{"id":"https://openalex.org/W1998202021","doi":"https://doi.org/10.1109/jstsp.2013.2241014","title":"Minkovskian Gradient for Sparse Optimization","display_name":"Minkovskian Gradient for Sparse Optimization","publication_year":2013,"publication_date":"2013-01-17","ids":{"openalex":"https://openalex.org/W1998202021","doi":"https://doi.org/10.1109/jstsp.2013.2241014","mag":"1998202021"},"language":"en","primary_location":{"id":"doi:10.1109/jstsp.2013.2241014","is_oa":false,"landing_page_url":"https://doi.org/10.1109/jstsp.2013.2241014","pdf_url":null,"source":{"id":"https://openalex.org/S42167783","display_name":"IEEE Journal of Selected Topics in Signal Processing","issn_l":"1932-4553","issn":["1932-4553","1941-0484"],"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 Journal of Selected Topics in Signal Processing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055812530","display_name":"\u0428\u0443\u043d-\u0438\u0447\u0438 \u0410\u043c\u0430\u0440\u0438","orcid":"https://orcid.org/0000-0001-8860-8675"},"institutions":[{"id":"https://openalex.org/I2800939219","display_name":"RIKEN Center for Brain Science","ror":"https://ror.org/04j1n1c04","country_code":"JP","type":"facility","lineage":["https://openalex.org/I2800939219","https://openalex.org/I4210110652"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Shun-ichi Amari","raw_affiliation_strings":["RIKEN Brain Science Institute, Saitama, Japan","RIKEN, Brain Science Institute, Wako, Japan"],"affiliations":[{"raw_affiliation_string":"RIKEN Brain Science Institute, Saitama, Japan","institution_ids":["https://openalex.org/I2800939219"]},{"raw_affiliation_string":"RIKEN, Brain Science Institute, Wako, Japan","institution_ids":["https://openalex.org/I2800939219"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029561892","display_name":"Masahiro Yukawa","orcid":"https://orcid.org/0000-0002-3709-275X"},"institutions":[{"id":"https://openalex.org/I71395657","display_name":"Niigata University","ror":"https://ror.org/04ww21r56","country_code":"JP","type":"education","lineage":["https://openalex.org/I71395657"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Masahiro Yukawa","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, Niigata University, Niigata, Japan","Dept. of Electr. & Electron. Eng., Niigata Univ., Niigata, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, Niigata University, Niigata, Japan","institution_ids":["https://openalex.org/I71395657"]},{"raw_affiliation_string":"Dept. of Electr. & Electron. Eng., Niigata Univ., Niigata, Japan","institution_ids":["https://openalex.org/I71395657"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5055812530"],"corresponding_institution_ids":["https://openalex.org/I2800939219"],"apc_list":null,"apc_paid":null,"fwci":1.4059,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.80199671,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"7","issue":"4","first_page":"576","last_page":"585"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"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":0.9998999834060669,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9973000288009644,"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"}},{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9932000041007996,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/pythagorean-theorem","display_name":"Pythagorean theorem","score":0.622117280960083},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.5791826248168945},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.5684478878974915},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5427212715148926},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5099924802780151},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.5063542127609253},{"id":"https://openalex.org/keywords/information-geometry","display_name":"Information geometry","score":0.48768579959869385},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.46555405855178833},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.44431281089782715},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.44163915514945984},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.43208047747612},{"id":"https://openalex.org/keywords/stochastic-gradient-descent","display_name":"Stochastic gradient descent","score":0.4109153151512146},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.3879106342792511},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3684622645378113},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.35384848713874817},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3394244611263275},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3343126177787781},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2423597276210785},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.16201964020729065},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12695831060409546}],"concepts":[{"id":"https://openalex.org/C100461760","wikidata":"https://www.wikidata.org/wiki/Q11518","display_name":"Pythagorean theorem","level":2,"score":0.622117280960083},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.5791826248168945},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.5684478878974915},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5427212715148926},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5099924802780151},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.5063542127609253},{"id":"https://openalex.org/C109546454","wikidata":"https://www.wikidata.org/wiki/Q3798604","display_name":"Information geometry","level":4,"score":0.48768579959869385},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.46555405855178833},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.44431281089782715},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.44163915514945984},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.43208047747612},{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.4109153151512146},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3879106342792511},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3684622645378113},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35384848713874817},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3394244611263275},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3343126177787781},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2423597276210785},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.16201964020729065},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12695831060409546},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C12520029","wikidata":"https://www.wikidata.org/wiki/Q1147161","display_name":"Scalar curvature","level":3,"score":0.0},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/jstsp.2013.2241014","is_oa":false,"landing_page_url":"https://doi.org/10.1109/jstsp.2013.2241014","pdf_url":null,"source":{"id":"https://openalex.org/S42167783","display_name":"IEEE Journal of Selected Topics in Signal Processing","issn_l":"1932-4553","issn":["1932-4553","1941-0484"],"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 Journal of Selected Topics in Signal Processing","raw_type":"journal-article"},{"id":"pmh:oai:irdb.nii.ac.jp:00953:0006741406","is_oa":false,"landing_page_url":"https://teikyo-u.repo.nii.ac.jp/records/2026314","pdf_url":null,"source":{"id":"https://openalex.org/S7407056385","display_name":"Institutional Repositories DataBase (IRDB)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I184597095","host_organization_name":"National Institute of Informatics","host_organization_lineage":["https://openalex.org/I184597095"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Journal on Selected Topics in Signal Processing","raw_type":"journal article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W15330580","https://openalex.org/W340244495","https://openalex.org/W1573082642","https://openalex.org/W1583497301","https://openalex.org/W1976709621","https://openalex.org/W1986931325","https://openalex.org/W1989982096","https://openalex.org/W2020925091","https://openalex.org/W2056201402","https://openalex.org/W2063978378","https://openalex.org/W2074269613","https://openalex.org/W2074682976","https://openalex.org/W2097360283","https://openalex.org/W2098012923","https://openalex.org/W2119667497","https://openalex.org/W2129638195","https://openalex.org/W2135046866","https://openalex.org/W2164452299","https://openalex.org/W2196956961","https://openalex.org/W2296319761","https://openalex.org/W2296616510","https://openalex.org/W4235713725","https://openalex.org/W4250589301","https://openalex.org/W4250955649","https://openalex.org/W4294541781","https://openalex.org/W4300263211"],"related_works":["https://openalex.org/W4297986345","https://openalex.org/W2950501992","https://openalex.org/W1581294689","https://openalex.org/W3020853991","https://openalex.org/W1971945429","https://openalex.org/W3128680160","https://openalex.org/W3042271683","https://openalex.org/W3093180793","https://openalex.org/W2808489849","https://openalex.org/W2804758771"],"abstract_inverted_index":{"Information":[0],"geometry":[1],"is":[2,58,70],"used":[3],"to":[4,52,72],"elucidate":[5],"convex":[6,16],"optimization":[7],"problems":[8],"under":[9,88],"L":[10,91],"<sub":[11,92],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[12,93],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1</sub>":[13,94],"constraint.":[14],"A":[15,35],"function":[17,87],"induces":[18],"a":[19,45,74,85],"Riemannian":[20],"metric":[21],"and":[22,39,55,60],"two":[23],"dually":[24,97],"coupled":[25,98],"affine":[26,99],"connections":[27],"in":[28,43,80],"the":[29,81,89,106],"manifold":[30],"of":[31,33,62,84],"parameters":[32],"interest.":[34],"generalized":[36],"Pythagorean":[37],"theorem":[38,41],"projection":[40],"hold":[42],"such":[44],"manifold.":[46],"An":[47],"extended":[48],"LARS":[49],"algorithm,":[50],"applicable":[51],"both":[53],"under-determined":[54],"over-determined":[56],"cases,":[57],"studied":[59],"properties":[61],"its":[63],"solution":[64,107],"path":[65],"are":[66,102],"given.":[67],"The":[68],"algorithm":[69],"shown":[71],"be":[73],"Minkovskian":[75,90],"gradient-descent":[76],"method,":[77],"which":[78],"moves":[79],"steepest":[82],"direction":[83],"target":[86],"norm.":[95],"Two":[96],"coordinate":[100],"systems":[101],"useful":[103],"for":[104],"analyzing":[105],"path.":[108]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}