{"id":"https://openalex.org/W2156433372","doi":"https://doi.org/10.1109/ijcnn.2004.1380955","title":"Approximating nonlinear transformations of probability distributions for nonlinear independent component analysis","display_name":"Approximating nonlinear transformations of probability distributions for nonlinear independent component analysis","publication_year":2005,"publication_date":"2005-01-31","ids":{"openalex":"https://openalex.org/W2156433372","doi":"https://doi.org/10.1109/ijcnn.2004.1380955","mag":"2156433372"},"language":"en","primary_location":{"id":"doi:10.1109/ijcnn.2004.1380955","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ijcnn.2004.1380955","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2004 IEEE International Joint Conference on Neural Networks (IEEE Cat. No.04CH37541)","raw_type":"proceedings-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/A5071329195","display_name":"Antti Honkela","orcid":"https://orcid.org/0000-0001-9193-8093"},"institutions":[{"id":"https://openalex.org/I133731052","display_name":"University of Helsinki","ror":"https://ror.org/040af2s02","country_code":"FI","type":"education","lineage":["https://openalex.org/I133731052"]}],"countries":["FI"],"is_corresponding":true,"raw_author_name":"A. Honkela","raw_affiliation_strings":["Neural Networks Research Centre, Helsinki University of Technology, Finland"],"affiliations":[{"raw_affiliation_string":"Neural Networks Research Centre, Helsinki University of Technology, Finland","institution_ids":["https://openalex.org/I133731052"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5071329195"],"corresponding_institution_ids":["https://openalex.org/I133731052"],"apc_list":null,"apc_paid":null,"fwci":1.6213,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.84968211,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"3","issue":null,"first_page":"2169","last_page":"2174"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9718999862670898,"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/T10640","display_name":"Spectroscopy and Chemometric Analyses","score":0.9696999788284302,"subfield":{"id":"https://openalex.org/subfields/1602","display_name":"Analytical Chemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/taylor-series","display_name":"Taylor series","score":0.7278314828872681},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6738197207450867},{"id":"https://openalex.org/keywords/hermite-polynomials","display_name":"Hermite polynomials","score":0.5871890187263489},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.557601809501648},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.547698438167572},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5429506301879883},{"id":"https://openalex.org/keywords/independent-component-analysis","display_name":"Independent component analysis","score":0.5402562022209167},{"id":"https://openalex.org/keywords/variance","display_name":"Variance (accounting)","score":0.5242283940315247},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.4755637049674988},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.4703303277492523},{"id":"https://openalex.org/keywords/gaussian-quadrature","display_name":"Gaussian quadrature","score":0.4479250907897949},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.44238218665122986},{"id":"https://openalex.org/keywords/component","display_name":"Component (thermodynamics)","score":0.4301775097846985},{"id":"https://openalex.org/keywords/gauss","display_name":"Gauss","score":0.41385558247566223},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36773669719696045},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.33418720960617065},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20361381769180298},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.15454387664794922},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.09966596961021423},{"id":"https://openalex.org/keywords/nystr\u00f6m-method","display_name":"Nystr\u00f6m method","score":0.08284428715705872}],"concepts":[{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.7278314828872681},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6738197207450867},{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.5871890187263489},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.557601809501648},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.547698438167572},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5429506301879883},{"id":"https://openalex.org/C51432778","wikidata":"https://www.wikidata.org/wiki/Q1259145","display_name":"Independent component analysis","level":2,"score":0.5402562022209167},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.5242283940315247},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4755637049674988},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.4703303277492523},{"id":"https://openalex.org/C167196314","wikidata":"https://www.wikidata.org/wiki/Q767680","display_name":"Gaussian quadrature","level":4,"score":0.4479250907897949},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.44238218665122986},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.4301775097846985},{"id":"https://openalex.org/C161794534","wikidata":"https://www.wikidata.org/wiki/Q177493","display_name":"Gauss","level":2,"score":0.41385558247566223},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36773669719696045},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33418720960617065},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20361381769180298},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15454387664794922},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.09966596961021423},{"id":"https://openalex.org/C48265008","wikidata":"https://www.wikidata.org/wiki/Q7071295","display_name":"Nystr\u00f6m method","level":3,"score":0.08284428715705872},{"id":"https://openalex.org/C121955636","wikidata":"https://www.wikidata.org/wiki/Q4116214","display_name":"Accounting","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/ijcnn.2004.1380955","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ijcnn.2004.1380955","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2004 IEEE International Joint Conference on Neural Networks (IEEE Cat. No.04CH37541)","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.108.2794","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.108.2794","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cis.hut.fi/ahonkela/papers/ijcnn04.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.114.48","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.114.48","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://lib.tkk.fi/diss/2005/isbn9512276550/article6.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"No poverty","id":"https://metadata.un.org/sdg/1","score":0.46000000834465027}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W111933772","https://openalex.org/W179909587","https://openalex.org/W1528993561","https://openalex.org/W1562345118","https://openalex.org/W1579063588","https://openalex.org/W2030142453","https://openalex.org/W2047229728","https://openalex.org/W2099544223","https://openalex.org/W2125392257","https://openalex.org/W2126964567","https://openalex.org/W2137969290","https://openalex.org/W2156436462","https://openalex.org/W2259546388","https://openalex.org/W6633904780"],"related_works":["https://openalex.org/W2963795429","https://openalex.org/W3109298388","https://openalex.org/W2758946633","https://openalex.org/W2085681042","https://openalex.org/W2607185056","https://openalex.org/W2056192452","https://openalex.org/W3110797384","https://openalex.org/W2317230014","https://openalex.org/W2965909347","https://openalex.org/W2168497266"],"abstract_inverted_index":{"The":[0,28,78,94],"nonlinear":[1,22],"independent":[2],"component":[3],"analysis":[4],"method":[5],"introduced":[6],"by":[7,90],"Lappalainen":[8],"and":[9,40,104],"Honkela":[10],"in":[11,81],"2000":[12],"uses":[13,30],"a":[14],"truncated":[15],"Taylor":[16,83],"series":[17],"representation":[18],"to":[19,26,57],"approximate":[20],"the":[21,34,46,59,64,82,105],"transformation":[23],"from":[24],"sources":[25],"observations.":[27],"approach":[29],"information":[31],"only":[32],"at":[33],"single":[35],"point":[36],"of":[37,61,63],"input":[38,47,102],"mean":[39],"can":[41],"produce":[42],"poor":[43],"results":[44],"if":[45],"variance":[48,103],"is":[49,76,97,109],"large.":[50],"This":[51],"feature":[52],"has":[53],"recently":[54],"been":[55],"identified":[56],"be":[58],"cause":[60],"instability":[62],"algorithm":[65,108],"with":[66,87,112],"large":[67],"source":[68,114],"dimensionalities.":[69,115],"In":[70],"this":[71],"paper,":[72],"an":[73],"improved":[74],"approximation":[75,96],"presented.":[77],"derivatives":[79],"used":[80],"scheme":[84],"are":[85],"replaced":[86],"slopes":[88],"evaluated":[89],"global":[91],"Gauss-Hermite":[92],"quadrature.":[93],"resulting":[95],"more":[98,110],"accurate":[99],"under":[100],"high":[101,113],"new":[106],"learning":[107],"stable":[111]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}