{"id":"https://openalex.org/W2950919324","doi":"https://doi.org/10.1561/2200000055","title":"Generalized Low Rank Models","display_name":"Generalized Low Rank Models","publication_year":2016,"publication_date":"2016-06-23","ids":{"openalex":"https://openalex.org/W2950919324","doi":"https://doi.org/10.1561/2200000055","mag":"2950919324"},"language":"en","primary_location":{"id":"doi:10.1561/2200000055","is_oa":false,"landing_page_url":"https://doi.org/10.1561/2200000055","pdf_url":null,"source":{"id":"https://openalex.org/S4210188176","display_name":"Foundations and Trends\u00ae in Machine Learning","issn_l":"1935-8237","issn":["1935-8237","1935-8245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318575","host_organization_name":"Now Publishers","host_organization_lineage":["https://openalex.org/P4310318575"],"host_organization_lineage_names":["Now Publishers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations and Trends\u00ae in Machine Learning","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1410.0342","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084564811","display_name":"Madeleine Udell","orcid":"https://orcid.org/0000-0002-3985-915X"},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Madeleine Udell","raw_affiliation_strings":["Operations Research and Information Engineering Cornell University","cornell University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Operations Research and Information Engineering Cornell University","institution_ids":["https://openalex.org/I205783295"]},{"raw_affiliation_string":"cornell University","institution_ids":["https://openalex.org/I205783295"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009242602","display_name":"Corinne Horn","orcid":null},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Corinne Horn","raw_affiliation_strings":["Electrical Engineering Stanford University","Stanford University ()"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electrical Engineering Stanford University","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"Stanford University ()","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110281879","display_name":"Reza Bosagh Zadeh","orcid":null},"institutions":[{"id":"https://openalex.org/I4210153325","display_name":"Institute of Mathematical Statistics","ror":"https://ror.org/043f04882","country_code":"US","type":"other","lineage":["https://openalex.org/I4210153325"]},{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Reza Zadeh","raw_affiliation_strings":["Computational and Mathematical Engineering Stanford University","Stanford University ()"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computational and Mathematical Engineering Stanford University","institution_ids":["https://openalex.org/I4210153325"]},{"raw_affiliation_string":"Stanford University ()","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011176205","display_name":"Stephen Boyd","orcid":"https://orcid.org/0000-0001-8353-6000"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Stephen Boyd","raw_affiliation_strings":["Electrical Engineering Stanford University","Stanford University ()"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electrical Engineering Stanford University","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"Stanford University ()","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.7053,"has_fulltext":true,"cited_by_count":19,"citation_normalized_percentile":{"value":0.92962349,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"9","issue":"1","first_page":"1","last_page":"118"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9976000189781189,"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"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9976000189781189,"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"}},{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9951000213623047,"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9851999878883362,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/matrix-decomposition","display_name":"Matrix decomposition","score":0.6467927694320679},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6071264743804932},{"id":"https://openalex.org/keywords/singular-value-decomposition","display_name":"Singular value decomposition","score":0.5946940183639526},{"id":"https://openalex.org/keywords/categorical-variable","display_name":"Categorical variable","score":0.5708054304122925},{"id":"https://openalex.org/keywords/missing-data","display_name":"Missing data","score":0.5197736620903015},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5142392516136169},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5130661725997925},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.5023353099822998},{"id":"https://openalex.org/keywords/data-set","display_name":"Data set","score":0.4893736243247986},{"id":"https://openalex.org/keywords/non-negative-matrix-factorization","display_name":"Non-negative matrix factorization","score":0.4754319190979004},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4680832028388977},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.458754301071167},{"id":"https://openalex.org/keywords/low-rank-approximation","display_name":"Low-rank approximation","score":0.454124391078949},{"id":"https://openalex.org/keywords/margin","display_name":"Margin (machine learning)","score":0.4511786699295044},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.4330301284790039},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.4129270613193512},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40679776668548584},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.3604382574558258},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.21814501285552979},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.15383023023605347},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.13982102274894714},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.09704786539077759}],"concepts":[{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.6467927694320679},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6071264743804932},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.5946940183639526},{"id":"https://openalex.org/C5274069","wikidata":"https://www.wikidata.org/wiki/Q2285707","display_name":"Categorical variable","level":2,"score":0.5708054304122925},{"id":"https://openalex.org/C9357733","wikidata":"https://www.wikidata.org/wiki/Q6878417","display_name":"Missing data","level":2,"score":0.5197736620903015},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5142392516136169},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5130661725997925},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.5023353099822998},{"id":"https://openalex.org/C58489278","wikidata":"https://www.wikidata.org/wiki/Q1172284","display_name":"Data set","level":2,"score":0.4893736243247986},{"id":"https://openalex.org/C152671427","wikidata":"https://www.wikidata.org/wiki/Q10843505","display_name":"Non-negative matrix factorization","level":4,"score":0.4754319190979004},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4680832028388977},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.458754301071167},{"id":"https://openalex.org/C90199385","wikidata":"https://www.wikidata.org/wiki/Q6692777","display_name":"Low-rank approximation","level":3,"score":0.454124391078949},{"id":"https://openalex.org/C774472","wikidata":"https://www.wikidata.org/wiki/Q6760393","display_name":"Margin (machine learning)","level":2,"score":0.4511786699295044},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.4330301284790039},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.4129270613193512},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40679776668548584},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3604382574558258},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.21814501285552979},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.15383023023605347},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.13982102274894714},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.09704786539077759},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C25023664","wikidata":"https://www.wikidata.org/wiki/Q1575637","display_name":"Hankel matrix","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1561/2200000055","is_oa":false,"landing_page_url":"https://doi.org/10.1561/2200000055","pdf_url":null,"source":{"id":"https://openalex.org/S4210188176","display_name":"Foundations and Trends\u00ae in Machine Learning","issn_l":"1935-8237","issn":["1935-8237","1935-8245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318575","host_organization_name":"Now Publishers","host_organization_lineage":["https://openalex.org/P4310318575"],"host_organization_lineage_names":["Now Publishers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations and Trends\u00ae in Machine Learning","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1410.0342","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1410.0342","pdf_url":"https://arxiv.org/pdf/1410.0342","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":"","raw_type":"text"},{"id":"mag:2950919324","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1410.0342.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:CiteSeerX.psu:10.1.1.681.9416","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.681.9416","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://stanford.edu/%7Erezab/papers/glrm.pdf","raw_type":"text"},{"id":"pmh:oai:cds.cern.ch:2761916","is_oa":false,"landing_page_url":"http://cds.cern.ch/record/2761916","pdf_url":null,"source":{"id":"https://openalex.org/S4306402195","display_name":"CERN Document Server (European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},{"id":"doi:10.48550/arxiv.1410.0342","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1410.0342","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:1410.0342","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1410.0342","pdf_url":"https://arxiv.org/pdf/1410.0342","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":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6109515352","display_name":null,"funder_award_id":"DGE-1147470","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320332180","display_name":"Defense Advanced Research Projects Agency","ror":"https://ror.org/02caytj08"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2950919324.pdf","grobid_xml":"https://content.openalex.org/works/W2950919324.grobid-xml"},"referenced_works_count":138,"referenced_works":["https://openalex.org/W138552861","https://openalex.org/W653924242","https://openalex.org/W1503442267","https://openalex.org/W1509803206","https://openalex.org/W1542014621","https://openalex.org/W1568698519","https://openalex.org/W1614298861","https://openalex.org/W1676820704","https://openalex.org/W1798398164","https://openalex.org/W1823564171","https://openalex.org/W1902027874","https://openalex.org/W1904809838","https://openalex.org/W1912120252","https://openalex.org/W1962325108","https://openalex.org/W1968598835","https://openalex.org/W1975900269","https://openalex.org/W1976618413","https://openalex.org/W1986931325","https://openalex.org/W1987063155","https://openalex.org/W1989718642","https://openalex.org/W1992359411","https://openalex.org/W1994719275","https://openalex.org/W1995168330","https://openalex.org/W1996023858","https://openalex.org/W2003217181","https://openalex.org/W2004026774","https://openalex.org/W2004791924","https://openalex.org/W2005876975","https://openalex.org/W2017288758","https://openalex.org/W2025341678","https://openalex.org/W2027982384","https://openalex.org/W2039844283","https://openalex.org/W2041963641","https://openalex.org/W2043545458","https://openalex.org/W2044809283","https://openalex.org/W2059283452","https://openalex.org/W2071128523","https://openalex.org/W2071389326","https://openalex.org/W2073459066","https://openalex.org/W2074471762","https://openalex.org/W2076566842","https://openalex.org/W2078626246","https://openalex.org/W2083620785","https://openalex.org/W2087196505","https://openalex.org/W2088477804","https://openalex.org/W2089294058","https://openalex.org/W2093492509","https://openalex.org/W2095705004","https://openalex.org/W2097303721","https://openalex.org/W2098290597","https://openalex.org/W2102138843","https://openalex.org/W2102765684","https://openalex.org/W2103325283","https://openalex.org/W2105464873","https://openalex.org/W2105767123","https://openalex.org/W2106005123","https://openalex.org/W2109999391","https://openalex.org/W2110096996","https://openalex.org/W2112680395","https://openalex.org/W2113359929","https://openalex.org/W2113606819","https://openalex.org/W2116413942","https://openalex.org/W2116444583","https://openalex.org/W2117202609","https://openalex.org/W2117756735","https://openalex.org/W2117986441","https://openalex.org/W2118550318","https://openalex.org/W2118858274","https://openalex.org/W2119556711","https://openalex.org/W2120816706","https://openalex.org/W2122090912","https://openalex.org/W2122922389","https://openalex.org/W2124172487","https://openalex.org/W2124608575","https://openalex.org/W2125027820","https://openalex.org/W2127271355","https://openalex.org/W2127971792","https://openalex.org/W2128638419","https://openalex.org/W2130121108","https://openalex.org/W2131628350","https://openalex.org/W2133028937","https://openalex.org/W2133097426","https://openalex.org/W2133864802","https://openalex.org/W2133907989","https://openalex.org/W2134130436","https://openalex.org/W2134332047","https://openalex.org/W2135001774","https://openalex.org/W2135029798","https://openalex.org/W2138243089","https://openalex.org/W2138505091","https://openalex.org/W2139054653","https://openalex.org/W2139285440","https://openalex.org/W2143075842","https://openalex.org/W2144351558","https://openalex.org/W2144730813","https://openalex.org/W2144931885","https://openalex.org/W2145962650","https://openalex.org/W2146130798","https://openalex.org/W2150415460","https://openalex.org/W2150593711","https://openalex.org/W2151166364","https://openalex.org/W2153579005","https://openalex.org/W2157239837","https://openalex.org/W2157791002","https://openalex.org/W2159857890","https://openalex.org/W2160547390","https://openalex.org/W2160569988","https://openalex.org/W2161374719","https://openalex.org/W2162171343","https://openalex.org/W2164278908","https://openalex.org/W2165395308","https://openalex.org/W2165685007","https://openalex.org/W2165693128","https://openalex.org/W2172099713","https://openalex.org/W2189465200","https://openalex.org/W2250539671","https://openalex.org/W2258617614","https://openalex.org/W2275465943","https://openalex.org/W2294798173","https://openalex.org/W2296319761","https://openalex.org/W2322584079","https://openalex.org/W2336187369","https://openalex.org/W2467663826","https://openalex.org/W2553563233","https://openalex.org/W2913535645","https://openalex.org/W2949273884","https://openalex.org/W2951734015","https://openalex.org/W2951781666","https://openalex.org/W2952066970","https://openalex.org/W2952603020","https://openalex.org/W2952716509","https://openalex.org/W2953139536","https://openalex.org/W2953281140","https://openalex.org/W2999729612","https://openalex.org/W3099514962","https://openalex.org/W3099880660","https://openalex.org/W3104577407","https://openalex.org/W3143596294"],"related_works":["https://openalex.org/W2164616133","https://openalex.org/W2611328865","https://openalex.org/W2789229307","https://openalex.org/W3022251574","https://openalex.org/W2149532724","https://openalex.org/W2405493940","https://openalex.org/W293447437","https://openalex.org/W2949469590","https://openalex.org/W2616654950","https://openalex.org/W3016426920","https://openalex.org/W3018386064","https://openalex.org/W1826721227","https://openalex.org/W76897483","https://openalex.org/W2750458177","https://openalex.org/W2178047982","https://openalex.org/W3026594100","https://openalex.org/W2950894539","https://openalex.org/W2968571553","https://openalex.org/W2054141820","https://openalex.org/W2902307923"],"abstract_inverted_index":{"Principal":[0],"components":[1],"analysis":[2],"(PCA)":[3],"is":[4],"a":[5,10,15,94],"well-known":[6,45],"technique":[7],"for":[8,79,117],"approximating":[9],"tabular":[11],"data":[12,29,39,48,72,88],"set":[13],"by":[14],"low":[16,101,120],"rank":[17,102,121],"matrix.":[18],"Here,":[19],"we":[20],"extend":[21],"the":[22,100],"idea":[23],"of":[24,32,96,99,107,110],"PCA":[25],"to":[26,76],"handle":[27],"arbitrary":[28],"sets":[30],"consisting":[31],"numerical,":[33],"Boolean,":[34],"categorical,":[35],"ordinal,":[36],"and":[37,58,63,74,82,123,126],"other":[38],"types.":[40],"This":[41],"framework":[42],"encompasses":[43],"many":[44],"techniques":[46],"in":[47],"analysis,":[49],"such":[50],"as":[51],"nonnegative":[52],"matrix":[53,55,66],"factorization,":[54],"completion,":[56],"sparse":[57],"robust":[59],"PCA,":[60],"k-means,":[61],"k-SVD,":[62],"maximum":[64],"margin":[65],"factorization.":[67],"The":[68],"method":[69],"handles":[70],"heterogeneous":[71],"sets,":[73],"leads":[75],"coherent":[77],"schemes":[78],"compressing,":[80],"denoising,":[81],"imputing":[83],"missing":[84],"entries":[85],"across":[86],"all":[87],"types":[89],"simultaneously.":[90],"It":[91],"also":[92],"admits":[93],"number":[95],"interesting":[97],"interpretations":[98],"factors,":[103],"which":[104],"allow":[105],"clustering":[106],"examples":[108],"or":[109],"features.":[111],"We":[112],"propose":[113],"several":[114],"parallel":[115],"algorithms":[116],"fitting":[118],"generalized":[119],"models,":[122],"describe":[124],"implementations":[125],"numerical":[127],"results.":[128]},"counts_by_year":[{"year":2021,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
