{"id":"https://openalex.org/W2964617280","doi":"https://doi.org/10.24963/ijcai.2019/183","title":"Non-smooth Optimization over Stiefel Manifolds with Applications to Dimensionality Reduction and Graph Clustering","display_name":"Non-smooth Optimization over Stiefel Manifolds with Applications to Dimensionality Reduction and Graph Clustering","publication_year":2019,"publication_date":"2019-07-28","ids":{"openalex":"https://openalex.org/W2964617280","doi":"https://doi.org/10.24963/ijcai.2019/183","mag":"2964617280"},"language":"en","primary_location":{"id":"doi:10.24963/ijcai.2019/183","is_oa":true,"landing_page_url":"https://doi.org/10.24963/ijcai.2019/183","pdf_url":"https://www.ijcai.org/proceedings/2019/0183.pdf","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.ijcai.org/proceedings/2019/0183.pdf","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002638643","display_name":"Fariba Zohrizadeh","orcid":null},"institutions":[{"id":"https://openalex.org/I189196454","display_name":"The University of Texas at Arlington","ror":"https://ror.org/019kgqr73","country_code":"US","type":"education","lineage":["https://openalex.org/I189196454"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Fariba Zohrizadeh","raw_affiliation_strings":["The University of Texas at Arlington"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The University of Texas at Arlington","institution_ids":["https://openalex.org/I189196454"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054855377","display_name":"Mohsen Kheirandishfard","orcid":null},"institutions":[{"id":"https://openalex.org/I189196454","display_name":"The University of Texas at Arlington","ror":"https://ror.org/019kgqr73","country_code":"US","type":"education","lineage":["https://openalex.org/I189196454"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mohsen Kheirandishfard","raw_affiliation_strings":["The University of Texas at Arlington"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The University of Texas at Arlington","institution_ids":["https://openalex.org/I189196454"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001793251","display_name":"Farhad Kamangar","orcid":"https://orcid.org/0000-0001-7204-0296"},"institutions":[{"id":"https://openalex.org/I189196454","display_name":"The University of Texas at Arlington","ror":"https://ror.org/019kgqr73","country_code":"US","type":"education","lineage":["https://openalex.org/I189196454"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Farhad Kamangar","raw_affiliation_strings":["The University of Texas at Arlington"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The University of Texas at Arlington","institution_ids":["https://openalex.org/I189196454"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015341130","display_name":"Ramtin Madani","orcid":"https://orcid.org/0000-0001-9246-2357"},"institutions":[{"id":"https://openalex.org/I189196454","display_name":"The University of Texas at Arlington","ror":"https://ror.org/019kgqr73","country_code":"US","type":"education","lineage":["https://openalex.org/I189196454"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ramtin Madani","raw_affiliation_strings":["The University of Texas at Arlington"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The University of Texas at Arlington","institution_ids":["https://openalex.org/I189196454"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I189196454"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.08256173,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"1319","last_page":"1326"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9983000159263611,"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":0.9983000159263611,"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":0.989300012588501,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9678999781608582,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/orthogonality","display_name":"Orthogonality","score":0.7198961973190308},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6111642122268677},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.5868951678276062},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.5721768140792847},{"id":"https://openalex.org/keywords/stiefel-manifold","display_name":"Stiefel manifold","score":0.5716269612312317},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4966798424720764},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4937528073787689},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.48944059014320374},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4786709249019623},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.47837844491004944},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4611836075782776},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.41636669635772705},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.41276800632476807},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41172608733177185},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3346344828605652},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.23707517981529236},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.19283324480056763}],"concepts":[{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.7198961973190308},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6111642122268677},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.5868951678276062},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.5721768140792847},{"id":"https://openalex.org/C612670","wikidata":"https://www.wikidata.org/wiki/Q7616373","display_name":"Stiefel manifold","level":2,"score":0.5716269612312317},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4966798424720764},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4937528073787689},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.48944059014320374},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4786709249019623},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.47837844491004944},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4611836075782776},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.41636669635772705},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.41276800632476807},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41172608733177185},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3346344828605652},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.23707517981529236},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.19283324480056763},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.24963/ijcai.2019/183","is_oa":true,"landing_page_url":"https://doi.org/10.24963/ijcai.2019/183","pdf_url":"https://www.ijcai.org/proceedings/2019/0183.pdf","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence","raw_type":"proceedings-article"}],"best_oa_location":{"id":"doi:10.24963/ijcai.2019/183","is_oa":true,"landing_page_url":"https://doi.org/10.24963/ijcai.2019/183","pdf_url":"https://www.ijcai.org/proceedings/2019/0183.pdf","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence","raw_type":"proceedings-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.6499999761581421}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2964617280.pdf","grobid_xml":"https://content.openalex.org/works/W2964617280.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W1524324710","https://openalex.org/W1888898201","https://openalex.org/W1967138577","https://openalex.org/W1972649461","https://openalex.org/W2020652789","https://openalex.org/W2045512849","https://openalex.org/W2102461053","https://openalex.org/W2111136894","https://openalex.org/W2123921160","https://openalex.org/W2125464731","https://openalex.org/W2146826069","https://openalex.org/W2147191758","https://openalex.org/W2156571432","https://openalex.org/W2165874743","https://openalex.org/W2177287823","https://openalex.org/W2295256067","https://openalex.org/W2572455488","https://openalex.org/W2604427716","https://openalex.org/W2741236095","https://openalex.org/W2787425086","https://openalex.org/W2962862352","https://openalex.org/W2963223119","https://openalex.org/W4205293427","https://openalex.org/W4292363360"],"related_works":["https://openalex.org/W1995622179","https://openalex.org/W1484111231","https://openalex.org/W4391160746","https://openalex.org/W1552543208","https://openalex.org/W2074396517","https://openalex.org/W2166963679","https://openalex.org/W2187269125","https://openalex.org/W1641615907","https://openalex.org/W3089231081","https://openalex.org/W2093956241"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2,33],"concerned":[3],"with":[4,11],"the":[5,44,47,83,86],"class":[6],"of":[7,46,85],"non-convex":[8,21,49],"optimization":[9],"problems":[10,24],"orthogonality":[12,22],"constraints.":[13],"We":[14],"develop":[15],"computationally":[16],"efficient":[17],"relaxations":[18],"that":[19,66],"transform":[20],"constrained":[23],"into":[25],"polynomial-time":[26],"solvable":[27],"surrogates.":[28],"A":[29],"novel":[30],"penalization":[31],"technique":[32],"used":[34],"to":[35,53,61,70],"enforce":[36],"feasibility":[37],"and":[38,79],"derive":[39],"certain":[40],"conditions":[41],"under":[42],"which":[43],"constraints":[45],"original":[48],"problem":[50],"are":[51],"guaranteed":[52],"be":[54],"satisfied.":[55],"Moreover,":[56],"we":[57],"extend":[58],"our":[59],"approach":[60,88],"a":[62],"feasibility-preserving":[63],"sequential":[64],"scheme":[65],"solves":[67],"penalized":[68],"relaxation":[69],"obtain":[71],"near-globally":[72],"optimal":[73],"points.":[74],"Experimental":[75],"results":[76],"on":[77,89],"synthetic":[78],"real":[80],"datasets":[81],"demonstrate":[82],"effectiveness":[84],"proposed":[87],"two":[90],"practical":[91],"applications":[92],"in":[93],"machine":[94],"learning.":[95]},"counts_by_year":[{"year":2023,"cited_by_count":2}],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}