5964898467063904},{"id":"https://openalex.org/C181104567","wikidata":"https://www.wikidata.org/wiki/Q761383","display_name":"Riemannian geometry","level":2,"score":0.5716925859451294},{"id":"https://openalex.org/C108598597","wikidata":"https://www.wikidata.org/wiki/Q124255","display_name":"Conic section","level":2,"score":0.5006632804870605},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.494655579328537},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.48419955372810364},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.4795365333557129},{"id":"https://openalex.org/C154771677","wikidata":"https://www.wikidata.org/wiki/Q17098361","display_name":"K-SVD","level":3,"score":0.4715440571308136},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.47147348523139954},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.4616900682449341},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.45040684938430786},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4239116609096527},{"id":"https://openalex.org/C124066611","wikidata":"https://www.wikidata.org/wiki/Q28684319","display_name":"Sparse approximation","level":2,"score":0.42108193039894104},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.392220675945282},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3395228385925293},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.23182591795921326},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13031312823295593},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1109/tnnls.2016.2601307","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2016.2601307","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Neural Networks and Learning Systems","raw_type":"journal-article"},{"id":"pmid:28113681","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/28113681","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on neural networks and learning systems","raw_type":null},{"id":"pmh:oai:arXiv.org:1507.02772","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1507.02772","pdf_url":"https://arxiv.org/pdf/1507.02772","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"raw_type":"text"},{"id":"mag:2218916852","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1507.02772.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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},{"id":"pmh:oai:openresearch-repository.anu.edu.au:1885/247768","is_oa":false,"landing_page_url":"https://openresearch-repository.anu.edu.au/bitstream/1885/247768/3/01_Cherian_Riemannian_Dictionary_Learning_2017.pdf.jpg","pdf_url":null,"source":{"id":"https://openalex.org/S4306402539","display_name":"ANU Open Research (Australian National University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I118347636","host_organization_name":"Australian National University","host_organization_lineage":["https://openalex.org/I118347636"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Neural Networks and Learning Systems","raw_type":"Journal article"},{"id":"doi:10.48550/arxiv.1507.02772","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1507.02772","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1507.02772","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1507.02772","pdf_url":"https://arxiv.org/pdf/1507.02772","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"raw_type":"text"},"sustainable_development_goals":[{"display_name":"Quality Education","id":"https://metadata.un.org/sdg/4","score":0.6899999976158142}],"awards":[{"id":"https://openalex.org/G3800762947","display_name":null,"funder_award_id":"CE140100016","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"}],"funders":[{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2218916852.pdf","grobid_xml":"https://content.openalex.org/works/W2218916852.grobid-xml"},"referenced_works_count":63,"referenced_works":["https://openalex.org/W92310073","https://openalex.org/W1141113796","https://openalex.org/W1479760883","https://openalex.org/W1483531051","https://openalex.org/W1483804921","https://openalex.org/W1549083695","https://openalex.org/W1585720092","https://openalex.org/W1606263802","https://openalex.org/W1862697533","https://openalex.org/W1961095629","https://openalex.org/W1964321627","https://openalex.org/W1978100686","https://openalex.org/W1981560592","https://openalex.org/W1983496390","https://openalex.org/W2004996467","https://openalex.org/W2008732654","https://openalex.org/W2009799921","https://openalex.org/W2017262657","https://openalex.org/W2019464758","https://openalex.org/W2039051707","https://openalex.org/W2047508432","https://openalex.org/W2048192550","https://openalex.org/W2055597244","https://openalex.org/W2056380775","https://openalex.org/W2062677035","https://openalex.org/W2076605490","https://openalex.org/W2098699644","https://openalex.org/W2103096501","https://openalex.org/W2110662303","https://openalex.org/W2111339618","https://openalex.org/W2116836863","https://openalex.org/W2118163005","https://openalex.org/W2122378993","https://openalex.org/W2125389556","https://openalex.org/W2129812935","https://openalex.org/W2133848164","https://openalex.org/W2142040002","https://openalex.org/W2147942061","https://openalex.org/W2154059477","https://openalex.org/W2156222070","https://openalex.org/W2158225132","https://openalex.org/W2160547390","https://openalex.org/W2164647001","https://openalex.org/W2165797462","https://openalex.org/W2167164761","https://openalex.org/W2167623372","https://openalex.org/W2223353064","https://openalex.org/W2242953327","https://openalex.org/W2321395385","https://openalex.org/W2443864910","https://openalex.org/W2949406149","https://openalex.org/W2950254505","https://openalex.org/W2963532276","https://openalex.org/W2963959237","https://openalex.org/W4206310440","https://openalex.org/W4206551434","https://openalex.org/W6662335928","https://openalex.org/W6676630944","https://openalex.org/W6677219054","https://openalex.org/W6677527051","https://openalex.org/W6681717327","https://openalex.org/W6684641359","https://openalex.org/W6688755868"],"related_works":["https://openalex.org/W2962905348","https://openalex.org/W2396696339","https://openalex.org/W1804110266","https://openalex.org/W2169579681","https://openalex.org/W2528144786","https://openalex.org/W1961095629","https://openalex.org/W3093889873","https://openalex.org/W2804193236","https://openalex.org/W3203819040","https://openalex.org/W2600467585","https://openalex.org/W3127442541","https://openalex.org/W2795353055","https://openalex.org/W2776085193","https://openalex.org/W2971312107","https://openalex.org/W2903561637","https://openalex.org/W1515954165","https://openalex.org/W1983496390","https://openalex.org/W1479760883","https://openalex.org/W2295272704","https://openalex.org/W1674203940"],"abstract_inverted_index":{"Data":[0],"encoded":[1],"as":[2,86],"symmetric":[3,31],"positive":[4],"definite":[5],"(SPD)":[6],"matrices":[7,21,85],"frequently":[8],"arise":[9],"in":[10,50,73,80,114],"many":[11],"areas":[12],"of":[13,26,30,38,61,83,90],"computer":[14,140],"vision":[15,141],"and":[16,64,147],"machine":[17],"learning.":[18],"While":[19],"these":[20],"form":[22,82],"an":[23],"open":[24],"subset":[25],"the":[27,36,58,81,116,122],"Euclidean":[28],"space":[29],"matrices,":[32],"viewing":[33],"them":[34],"through":[35],"lens":[37],"non-Euclidean":[39],"Riemannian":[40],"(Riem)":[41],"geometry":[42],"often":[43],"turns":[44],"out":[45],"to":[46,77],"be":[47],"better":[48],"suited":[49],"capturing":[51],"several":[52,139],"desirable":[53],"data":[54,79,142],"properties.":[55],"Inspired":[56],"by":[57],"great":[59],"success":[60],"dictionary":[62,96],"learning":[63],"sparse":[65,87],"coding":[66],"(DLSC)":[67],"for":[68,112,133],"vector-valued":[69],"data,":[70],"our":[71,135,151],"goal":[72],"this":[74],"paper":[75],"is":[76,119],"represent":[78],"SPD":[84,91],"conic":[88],"combinations":[89],"atoms":[92],"from":[93],"a":[94,98,107,129],"learned":[95],"via":[97,121,157],"Riem":[99,109,124],"geometric":[100],"approach.":[101],"To":[102],"that":[103],"end,":[104],"we":[105],"formulate":[106],"novel":[108],"optimization":[110],"objective":[111],"DLSC,":[113],"which":[115],"representation":[117],"loss":[118],"characterized":[120],"affine-invariant":[123],"metric.":[125],"We":[126],"also":[127],"present":[128],"computationally":[130],"simple":[131],"algorithm":[132],"optimizing":[134],"model.":[136],"Experiments":[137],"on":[138],"sets":[143],"demonstrate":[144],"superior":[145],"classification":[146],"retrieval":[148],"performance":[149],"using":[150],"approach":[152],"when":[153],"compared":[154],"with":[155],"SC":[156],"alternative":[158],"non-Riem":[159],"formulations.":[160]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":5}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}