{"id":"https://openalex.org/W2106995321","doi":"https://doi.org/10.1109/tsp.2010.2077630","title":"Algorithms for Complex ML ICA and Their Stability Analysis Using Wirtinger Calculus","display_name":"Algorithms for Complex ML ICA and Their Stability Analysis Using Wirtinger Calculus","publication_year":2010,"publication_date":"2010-09-22","ids":{"openalex":"https://openalex.org/W2106995321","doi":"https://doi.org/10.1109/tsp.2010.2077630","mag":"2106995321"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2010.2077630","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2010.2077630","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":["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/A5006405359","display_name":"Hualiang Li","orcid":"https://orcid.org/0000-0003-0126-2056"},"institutions":[{"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":["US"],"is_corresponding":false,"raw_author_name":"Hualiang Li","raw_affiliation_strings":["University of Maryland Baltimore County, Catonsville, MD, USA","University of Maryland, Baltimore County, Catonsville, MD, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Maryland Baltimore County, Catonsville, MD, USA","institution_ids":["https://openalex.org/I79272384"]},{"raw_affiliation_string":"University of Maryland, Baltimore County, Catonsville, MD, USA","institution_ids":["https://openalex.org/I79272384"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060798483","display_name":"T\u00fclay Adal\u0131","orcid":"https://orcid.org/0000-0003-0594-2796"},"institutions":[{"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":["US"],"is_corresponding":false,"raw_author_name":"T\u00fclay Adali","raw_affiliation_strings":["University of Maryland Baltimore County, Catonsville, MD, USA","University of Maryland, Baltimore County, Catonsville, MD, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Maryland Baltimore County, Catonsville, MD, USA","institution_ids":["https://openalex.org/I79272384"]},{"raw_affiliation_string":"University of Maryland, Baltimore County, Catonsville, MD, USA","institution_ids":["https://openalex.org/I79272384"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.4022,"has_fulltext":false,"cited_by_count":31,"citation_normalized_percentile":{"value":0.95057179,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"58","issue":"12","first_page":"6156","last_page":"6167"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":1.0,"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"}},{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9812999963760376,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10429","display_name":"EEG and Brain-Computer Interfaces","score":0.9696999788284302,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/independent-component-analysis","display_name":"Independent component analysis","score":0.798737108707428},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5942755937576294},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.5863872766494751},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5815678834915161},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5621671080589294},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5011131763458252},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.47324758768081665},{"id":"https://openalex.org/keywords/unitary-state","display_name":"Unitary state","score":0.4443497955799103},{"id":"https://openalex.org/keywords/blind-signal-separation","display_name":"Blind signal separation","score":0.429074227809906},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.40500307083129883},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36624082922935486},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.33132171630859375},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.32779017090797424},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.08060720562934875}],"concepts":[{"id":"https://openalex.org/C51432778","wikidata":"https://www.wikidata.org/wiki/Q1259145","display_name":"Independent component analysis","level":2,"score":0.798737108707428},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5942755937576294},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.5863872766494751},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5815678834915161},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5621671080589294},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5011131763458252},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.47324758768081665},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.4443497955799103},{"id":"https://openalex.org/C120317606","wikidata":"https://www.wikidata.org/wiki/Q17105967","display_name":"Blind signal separation","level":3,"score":0.429074227809906},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40500307083129883},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36624082922935486},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.33132171630859375},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.32779017090797424},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.08060720562934875},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tsp.2010.2077630","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2010.2077630","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:CiteSeerX.psu:10.1.1.310.1015","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.310.1015","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.csee.umbc.edu/~adali/pubs/IEEEpubs/TSP2010li_stability.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W1487444668","https://openalex.org/W1488435683","https://openalex.org/W1491109205","https://openalex.org/W1917576720","https://openalex.org/W1974388905","https://openalex.org/W1977067929","https://openalex.org/W1979850790","https://openalex.org/W1989342698","https://openalex.org/W1999766892","https://openalex.org/W2036043111","https://openalex.org/W2064487828","https://openalex.org/W2065234731","https://openalex.org/W2082542187","https://openalex.org/W2104072768","https://openalex.org/W2112044221","https://openalex.org/W2112345337","https://openalex.org/W2124757684","https://openalex.org/W2127737934","https://openalex.org/W2128967371","https://openalex.org/W2129076207","https://openalex.org/W2140638323","https://openalex.org/W2143410296","https://openalex.org/W2157690501","https://openalex.org/W2166288622","https://openalex.org/W2171285230","https://openalex.org/W2294288691","https://openalex.org/W2544829973","https://openalex.org/W2808882910","https://openalex.org/W3029645440","https://openalex.org/W3095095911","https://openalex.org/W3100792434","https://openalex.org/W3140025309","https://openalex.org/W4242259102","https://openalex.org/W4293775970","https://openalex.org/W4297913868","https://openalex.org/W4301621763","https://openalex.org/W6640200869","https://openalex.org/W6685260304"],"related_works":["https://openalex.org/W2390344110","https://openalex.org/W2046761971","https://openalex.org/W2364896863","https://openalex.org/W2361066326","https://openalex.org/W2182042810","https://openalex.org/W2156932837","https://openalex.org/W2380698615","https://openalex.org/W374502268","https://openalex.org/W2103029460","https://openalex.org/W1785857632"],"abstract_inverted_index":{"We":[0,63],"derive":[1,64],"a":[2,76,82,99,134],"class":[3],"of":[4,21,129],"algorithms":[5],"for":[6,31,59,85,91],"independent":[7],"component":[8],"analysis":[9,20,50],"(ICA)":[10],"based":[11],"on":[12],"maximum":[13],"likelihood":[14],"(ML)":[15],"estimation":[16],"and":[17,27,45,55,72,96,111,120,142],"perform":[18],"stability":[19,93],"natural":[22,65],"gradient":[23,66],"ML":[24,68,119,149],"ICA":[25,69,122,150,159],"with":[26,75],"without":[28],"the":[29,36,52,57,107,118,127,138,147,157,163,175],"constraint":[30],"unitary":[32,77],"demixing":[33],"matrix.":[34],"In":[35],"process,":[37],"we":[38,113,144],"demonstrate":[39],"how":[40],"Wirtinger":[41],"calculus":[42],"facilitates":[43],"derivations,":[44],"most":[46],"importantly,":[47],"performing":[48],"second-order":[49],"in":[51],"complex":[53,67],"domain":[54],"eliminates":[56],"need":[58],"making":[60],"simplifying":[61],"assumptions.":[62],"update":[70,123,151,160,169],"rule":[71,152],"its":[73],"variant":[74],"constraint,":[78],"as":[79,81],"well":[80],"Newton":[83],"algorithm":[84],"better":[86],"convergence":[87],"behavior.":[88],"The":[89],"conditions":[90],"local":[92],"are":[94,109,140,165,171,183],"derived":[95],"studied":[97],"using":[98],"generalized":[100],"Gaussian":[101],"density":[102],"(GGD)":[103],"source":[104],"model.":[105],"When":[106,137,162],"sources":[108,139,164,176],"circular":[110],"non-Gaussian,":[112,143],"show":[114,145],"analytically":[115],"that":[116,146],"both":[117,168],"ML-unitary":[121,158],"rules":[124,170],"converge":[125],"to":[126,133,185],"inverse":[128],"mixing":[130],"matrix":[131],"subject":[132],"phase":[135],"shift.":[136],"noncircular":[141,166],"nonunitary":[148],"is":[153],"more":[154],"stable":[155,172],"than":[156],"rule.":[161],"Gaussians,":[167],"only":[173],"when":[174],"have":[177],"distinct":[178],"noncircularity":[179],"indices.":[180],"Simulation":[181],"results":[182],"given":[184],"support":[186],"these":[187],"results.":[188]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":6}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
