{"id":"https://openalex.org/W3043936881","doi":"https://doi.org/10.1109/tsp.2021.3071293","title":"Positive Semidefinite Matrix Factorization: A Connection With Phase Retrieval and Affine Rank Minimization","display_name":"Positive Semidefinite Matrix Factorization: A Connection With Phase Retrieval and Affine Rank Minimization","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3043936881","doi":"https://doi.org/10.1109/tsp.2021.3071293","mag":"3043936881"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2021.3071293","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2021.3071293","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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 Signal Processing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2007.12364","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057160666","display_name":"Dana Lahat","orcid":"https://orcid.org/0000-0001-6179-0219"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I134560555","display_name":"Universit\u00e9 Toulouse III - Paul Sabatier","ror":"https://ror.org/02v6kpv12","country_code":"FR","type":"education","lineage":["https://openalex.org/I134560555"]},{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]},{"id":"https://openalex.org/I17866349","display_name":"Universit\u00e9 F\u00e9d\u00e9rale de Toulouse Midi-Pyr\u00e9n\u00e9es","ror":"https://ror.org/004raaa70","country_code":"FR","type":"education","lineage":["https://openalex.org/I17866349"]},{"id":"https://openalex.org/I3131550300","display_name":"Universit\u00e9 Toulouse-I-Capitole","ror":"https://ror.org/0443n9e75","country_code":"FR","type":"education","lineage":["https://openalex.org/I3131550300"]},{"id":"https://openalex.org/I4210119061","display_name":"Institut de Recherche en Informatique de Toulouse","ror":"https://ror.org/01rx4qw44","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I205747304","https://openalex.org/I4210119061","https://openalex.org/I4210152422","https://openalex.org/I4405258862","https://openalex.org/I4405259414"]},{"id":"https://openalex.org/I4210152422","display_name":"Universit\u00e9 Toulouse - Jean Jaur\u00e8s","ror":"https://ror.org/04ezk3x31","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210152422"]},{"id":"https://openalex.org/I4210160189","display_name":"Institut Polytechnique de Bordeaux","ror":"https://ror.org/054qv7y42","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210160189"]},{"id":"https://openalex.org/I79272384","display_name":"University of Maryland, Baltimore County","ror":"https://ror.org/02qskvh78","country_code":"US","type":"education","lineage":["https://openalex.org/I79272384"]}],"countries":["FR","IL","US"],"is_corresponding":false,"raw_author_name":"Dana Lahat","raw_affiliation_strings":["Department of Computer Science and Electrical Engineering, University of Maryland, Baltimore County, Baltimore, MD, USA","IRIT, Universit\u00e9 de Toulouse, CNRS, Toulouse, France","School of Electrical Engineering, Tel Aviv University, Tel Aviv, Israel"],"raw_orcid":"https://orcid.org/0000-0001-6179-0219","affiliations":[{"raw_affiliation_string":"Department of Computer Science and Electrical Engineering, University of Maryland, Baltimore County, Baltimore, MD, USA","institution_ids":["https://openalex.org/I79272384"]},{"raw_affiliation_string":"IRIT, Universit\u00e9 de Toulouse, CNRS, Toulouse, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I134560555","https://openalex.org/I17866349","https://openalex.org/I3131550300","https://openalex.org/I4210119061","https://openalex.org/I4210152422","https://openalex.org/I4210160189"]},{"raw_affiliation_string":"School of Electrical Engineering, Tel Aviv University, Tel Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108434862","display_name":"Yanbin Lang","orcid":null},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Yanbin Lang","raw_affiliation_strings":["Department of Mathematics, National University of Singapore, Singapore, Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, National University of Singapore, Singapore, Singapore","institution_ids":["https://openalex.org/I165932596"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058345431","display_name":"Vincent Y. F. Tan","orcid":"https://orcid.org/0000-0002-5008-4527"},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Vincent Y. F. Tan","raw_affiliation_strings":["Department of Mathematics, National University of Singapore, Singapore, Singapore"],"raw_orcid":"https://orcid.org/0000-0002-5008-4527","affiliations":[{"raw_affiliation_string":"Department of Mathematics, National University of Singapore, Singapore, Singapore","institution_ids":["https://openalex.org/I165932596"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022368934","display_name":"C\u00e9dric F\u00e9votte","orcid":"https://orcid.org/0000-0003-3801-5534"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I134560555","display_name":"Universit\u00e9 Toulouse III - Paul Sabatier","ror":"https://ror.org/02v6kpv12","country_code":"FR","type":"education","lineage":["https://openalex.org/I134560555"]},{"id":"https://openalex.org/I17866349","display_name":"Universit\u00e9 F\u00e9d\u00e9rale de Toulouse Midi-Pyr\u00e9n\u00e9es","ror":"https://ror.org/004raaa70","country_code":"FR","type":"education","lineage":["https://openalex.org/I17866349"]},{"id":"https://openalex.org/I3131550300","display_name":"Universit\u00e9 Toulouse-I-Capitole","ror":"https://ror.org/0443n9e75","country_code":"FR","type":"education","lineage":["https://openalex.org/I3131550300"]},{"id":"https://openalex.org/I4210119061","display_name":"Institut de Recherche en Informatique de Toulouse","ror":"https://ror.org/01rx4qw44","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I205747304","https://openalex.org/I4210119061","https://openalex.org/I4210152422","https://openalex.org/I4405258862","https://openalex.org/I4405259414"]},{"id":"https://openalex.org/I4210152422","display_name":"Universit\u00e9 Toulouse - Jean Jaur\u00e8s","ror":"https://ror.org/04ezk3x31","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210152422"]},{"id":"https://openalex.org/I4210160189","display_name":"Institut Polytechnique de Bordeaux","ror":"https://ror.org/054qv7y42","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210160189"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Cedric Fevotte","raw_affiliation_strings":["IRIT, Universit\u00e9 de Toulouse, CNRS, Toulouse, France"],"raw_orcid":"https://orcid.org/0000-0003-3801-5534","affiliations":[{"raw_affiliation_string":"IRIT, Universit\u00e9 de Toulouse, CNRS, Toulouse, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I134560555","https://openalex.org/I17866349","https://openalex.org/I3131550300","https://openalex.org/I4210119061","https://openalex.org/I4210152422","https://openalex.org/I4210160189"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":10,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3632,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.53933216,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":96},"biblio":{"volume":"69","issue":null,"first_page":"3059","last_page":"3074"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10638","display_name":"Optical measurement and interference techniques","score":0.9950000047683716,"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/T10638","display_name":"Optical measurement and interference techniques","score":0.9950000047683716,"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/T11183","display_name":"Advanced X-ray Imaging Techniques","score":0.9922999739646912,"subfield":{"id":"https://openalex.org/subfields/3108","display_name":"Radiation"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9884999990463257,"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/leverage","display_name":"Leverage (statistics)","score":0.5339606404304504},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5289444923400879},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5109121203422546},{"id":"https://openalex.org/keywords/phase-retrieval","display_name":"Phase retrieval","score":0.4883691668510437},{"id":"https://openalex.org/keywords/diagonal-matrix","display_name":"Diagonal matrix","score":0.48676466941833496},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.45719754695892334},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.4567105174064636},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.45258626341819763},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.42869138717651367},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3989940285682678},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3924919068813324},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.20522013306617737},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1412944793701172},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.08350464701652527}],"concepts":[{"id":"https://openalex.org/C153083717","wikidata":"https://www.wikidata.org/wiki/Q6535263","display_name":"Leverage (statistics)","level":2,"score":0.5339606404304504},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5289444923400879},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5109121203422546},{"id":"https://openalex.org/C81793267","wikidata":"https://www.wikidata.org/wiki/Q7180962","display_name":"Phase retrieval","level":3,"score":0.4883691668510437},{"id":"https://openalex.org/C113313756","wikidata":"https://www.wikidata.org/wiki/Q332791","display_name":"Diagonal matrix","level":3,"score":0.48676466941833496},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.45719754695892334},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.4567105174064636},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.45258626341819763},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.42869138717651367},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3989940285682678},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3924919068813324},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.20522013306617737},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1412944793701172},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.08350464701652527},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tsp.2021.3071293","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2021.3071293","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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 Signal Processing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2007.12364","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2007.12364","pdf_url":"https://arxiv.org/pdf/2007.12364","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,"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":"pmh:oai:HAL:hal-03431503v1","is_oa":true,"landing_page_url":"https://hal.science/hal-03431503","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://ieeexplore.ieee.org/document/9397331","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2007.12364","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2007.12364","pdf_url":"https://arxiv.org/pdf/2007.12364","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,"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":[],"awards":[{"id":"https://openalex.org/G1938070154","display_name":"Artificial and Natural Intelligence Toulouse Institute","funder_award_id":"ANR-19-P3IA-0004","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G4456762200","display_name":null,"funder_award_id":"R-263-000-D02-281","funder_id":"https://openalex.org/F4320320709","funder_display_name":"National Research Foundation Singapore"},{"id":"https://openalex.org/G839184950","display_name":null,"funder_award_id":"681839","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"}],"funders":[{"id":"https://openalex.org/F4320320709","display_name":"National Research Foundation Singapore","ror":"https://ror.org/03cpyc314"},{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320334678","display_name":"European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":69,"referenced_works":["https://openalex.org/W1189174436","https://openalex.org/W1573301526","https://openalex.org/W1656332724","https://openalex.org/W1841418289","https://openalex.org/W1884015253","https://openalex.org/W1902027874","https://openalex.org/W1945057103","https://openalex.org/W2000345836","https://openalex.org/W2001801912","https://openalex.org/W2003234507","https://openalex.org/W2003994949","https://openalex.org/W2022851313","https://openalex.org/W2039156581","https://openalex.org/W2054443446","https://openalex.org/W2058078260","https://openalex.org/W2059745395","https://openalex.org/W2061987651","https://openalex.org/W2066019014","https://openalex.org/W2078397124","https://openalex.org/W2087315461","https://openalex.org/W2102019642","https://openalex.org/W2117377454","https://openalex.org/W2118550318","https://openalex.org/W2119368733","https://openalex.org/W2123023890","https://openalex.org/W2129908708","https://openalex.org/W2138677859","https://openalex.org/W2140318696","https://openalex.org/W2142949395","https://openalex.org/W2143075842","https://openalex.org/W2152557171","https://openalex.org/W2228046375","https://openalex.org/W2274439720","https://openalex.org/W2296418040","https://openalex.org/W2515384464","https://openalex.org/W2542482481","https://openalex.org/W2610498683","https://openalex.org/W2738180706","https://openalex.org/W2744182242","https://openalex.org/W2786336660","https://openalex.org/W2963099043","https://openalex.org/W2963240866","https://openalex.org/W2963322354","https://openalex.org/W2963449128","https://openalex.org/W2963960631","https://openalex.org/W2964014592","https://openalex.org/W2971159456","https://openalex.org/W3012036708","https://openalex.org/W3016208248","https://openalex.org/W3022030295","https://openalex.org/W3042637182","https://openalex.org/W3099415239","https://openalex.org/W3102206315","https://openalex.org/W3103310796","https://openalex.org/W3105890898","https://openalex.org/W3123950972","https://openalex.org/W4299602245","https://openalex.org/W6627707193","https://openalex.org/W6634173106","https://openalex.org/W6636866650","https://openalex.org/W6638932063","https://openalex.org/W6639384702","https://openalex.org/W6680770193","https://openalex.org/W6694291848","https://openalex.org/W6697652323","https://openalex.org/W6746304332","https://openalex.org/W6767407871","https://openalex.org/W6776420164","https://openalex.org/W6780816284"],"related_works":["https://openalex.org/W2794559785","https://openalex.org/W2950281908","https://openalex.org/W1754499339","https://openalex.org/W2013873776","https://openalex.org/W3188285573","https://openalex.org/W1973739845","https://openalex.org/W119752240","https://openalex.org/W2324840593","https://openalex.org/W1992564042","https://openalex.org/W3118621910"],"abstract_inverted_index":{"Positive":[0],"semidefinite":[1,19],"matrix":[2,11,38],"factorization":[3],"(PSDMF)":[4],"expresses":[5],"each":[6],"entry":[7],"of":[8,16,76,115,120,139,175,236],"a":[9,60,74,102,136,173,198],"nonnegative":[10,37],"as":[12,109],"the":[13,54,67,116,127,192,213,237],"inner":[14],"product":[15],"two":[17],"positive":[18],"(psd)":[20],"matrices.":[21],"When":[22],"all":[23],"these":[24,240],"psd":[25],"matrices":[26],"are":[27,191],"constrained":[28],"to":[29,36,112,126,171,181,196,227],"be":[30,86],"diagonal,":[31],"this":[32,70,132],"model":[33],"is":[34,160],"equivalent":[35],"factorization.":[39],"Applications":[40],"include":[41],"combinatorial":[42],"optimization,":[43],"quantum-based":[44],"statistical":[45],"models,":[46],"and":[47,93,123,223,232],"recommender":[48],"systems,":[49],"among":[50,163],"others.":[51],"However,":[52],"despite":[53],"increasing":[55],"interest":[56],"in":[57,66,104],"PSDMF,":[58,79],"only":[59,193],"few":[61],"PSDMF":[62,83,107,128,140,154,164,214,230],"algorithms":[63,84,141,194],"were":[64],"proposed":[65,189],"literature.":[68],"In":[69,185,200],"work,":[71],"we":[72,134],"provide":[73],"collection":[75],"tools":[77],"for":[78],"by":[80,131],"showing":[81],"that":[82,158,167,212],"can":[85,216],"designed":[87],"based":[88,142,177],"on":[89,143,178],"phase":[90],"retrieval":[91],"(PR)":[92],"affine":[94],"rank":[95],"minimization":[96],"(ARM)":[97],"algorithms.":[98],"This":[99,148],"procedure":[100],"allows":[101,111],"shortcut":[103],"designing":[105],"new":[106,137],"algorithms,":[108,225,231],"it":[110,169],"leverage":[113],"some":[114],"useful":[117],"numerical":[118,219],"properties":[119,220],"existing":[121],"PR":[122,222],"ARM":[124,224],"methods":[125,176,190],"framework.":[129],"Motivated":[130],"idea,":[133],"introduce":[135],"family":[138,149],"iterative":[144],"hard":[145],"thresholding":[146],"(IHT).":[147],"subsumes":[150],"previously-proposed":[151],"projected":[152],"gradient":[153],"methods.":[155],"We":[156],"show":[157],"there":[159],"high":[161],"variability":[162],"optimization":[165],"problems":[166],"makes":[168],"beneficial":[170],"try":[172],"number":[174],"different":[179],"principles":[180],"tackle":[182],"difficult":[183],"problems.":[184],"certain":[186,201],"cases,":[187,203],"our":[188,210],"able":[195],"find":[197],"solution.":[199],"other":[202],"they":[204],"converge":[205],"faster.":[206],"Our":[207],"results":[208],"support":[209],"claim":[211],"framework":[215],"inherit":[217],"desired":[218],"from":[221],"leading":[226],"more":[228],"efficient":[229],"motivate":[233],"further":[234],"study":[235],"links":[238],"between":[239],"models.":[241]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":2}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-10T00:00:00"}