{"id":"https://openalex.org/W317116022","doi":"https://doi.org/10.1007/978-3-662-01131-7_57","title":"A Wavelet Approach to Functional Principal Component Analysis","display_name":"A Wavelet Approach to Functional Principal Component Analysis","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W317116022","doi":"https://doi.org/10.1007/978-3-662-01131-7_57","mag":"317116022"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-662-01131-7_57","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-662-01131-7_57","pdf_url":null,"source":{"id":"https://openalex.org/S4306506691","display_name":"COMPSTAT","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"COMPSTAT","raw_type":"book-chapter"},"type":"book-chapter","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/A5109345909","display_name":"F. Oca\u00f1a","orcid":null},"institutions":[{"id":"https://openalex.org/I173304897","display_name":"Universidad de Granada","ror":"https://ror.org/04njjy449","country_code":"ES","type":"education","lineage":["https://openalex.org/I173304897"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Francisco A. Oca\u00f1a","raw_affiliation_strings":["Department of Statistics & Operations Research, University of Granada, Campus de Cartuja, 18071-Granada, Spain","Department of Statistics and Operations Research, University of Granada, 18071 Granada, Spain"],"affiliations":[{"raw_affiliation_string":"Department of Statistics & Operations Research, University of Granada, Campus de Cartuja, 18071-Granada, Spain","institution_ids":["https://openalex.org/I173304897"]},{"raw_affiliation_string":"Department of Statistics and Operations Research, University of Granada, 18071 Granada, Spain","institution_ids":["https://openalex.org/I173304897"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058407177","display_name":"Olga Valenzuela","orcid":"https://orcid.org/0000-0001-6034-9392"},"institutions":[{"id":"https://openalex.org/I173304897","display_name":"Universidad de Granada","ror":"https://ror.org/04njjy449","country_code":"ES","type":"education","lineage":["https://openalex.org/I173304897"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Olga Valenzuela","raw_affiliation_strings":["Department of Statistics & Operations Research, University of Granada, Campus de Cartuja, 18071-Granada, Spain","Department of Statistics and Operations Research, University of Granada, 18071 Granada, Spain"],"affiliations":[{"raw_affiliation_string":"Department of Statistics & Operations Research, University of Granada, Campus de Cartuja, 18071-Granada, Spain","institution_ids":["https://openalex.org/I173304897"]},{"raw_affiliation_string":"Department of Statistics and Operations Research, University of Granada, 18071 Granada, Spain","institution_ids":["https://openalex.org/I173304897"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083522316","display_name":"Ana M. Aguilera","orcid":"https://orcid.org/0000-0003-2425-6716"},"institutions":[{"id":"https://openalex.org/I173304897","display_name":"Universidad de Granada","ror":"https://ror.org/04njjy449","country_code":"ES","type":"education","lineage":["https://openalex.org/I173304897"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Ana M. Aguilera","raw_affiliation_strings":["Department of Statistics & Operations Research, University of Granada, Campus de Cartuja, 18071-Granada, Spain","Department of Statistics and Operations Research, University of Granada, 18071 Granada, Spain"],"affiliations":[{"raw_affiliation_string":"Department of Statistics & Operations Research, University of Granada, Campus de Cartuja, 18071-Granada, Spain","institution_ids":["https://openalex.org/I173304897"]},{"raw_affiliation_string":"Department of Statistics and Operations Research, University of Granada, 18071 Granada, Spain","institution_ids":["https://openalex.org/I173304897"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5109345909"],"corresponding_institution_ids":["https://openalex.org/I173304897"],"apc_list":null,"apc_paid":null,"fwci":0.385,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.54675232,"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":"413","last_page":"418"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9998000264167786,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9998000264167786,"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/T13487","display_name":"Statistical and numerical algorithms","score":0.9911999702453613,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10640","display_name":"Spectroscopy and Chemometric Analyses","score":0.9746999740600586,"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/wavelet","display_name":"Wavelet","score":0.8493220806121826},{"id":"https://openalex.org/keywords/principal-component-analysis","display_name":"Principal component analysis","score":0.7216066122055054},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.66096031665802},{"id":"https://openalex.org/keywords/kernel-principal-component-analysis","display_name":"Kernel principal component analysis","score":0.5789713263511658},{"id":"https://openalex.org/keywords/multiresolution-analysis","display_name":"Multiresolution analysis","score":0.5523937344551086},{"id":"https://openalex.org/keywords/discrete-wavelet-transform","display_name":"Discrete wavelet transform","score":0.5171172618865967},{"id":"https://openalex.org/keywords/functional-principal-component-analysis","display_name":"Functional principal component analysis","score":0.505742073059082},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.47098538279533386},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.4372820556163788},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.4163571894168854},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39209040999412537},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3920283317565918},{"id":"https://openalex.org/keywords/wavelet-transform","display_name":"Wavelet transform","score":0.3906964957714081},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.38778385519981384},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.304527223110199},{"id":"https://openalex.org/keywords/kernel-method","display_name":"Kernel method","score":0.25199341773986816},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.23906317353248596},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.07085517048835754}],"concepts":[{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.8493220806121826},{"id":"https://openalex.org/C27438332","wikidata":"https://www.wikidata.org/wiki/Q2873","display_name":"Principal component analysis","level":2,"score":0.7216066122055054},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.66096031665802},{"id":"https://openalex.org/C182335926","wikidata":"https://www.wikidata.org/wiki/Q17093020","display_name":"Kernel principal component analysis","level":4,"score":0.5789713263511658},{"id":"https://openalex.org/C121927907","wikidata":"https://www.wikidata.org/wiki/Q1952516","display_name":"Multiresolution analysis","level":5,"score":0.5523937344551086},{"id":"https://openalex.org/C46286280","wikidata":"https://www.wikidata.org/wiki/Q2414958","display_name":"Discrete wavelet transform","level":4,"score":0.5171172618865967},{"id":"https://openalex.org/C71176878","wikidata":"https://www.wikidata.org/wiki/Q17014987","display_name":"Functional principal component analysis","level":3,"score":0.505742073059082},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.47098538279533386},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.4372820556163788},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.4163571894168854},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39209040999412537},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3920283317565918},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.3906964957714081},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38778385519981384},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.304527223110199},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.25199341773986816},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.23906317353248596},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.07085517048835754},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-662-01131-7_57","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-662-01131-7_57","pdf_url":null,"source":{"id":"https://openalex.org/S4306506691","display_name":"COMPSTAT","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"COMPSTAT","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1489213177","https://openalex.org/W1494122956","https://openalex.org/W1559836864","https://openalex.org/W1560384356","https://openalex.org/W1590869801","https://openalex.org/W1606846851","https://openalex.org/W1983960282","https://openalex.org/W2071723512","https://openalex.org/W2086248341","https://openalex.org/W2098914003","https://openalex.org/W2111574985","https://openalex.org/W2140832824","https://openalex.org/W2145184594","https://openalex.org/W2171301910","https://openalex.org/W2506196914","https://openalex.org/W2526161751","https://openalex.org/W2569586013","https://openalex.org/W2803056817","https://openalex.org/W4256555983","https://openalex.org/W4293747882","https://openalex.org/W6629228971","https://openalex.org/W6633746528"],"related_works":["https://openalex.org/W2534878021","https://openalex.org/W2963184067","https://openalex.org/W2605967135","https://openalex.org/W2376141492","https://openalex.org/W2512565647","https://openalex.org/W1174192761","https://openalex.org/W1988336897","https://openalex.org/W2249549849","https://openalex.org/W2139392257","https://openalex.org/W137536763"],"abstract_inverted_index":{"The":[0,110],"aim":[1],"of":[2,15,30,40,107,112,122],"this":[3,113],"paper":[4],"is":[5,58,98,115],"to":[6,37,61,80],"approximate":[7,63],"the":[8,11,33,38,42,46,123],"estimates":[9],"in":[10,32],"principal":[12],"component":[13],"analysis":[14,69],"a":[16,92],"continuous":[17],"time":[18],"stochastic":[19],"process":[20,114],"(functional":[21],"PCA)":[22],"by":[23,100,120],"using":[24],"wavelet":[25,56,96,124],"methods.":[26],"A":[27],"short":[28],"review":[29],"estimating":[31,52],"functional":[34,82],"PCA":[35,83,111],"leads":[36],"problem":[39],"solving":[41],"integral":[43],"equation":[44],"with":[45,117],"covariance":[47],"function":[48],"as":[49],"kernel.":[50],"An":[51],"procedure":[53],"based":[54],"on":[55,91],"methods":[57,66],"then":[59],"provided":[60],"obtain":[62],"estimates.":[64],"Wavelet":[65],"and":[67],"multiresolution":[68],"(MRA)":[70],"are":[71,86],"jointly":[72],"considered.":[73],"Furthermore,":[74],"MRA":[75],"provides":[76],"an":[77],"approximating":[78],"framework":[79],"estimate":[81],"when":[84],"data":[85],"observed":[87],"at":[88,102],"discrete":[89,103],"knots":[90,104],"real":[93],"interval.":[94],"This":[95],"approach":[97],"tested":[99],"simulating":[101],"sample":[105],"functions":[106],"Brownian":[108],"motion.":[109],"compared":[116],"those":[118],"estimated":[119],"means":[121],"approach.":[125]},"counts_by_year":[{"year":2019,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
