{"id":"https://openalex.org/W2965757618","doi":"https://doi.org/10.24963/ijcai.2019/579","title":"Geometric Understanding for Unsupervised Subspace Learning","display_name":"Geometric Understanding for Unsupervised Subspace Learning","publication_year":2019,"publication_date":"2019-07-28","ids":{"openalex":"https://openalex.org/W2965757618","doi":"https://doi.org/10.24963/ijcai.2019/579","mag":"2965757618"},"language":"en","primary_location":{"id":"doi:10.24963/ijcai.2019/579","is_oa":true,"landing_page_url":"https://doi.org/10.24963/ijcai.2019/579","pdf_url":"https://www.ijcai.org/proceedings/2019/0579.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":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.ijcai.org/proceedings/2019/0579.pdf","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063863772","display_name":"Shihui Ying","orcid":"https://orcid.org/0000-0001-9423-0146"},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]},{"id":"https://openalex.org/I141962983","display_name":"Shanghai University of Engineering Science","ror":"https://ror.org/0557b9y08","country_code":"CN","type":"education","lineage":["https://openalex.org/I141962983"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shihui Ying","raw_affiliation_strings":["Department of Mathematics\uff0cSchool of Science, Shanghai University, Shanghai, China","Department of Mathematics, School of Science, Shanghai University, Shanghai, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics\uff0cSchool of Science, Shanghai University, Shanghai, China","institution_ids":["https://openalex.org/I113940042","https://openalex.org/I141962983"]},{"raw_affiliation_string":"Department of Mathematics, School of Science, Shanghai University, Shanghai, China","institution_ids":["https://openalex.org/I113940042"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054794408","display_name":"Li-Peng Cai","orcid":"https://orcid.org/0000-0003-1040-2081"},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]},{"id":"https://openalex.org/I141962983","display_name":"Shanghai University of Engineering Science","ror":"https://ror.org/0557b9y08","country_code":"CN","type":"education","lineage":["https://openalex.org/I141962983"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lipeng Cai","raw_affiliation_strings":["Department of Mathematics\uff0cSchool of Science, Shanghai University, Shanghai, China","Department of Mathematics, School of Science, Shanghai University, Shanghai, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics\uff0cSchool of Science, Shanghai University, Shanghai, China","institution_ids":["https://openalex.org/I113940042","https://openalex.org/I141962983"]},{"raw_affiliation_string":"Department of Mathematics, School of Science, Shanghai University, Shanghai, China","institution_ids":["https://openalex.org/I113940042"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006262967","display_name":"Changzhou He","orcid":null},"institutions":[{"id":"https://openalex.org/I19268510","display_name":"Qualcomm (United Kingdom)","ror":"https://ror.org/04d3djg48","country_code":"GB","type":"company","lineage":["https://openalex.org/I19268510","https://openalex.org/I4210087596"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Changzhou He","raw_affiliation_strings":["Qualcomm (Shanghai) Co. Ltd, China","Qualcomm (Shanghai) Co. Ltd., China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Qualcomm (Shanghai) Co. Ltd, China","institution_ids":["https://openalex.org/I19268510"]},{"raw_affiliation_string":"Qualcomm (Shanghai) Co. Ltd., China","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033203506","display_name":"Yaxin Peng","orcid":"https://orcid.org/0000-0002-2983-555X"},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]},{"id":"https://openalex.org/I141962983","display_name":"Shanghai University of Engineering Science","ror":"https://ror.org/0557b9y08","country_code":"CN","type":"education","lineage":["https://openalex.org/I141962983"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yaxin Peng","raw_affiliation_strings":["Department of Mathematics\uff0cSchool of Science, Shanghai University, Shanghai, China","Department of Mathematics, School of Science, Shanghai University, Shanghai, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics\uff0cSchool of Science, Shanghai University, Shanghai, China","institution_ids":["https://openalex.org/I113940042","https://openalex.org/I141962983"]},{"raw_affiliation_string":"Department of Mathematics, School of Science, Shanghai University, Shanghai, China","institution_ids":["https://openalex.org/I113940042"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"4171","last_page":"4177"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9890000224113464,"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":0.9890000224113464,"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/T10534","display_name":"Structural Health Monitoring Techniques","score":0.982200026512146,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"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/T12740","display_name":"Gait Recognition and Analysis","score":0.9646000266075134,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"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/grassmannian","display_name":"Grassmannian","score":0.8945490121841431},{"id":"https://openalex.org/keywords/orthonormal-basis","display_name":"Orthonormal basis","score":0.7554538249969482},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.7540028095245361},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.7520366907119751},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.5359310507774353},{"id":"https://openalex.org/keywords/geodesic","display_name":"Geodesic","score":0.4996047019958496},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4798150062561035},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4633987247943878},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.45220115780830383},{"id":"https://openalex.org/keywords/unsupervised-learning","display_name":"Unsupervised learning","score":0.4157774746417999},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.3708622455596924},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32743537425994873},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.16573941707611084},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1098778247833252},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07850301265716553}],"concepts":[{"id":"https://openalex.org/C162929932","wikidata":"https://www.wikidata.org/wiki/Q129638","display_name":"Grassmannian","level":2,"score":0.8945490121841431},{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.7554538249969482},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.7540028095245361},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.7520366907119751},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.5359310507774353},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.4996047019958496},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4798150062561035},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4633987247943878},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.45220115780830383},{"id":"https://openalex.org/C8038995","wikidata":"https://www.wikidata.org/wiki/Q1152135","display_name":"Unsupervised learning","level":2,"score":0.4157774746417999},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3708622455596924},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32743537425994873},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.16573941707611084},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1098778247833252},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07850301265716553},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.24963/ijcai.2019/579","is_oa":true,"landing_page_url":"https://doi.org/10.24963/ijcai.2019/579","pdf_url":"https://www.ijcai.org/proceedings/2019/0579.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.2019/579","is_oa":true,"landing_page_url":"https://doi.org/10.24963/ijcai.2019/579","pdf_url":"https://www.ijcai.org/proceedings/2019/0579.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":[],"awards":[{"id":"https://openalex.org/G3207659635","display_name":null,"funder_award_id":"18010500600","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5221450027","display_name":"\u4e09\u7ef4\u533b\u5b66\u5f71\u50cf\u56fe\u8c31\u51e0\u4f55\u5efa\u6a21\u4e0e\u5185\u8574\u7b97\u6cd5\u7814\u7a76","funder_award_id":"11771276","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5391332462","display_name":null,"funder_award_id":"61731009","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5920518074","display_name":null,"funder_award_id":"61573274","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2965757618.pdf","grobid_xml":"https://content.openalex.org/works/W2965757618.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W79405465","https://openalex.org/W191001584","https://openalex.org/W1576613474","https://openalex.org/W1876688746","https://openalex.org/W1969792798","https://openalex.org/W1983894121","https://openalex.org/W1993962865","https://openalex.org/W1997201895","https://openalex.org/W2001141328","https://openalex.org/W2056935845","https://openalex.org/W2092272609","https://openalex.org/W2103250033","https://openalex.org/W2112796928","https://openalex.org/W2117553576","https://openalex.org/W2121647436","https://openalex.org/W2129812935","https://openalex.org/W2145152441","https://openalex.org/W2145962650","https://openalex.org/W2160788267","https://openalex.org/W2177287823","https://openalex.org/W2273827415","https://openalex.org/W2342774626","https://openalex.org/W2591898103","https://openalex.org/W2606011186","https://openalex.org/W2612496192","https://openalex.org/W2765158981","https://openalex.org/W2951401720","https://openalex.org/W4285719527","https://openalex.org/W4298017672","https://openalex.org/W6648938636","https://openalex.org/W6675110806","https://openalex.org/W6680296241","https://openalex.org/W6681535120","https://openalex.org/W6694414743","https://openalex.org/W6736197563","https://openalex.org/W6803771590","https://openalex.org/W6893374194"],"related_works":["https://openalex.org/W2949616856","https://openalex.org/W1804640662","https://openalex.org/W2146523743","https://openalex.org/W2287336960","https://openalex.org/W2074005788","https://openalex.org/W2963346868","https://openalex.org/W4297634020","https://openalex.org/W3159603713","https://openalex.org/W112369303","https://openalex.org/W2057238507"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,14,40,69,102,132],"address":[4],"the":[5,16,37,42,61,67,76,85,104,110,118,122,129,134],"unsupervised":[6],"subspace":[7,17,79,86],"learning":[8,18,87],"from":[9],"a":[10,71,92,113],"geometric":[11],"viewpoint.":[12],"First,":[13],"formulate":[15],"as":[19,30,80,82],"an":[20,47],"inverse":[21],"problem":[22,88,94],"on":[23,32,53,117,141],"Grassmannian":[24,43],"manifold":[25,44],"by":[26,45,60],"considering":[27],"all":[28,54,157],"subspaces":[29],"points":[31],"it.":[33],"Then,":[34,101],"to":[35,65,91,108,127],"make":[36],"model":[38],"computable,":[39],"parameterize":[41],"using":[46],"orbit":[48],"of":[49,78,97,121,145],"rotation":[50,98,123],"group":[51],"action":[52],"standard":[55],"subspaces,":[56],"which":[57,74],"are":[58],"spanned":[59],"orthonormal":[62],"basis.":[63],"Further,":[64],"improve":[66],"robustness,":[68],"introduce":[70],"low-rank":[72],"regularizer":[73],"makes":[75],"dimension":[77],"low":[81],"possible.":[83],"Thus,":[84],"is":[89,125],"transferred":[90],"minimization":[93],"with":[95,137],"variables":[96],"and":[99],"dimension.":[100],"adopt":[103],"alternately":[105],"iterative":[106],"strategy":[107],"optimize":[109],"variables,":[111],"where":[112],"structure-preserving":[114],"method,":[115],"based":[116],"geodesic":[119],"structure":[120],"group,":[124],"designed":[126],"update":[128],"rotation.":[130],"Finally,":[131],"compare":[133],"proposed":[135,154],"approach":[136],"six":[138],"state-of-the-art":[139],"methods":[140],"three":[142],"different":[143],"kinds":[144],"real":[146],"datasets.":[147],"The":[148],"experimental":[149],"results":[150],"validate":[151],"that":[152],"our":[153],"method":[155],"outperforms":[156],"compared":[158],"methods.":[159]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}