Adaptive Learning in Complex Reproducing Kernel Hilbert Spaces Employing Wirtinger's Subgradients

This paper presents a wide framework for non-linear online supervised learning tasks in the context of complex valued signal processing. The (complex) input data are mapped into a complex reproducing kernel Hilbert space (RKHS), where the learning phase is taking place. Both pure complex kernels and...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	IEEE transaction on neural networks and learning systems Jg. 23; H. 3; S. 425 - 438
Hauptverfasser:	Bouboulis, P., Slavakis, K., Theodoridis, S.
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York, NY IEEE 01.03.2012 Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:	Adaptive kernel learning Applied sciences Artificial intelligence Calculus Channels complex kernels Computer science; control theory; systems Context Equalization Exact sciences and technology Hilbert space Kernel Kernels Learning Learning and adaptive systems Loss measurement Machine learning Mathematical analysis Nonlinearity On-line systems projection Signal processing Studies subgradient Tasks widely linear estimation Wirtinger's calculus complex kernels subgradient Non linear channel Complex signal Equalization widely linear estimation Adaptive method Quadrature phase shift keying Kernel method Complex variable method Loss function Supervised learning Efficiency Linear filter Signal processing Sparse representation Signal sources Adaptive kernel learning Hilbert space Linear estimation projection Wirtinger's calculus Learning algorithm
ISSN:	2162-237X, 2162-2388
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Abstract	This paper presents a wide framework for non-linear online supervised learning tasks in the context of complex valued signal processing. The (complex) input data are mapped into a complex reproducing kernel Hilbert space (RKHS), where the learning phase is taking place. Both pure complex kernels and real kernels (via the complexification trick) can be employed. Moreover, any convex, continuous and not necessarily differentiable function can be used to measure the loss between the output of the specific system and the desired response. The only requirement is the subgradient of the adopted loss function to be available in an analytic form. In order to derive analytically the subgradients, the principles of the (recently developed) Wirtinger's calculus in complex RKHS are exploited. Furthermore, both linear and widely linear (in RKHS) estimation filters are considered. To cope with the problem of increasing memory requirements, which is present in almost all online schemes in RKHS, the sparsification scheme, based on projection onto closed balls, has been adopted. We demonstrate the effectiveness of the proposed framework in a non-linear channel identification task, a non-linear channel equalization problem and a quadrature phase shift keying equalization scheme, using both circular and non circular synthetic signal sources.
AbstractList	This paper presents a wide framework for non-linear online supervised learning tasks in the context of complex valued signal processing. The (complex) input data are mapped into a complex reproducing kernel Hilbert space (RKHS), where the learning phase is taking place. Both pure complex kernels and real kernels (via the complexification trick) can be employed. Moreover, any convex, continuous and not necessarily differentiable function can be used to measure the loss between the output of the specific system and the desired response. The only requirement is the subgradient of the adopted loss function to be available in an analytic form. In order to derive analytically the subgradients, the principles of the (recently developed) Wirtinger's calculus in complex RKHS are exploited. Furthermore, both linear and widely linear (in RKHS) estimation filters are considered. To cope with the problem of increasing memory requirements, which is present in almost all online schemes in RKHS, the sparsification scheme, based on projection onto closed balls, has been adopted. We demonstrate the effectiveness of the proposed framework in a non-linear channel identification task, a non-linear channel equalization problem and a quadrature phase shift keying equalization scheme, using both circular and non circular synthetic signal sources. This paper presents a wide framework for non-linear online supervised learning tasks in the context of complex valued signal processing. The (complex) input data are mapped into a complex reproducing kernel Hilbert space (RKHS), where the learning phase is taking place. Both pure complex kernels and real kernels (via the complexification trick) can be employed. Moreover, any convex, continuous and not necessarily differentiable function can be used to measure the loss between the output of the specific system and the desired response. The only requirement is the subgradient of the adopted loss function to be available in an analytic form. In order to derive analytically the subgradients, the principles of the (recently developed) Wirtinger's calculus in complex RKHS are exploited. Furthermore, both linear and widely linear (in RKHS) estimation filters are considered. To cope with the problem of increasing memory requirements, which is present in almost all online schemes in RKHS, the sparsification scheme, based on projection onto closed balls, has been adopted. We demonstrate the effectiveness of the proposed framework in a non-linear channel identification task, a non-linear channel equalization problem and a quadrature phase shift keying equalization scheme, using both circular and non circular synthetic signal sources.This paper presents a wide framework for non-linear online supervised learning tasks in the context of complex valued signal processing. The (complex) input data are mapped into a complex reproducing kernel Hilbert space (RKHS), where the learning phase is taking place. Both pure complex kernels and real kernels (via the complexification trick) can be employed. Moreover, any convex, continuous and not necessarily differentiable function can be used to measure the loss between the output of the specific system and the desired response. The only requirement is the subgradient of the adopted loss function to be available in an analytic form. In order to derive analytically the subgradients, the principles of the (recently developed) Wirtinger's calculus in complex RKHS are exploited. Furthermore, both linear and widely linear (in RKHS) estimation filters are considered. To cope with the problem of increasing memory requirements, which is present in almost all online schemes in RKHS, the sparsification scheme, based on projection onto closed balls, has been adopted. We demonstrate the effectiveness of the proposed framework in a non-linear channel identification task, a non-linear channel equalization problem and a quadrature phase shift keying equalization scheme, using both circular and non circular synthetic signal sources.
Author	Slavakis, K. Bouboulis, P. Theodoridis, S.
Author_xml	– sequence: 1 givenname: P. surname: Bouboulis fullname: Bouboulis, P. email: pbouboulis@sch.gr organization: Dept. of Inf. & Telecommun., Univ. of Athens, Athens, Greece – sequence: 2 givenname: K. surname: Slavakis fullname: Slavakis, K. email: slavakis@uop.gr organization: Dept. of Telecommun. Sci. & Technol., Univ. of Peloponnese, Tripolis, Greece – sequence: 3 givenname: S. surname: Theodoridis fullname: Theodoridis, S. email: stheodor@di.uoa.gr organization: Dept. of Inf. & Telecommun., Univ. of Athens, Athens, Greece
BackLink	http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=25610449$$DView record in Pascal Francis https://www.ncbi.nlm.nih.gov/pubmed/24808549$$D View this record in MEDLINE/PubMed
BookMark	eNqFkVFvFCEUhYmpsbX2D2hiJiZGX3YFBhh4bDbVmm5q4tboG2HgTkMzy4zANO2_l-2ua9KHel8uge8A95yX6CAMARB6TfCcEKw-XV1eLldzigmZU9IoSfAzdESJoDNaS3mwXze_DtFJSje4lMBcMPUCHVImseRMHSFz6syY_S1USzAx-HBd-VAthvXYw131HcY4uMluti8gBuirc9-3EHO1Go2FVJ0VcLjfnP_0MZcO8UOqVlN7HY3zEHJ6hZ53pk9wsuvH6Mfns6vF-Wz57cvXxelyZlmj8sx2tWid6oRyLaei7joCDTaqa12tDIdOAAZoqWLYMYJ56xjURrasFC2z1Mfo4_be8uXfE6Ss1z5Z6HsTYJiSJpzWrFjA1P9RTJTgnEhR0HeP0JthiqEMohWtFRWSyQK93UFTuwanx-jXJt7rvzYX4P0OMMmavosmWJ_-cVwQzB44uuVsHFKK0O0RgvUmdv0Qu97ErnexF5F8JLI-m-yHkKPx_dPSN1upB4D9W4LQYlNT_wEob7lR
CODEN	ITNNAL
CitedBy_id	crossref_primary_10_1109_JIOT_2020_3015489 crossref_primary_10_1109_ACCESS_2019_2963360 crossref_primary_10_1109_TGRS_2020_3034102 crossref_primary_10_1016_j_sigpro_2013_02_012 crossref_primary_10_1109_TGRS_2021_3087610 crossref_primary_10_1109_TNNLS_2013_2256367 crossref_primary_10_1016_j_sigpro_2024_109573 crossref_primary_10_1109_TNNLS_2012_2200500 crossref_primary_10_1109_TWC_2019_2961673 crossref_primary_10_1109_TNNLS_2020_2995482 crossref_primary_10_1137_100807004 crossref_primary_10_1016_j_acha_2019_05_004 crossref_primary_10_1109_TSP_2012_2200479 crossref_primary_10_1109_TSP_2019_2912139 crossref_primary_10_1007_s00034_021_01804_8 crossref_primary_10_1109_MSP_2013_2287951 crossref_primary_10_1016_j_csda_2022_107557 crossref_primary_10_1109_LGRS_2021_3131201 crossref_primary_10_1109_TCSII_2022_3142167 crossref_primary_10_1109_TNNLS_2012_2229293 crossref_primary_10_1016_j_dsp_2021_103087 crossref_primary_10_1109_TCSII_2019_2957817 crossref_primary_10_1109_TNNLS_2012_2201261 crossref_primary_10_3390_s19204540 crossref_primary_10_1109_TNNLS_2012_2198889 crossref_primary_10_1109_TNNLS_2013_2242091 crossref_primary_10_1016_j_ecosta_2024_06_003 crossref_primary_10_1109_TNNLS_2013_2271356 crossref_primary_10_1109_TNNLS_2014_2336679 crossref_primary_10_1109_TNNLS_2013_2265397 crossref_primary_10_1109_TNNLS_2013_2241788 crossref_primary_10_1109_TSP_2013_2296881 crossref_primary_10_1016_j_sigpro_2019_107263 crossref_primary_10_1016_j_sigpro_2016_06_029 crossref_primary_10_1109_TNNLS_2013_2285783 crossref_primary_10_1109_TSP_2013_2254481 crossref_primary_10_1109_ACCESS_2020_2996796
Cites_doi	10.1007/BF01447872 10.1109/TSP.2009.2027771 10.1109/TSP.2010.2046637 10.1109/TNN.2009.2024202 10.1109/TSP.2007.911278 10.1109/TIT.2006.881713 10.1109/MSP.2007.361610 10.1109/TWC.2010.01.080897 10.1002/9780470608593 10.1109/TSP.2004.830991 10.1109/TSP.2003.822359 10.1109/TSP.2010.2096420 10.1109/TSP.2007.895997 10.1109/TIT.2010.2048440 10.1081/NFA-200045806 10.1109/MSP.2010.938752 10.1080/01630560600884661 10.1109/MSP.2004.1296543 10.1109/TSP.2009.2027461 10.1109/TNNLS.2011.2178321 10.1109/TNN.2004.824259 10.1098/rsta.1909.0016 10.1109/TNN.2007.900237 10.7551/mitpress/4057.001.0001 10.1109/TSP.2008.923807 10.1109/78.403373 10.1016/j.cam.2011.02.003 10.1109/78.340781 10.1007/978-3-642-04174-7_32 10.1109/TSP.2008.926104 10.1109/TSP.2006.877638 10.1109/TSP.2007.907881 10.1109/TSP.2008.2011828 10.1109/TIP.2010.2042995 10.1109/TSP.2005.862946 10.1016/0022-247X(71)90184-3 10.1090/S0002-9947-1950-0051437-7 10.1109/TCOMM.2009.0901.060565 10.1109/TSP.2008.917376 10.1049/el:20030945 10.1109/TSP.2008.2005085 10.1109/TNN.2010.2059042 10.1109/TSP.2007.908937 10.1002/9780470575758 10.1017/CBO9780511809682 10.1002/9780470742624 10.1007/978-1-4419-9467-7 10.1002/0471725250 10.1109/TSP.2004.830985 10.1109/TNN.2009.2014060 10.1007/BF00670335 10.1109/TSP.2006.870639
ContentType	Journal Article
Copyright	2015 INIST-CNRS Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Mar 2012
Copyright_xml	– notice: 2015 INIST-CNRS – notice: Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Mar 2012
DBID	97E RIA RIE AAYXX CITATION IQODW NPM 7QF 7QO 7QP 7QQ 7QR 7SC 7SE 7SP 7SR 7TA 7TB 7TK 7U5 8BQ 8FD F28 FR3 H8D JG9 JQ2 KR7 L7M L~C L~D P64 7X8
DOI	10.1109/TNNLS.2011.2179810
DatabaseName	IEEE All-Society Periodicals Package (ASPP) 2005–Present IEEE All-Society Periodicals Package (ASPP) 1998–Present IEEE Electronic Library (IEL) CrossRef Pascal-Francis PubMed Aluminium Industry Abstracts Biotechnology Research Abstracts Calcium & Calcified Tissue Abstracts Ceramic Abstracts Chemoreception Abstracts Computer and Information Systems Abstracts Corrosion Abstracts Electronics & Communications Abstracts Engineered Materials Abstracts Materials Business File Mechanical & Transportation Engineering Abstracts Neurosciences Abstracts Solid State and Superconductivity Abstracts METADEX Technology Research Database ANTE: Abstracts in New Technology & Engineering Engineering Research Database Aerospace Database Materials Research Database ProQuest Computer Science Collection Civil Engineering Abstracts Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional Biotechnology and BioEngineering Abstracts MEDLINE - Academic
DatabaseTitle	CrossRef PubMed Materials Research Database Technology Research Database Computer and Information Systems Abstracts – Academic Mechanical & Transportation Engineering Abstracts ProQuest Computer Science Collection Computer and Information Systems Abstracts Materials Business File Aerospace Database Engineered Materials Abstracts Biotechnology Research Abstracts Chemoreception Abstracts Advanced Technologies Database with Aerospace ANTE: Abstracts in New Technology & Engineering Civil Engineering Abstracts Aluminium Industry Abstracts Electronics & Communications Abstracts Ceramic Abstracts Neurosciences Abstracts METADEX Biotechnology and BioEngineering Abstracts Computer and Information Systems Abstracts Professional Solid State and Superconductivity Abstracts Engineering Research Database Calcium & Calcified Tissue Abstracts Corrosion Abstracts MEDLINE - Academic
DatabaseTitleList	Materials Research Database Technology Research Database PubMed MEDLINE - Academic
Database_xml	– sequence: 1 dbid: NPM name: PubMed url: http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed sourceTypes: Index Database – sequence: 2 dbid: RIE name: IEEE Electronic Library (IEL) url: https://ieeexplore.ieee.org/ sourceTypes: Publisher – sequence: 3 dbid: 7X8 name: MEDLINE - Academic url: https://search.proquest.com/medline sourceTypes: Aggregation Database
DeliveryMethod	fulltext_linktorsrc
Discipline	Computer Science Applied Sciences
EISSN	2162-2388
EndPage	438
ExternalDocumentID	2597240561 24808549 25610449 10_1109_TNNLS_2011_2179810 6126047
Genre	orig-research Journal Article
GroupedDBID	0R~ 4.4 5VS 6IK 97E AAJGR AARMG AASAJ AAWTH ABAZT ABQJQ ABVLG ACIWK ACPRK AENEX AFRAH AGQYO AGSQL AHBIQ AKJIK AKQYR ALMA_UNASSIGNED_HOLDINGS ATWAV BEFXN BFFAM BGNUA BKEBE BPEOZ EBS EJD IFIPE IPLJI JAVBF M43 MS~ O9- OCL PQQKQ RIA RIE RNS AAYXX CITATION IQODW RIG NPM 7QF 7QO 7QP 7QQ 7QR 7SC 7SE 7SP 7SR 7TA 7TB 7TK 7U5 8BQ 8FD F28 FR3 H8D JG9 JQ2 KR7 L7M L~C L~D P64 7X8
ID	FETCH-LOGICAL-c479t-cf36bd9f69db5263ff1e70a9fbd39a5ef6e0eeb2940d4105bd4e3a8b444428543
IEDL.DBID	RIE
ISICitedReferencesCount	42
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000302705100005&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	2162-237X
IngestDate	Thu Oct 02 07:03:04 EDT 2025 Sun Nov 09 09:39:03 EST 2025 Sun Nov 30 05:07:24 EST 2025 Mon Jul 21 05:54:45 EDT 2025 Mon Jul 21 09:14:39 EDT 2025 Tue Nov 18 21:45:10 EST 2025 Sat Nov 29 01:39:45 EST 2025 Tue Aug 26 17:19:06 EDT 2025
IsDoiOpenAccess	false
IsOpenAccess	true
IsPeerReviewed	false
IsScholarly	true
Issue	3
Keywords	complex kernels subgradient Non linear channel Complex signal Equalization widely linear estimation Adaptive method Quadrature phase shift keying Kernel method Complex variable method Loss function Supervised learning Efficiency Linear filter Signal processing Sparse representation Signal sources Adaptive kernel learning Hilbert space Linear estimation projection Wirtinger's calculus Learning algorithm
Language	English
License	https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html CC BY 4.0
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c479t-cf36bd9f69db5263ff1e70a9fbd39a5ef6e0eeb2940d4105bd4e3a8b444428543
Notes	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 ObjectType-Article-2 ObjectType-Feature-1 content type line 23
PMID	24808549
PQID	923926848
PQPubID	85436
PageCount	14
ParticipantIDs	crossref_primary_10_1109_TNNLS_2011_2179810 pubmed_primary_24808549 proquest_journals_923926848 pascalfrancis_primary_25610449 crossref_citationtrail_10_1109_TNNLS_2011_2179810 proquest_miscellaneous_1523406049 ieee_primary_6126047 proquest_miscellaneous_1019655186
PublicationCentury	2000
PublicationDate	2012-03-01
PublicationDateYYYYMMDD	2012-03-01
PublicationDate_xml	– month: 03 year: 2012 text: 2012-03-01 day: 01
PublicationDecade	2010
PublicationPlace	New York, NY
PublicationPlace_xml	– name: New York, NY – name: United States – name: Piscataway
PublicationTitle	IEEE transaction on neural networks and learning systems
PublicationTitleAbbrev	TNNLS
PublicationTitleAlternate	IEEE Trans Neural Netw Learn Syst
PublicationYear	2012
Publisher	IEEE Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher_xml	– name: IEEE – name: Institute of Electrical and Electronics Engineers – name: The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
References	ref57 ref13 ref12 ref15 bouboulis (ref58) 0 ref14 ref53 paulsen (ref52) 2009 ref55 ref11 ref54 sayed (ref49) 2003 bauschke (ref47) 2011 ref17 ref16 ref19 ref18 haykin (ref48) 1996 ref50 scholkopf (ref20) 2004 ref45 ref42 ref41 ref44 bouboulis (ref62) 2011 scholkopf (ref1) 2002 li (ref56) 2008 ref8 ref7 ref9 ref4 slavakis (ref46) 2011 ref6 ref5 ref40 hastie (ref63) 2009 ref35 sayed (ref64) 2003 ref34 ref37 rockafellar (ref61) 1970 ref36 ref31 ref30 ref33 ref32 wachman (ref21) 2009; 5782 vapnik (ref3) 1999 ref39 ref38 theodoridis (ref2) 2008 rockafellar (ref59) 2004 ref24 ref23 ref26 ref25 pun (ref43) 2008; 56 ref66 ref22 ref65 ref28 ref27 ref29 huber (ref51) 1981 ref60 xu (ref10) 2008; 56
References_xml	– ident: ref55 doi: 10.1007/BF01447872 – ident: ref12 doi: 10.1109/TSP.2009.2027771 – year: 2004 ident: ref59 publication-title: Variational Analysis – year: 2008 ident: ref56 publication-title: Complex-valued adaptive signal processing using Wirtinger calculus and its application to independent component analysis – year: 2009 ident: ref63 publication-title: The Elements of Statistical Learning Data Mining Inference and Prediction – ident: ref24 doi: 10.1109/TSP.2010.2046637 – ident: ref13 doi: 10.1109/TNN.2009.2024202 – year: 1999 ident: ref3 publication-title: The Nature of Statistical Learning Theory – ident: ref31 doi: 10.1109/TSP.2007.911278 – ident: ref54 doi: 10.1109/TIT.2006.881713 – ident: ref16 doi: 10.1109/MSP.2007.361610 – ident: ref34 doi: 10.1109/TWC.2010.01.080897 – ident: ref5 doi: 10.1002/9780470608593 – ident: ref6 doi: 10.1109/TSP.2004.830991 – ident: ref40 doi: 10.1109/TSP.2003.822359 – ident: ref19 doi: 10.1109/TSP.2010.2096420 – year: 1970 ident: ref61 publication-title: Convex Analysis Princeton Mathematics Series – ident: ref42 doi: 10.1109/TSP.2007.895997 – ident: ref35 doi: 10.1109/TIT.2010.2048440 – year: 0 ident: ref58 publication-title: Wirtinger's Calculus in General Hilbert Spaces – year: 2011 ident: ref46 publication-title: The Adaptive Projected Subgradient Method Constrained by Families of Quasi-Nonexpansive Mappings and Its Application to Online Learning – ident: ref44 doi: 10.1081/NFA-200045806 – ident: ref50 doi: 10.1109/MSP.2010.938752 – start-page: 1 year: 2011 ident: ref62 article-title: Widely linear kernel-based adaptive filters publication-title: Proc 19th Eur Sig Process Conf – ident: ref45 doi: 10.1080/01630560600884661 – ident: ref8 doi: 10.1109/MSP.2004.1296543 – ident: ref39 doi: 10.1109/TSP.2009.2027461 – ident: ref60 doi: 10.1109/TNNLS.2011.2178321 – ident: ref14 doi: 10.1109/TNN.2004.824259 – ident: ref26 doi: 10.1098/rsta.1909.0016 – ident: ref15 doi: 10.1109/TNN.2007.900237 – year: 2004 ident: ref20 publication-title: Kernel Methods in Computational Biology doi: 10.7551/mitpress/4057.001.0001 – volume: 56 start-page: 4544 year: 2008 ident: ref43 article-title: Widely linear filter bank equalizer for real STBC publication-title: IEEE Trans Sig Process doi: 10.1109/TSP.2008.923807 – ident: ref29 doi: 10.1109/78.403373 – ident: ref53 doi: 10.1016/j.cam.2011.02.003 – ident: ref30 doi: 10.1109/78.340781 – volume: 5782 start-page: 489 year: 2009 ident: ref21 article-title: Kernels for periodic time series arising in astronomy publication-title: Machine Learn Knowledge Discovery Databases Lecture Notes Comput Sci doi: 10.1007/978-3-642-04174-7_32 – ident: ref57 doi: 10.1109/TSP.2008.926104 – ident: ref66 doi: 10.1109/TSP.2006.877638 – ident: ref11 doi: 10.1109/TSP.2007.907881 – year: 1996 ident: ref48 publication-title: Adaptive Filter Theory – ident: ref37 doi: 10.1109/TSP.2008.2011828 – ident: ref18 doi: 10.1109/TIP.2010.2042995 – ident: ref32 doi: 10.1109/TSP.2005.862946 – ident: ref65 doi: 10.1016/0022-247X(71)90184-3 – ident: ref25 doi: 10.1090/S0002-9947-1950-0051437-7 – ident: ref38 doi: 10.1109/TCOMM.2009.0901.060565 – ident: ref9 doi: 10.1109/TSP.2008.917376 – ident: ref41 doi: 10.1049/el:20030945 – year: 2003 ident: ref64 publication-title: Fundamentals of Adaptive Filtering – volume: 56 start-page: 5891 year: 2008 ident: ref10 article-title: A reproducing kernel Hilbert space framework for information theoretic learning publication-title: IEEE Trans Sig Process doi: 10.1109/TSP.2008.2005085 – ident: ref23 doi: 10.1109/TNN.2010.2059042 – ident: ref36 doi: 10.1109/TSP.2007.908937 – ident: ref28 doi: 10.1002/9780470575758 – ident: ref4 doi: 10.1017/CBO9780511809682 – ident: ref27 doi: 10.1002/9780470742624 – year: 2011 ident: ref47 publication-title: Convex Analysis and Monotone Operator Theory in Hilbert Spaces doi: 10.1007/978-1-4419-9467-7 – year: 2009 ident: ref52 publication-title: An Introduction to the Theory of Reproducing Kernel Hilbert Spaces – year: 1981 ident: ref51 publication-title: Robust Statistics doi: 10.1002/0471725250 – ident: ref7 doi: 10.1109/TSP.2004.830985 – year: 2002 ident: ref1 publication-title: Learning With Kernels Support Vector Machines Regularization Optimization and Beyond – ident: ref17 doi: 10.1109/TNN.2009.2014060 – ident: ref22 doi: 10.1007/BF00670335 – year: 2003 ident: ref49 publication-title: Fundamentals of Adaptive Filtering – year: 2008 ident: ref2 publication-title: Pattern Recognition – ident: ref33 doi: 10.1109/TSP.2006.870639
SSID	ssj0000605649
Score	2.2927842
Snippet	This paper presents a wide framework for non-linear online supervised learning tasks in the context of complex valued signal processing. The (complex) input...
SourceID	proquest pubmed pascalfrancis crossref ieee
SourceType	Aggregation Database Index Database Enrichment Source Publisher
StartPage	425
SubjectTerms	Adaptive kernel learning Applied sciences Artificial intelligence Calculus Channels complex kernels Computer science; control theory; systems Context Equalization Exact sciences and technology Hilbert space Kernel Kernels Learning Learning and adaptive systems Loss measurement Machine learning Mathematical analysis Nonlinearity On-line systems projection Signal processing Studies subgradient Tasks widely linear estimation Wirtinger's calculus
Title	Adaptive Learning in Complex Reproducing Kernel Hilbert Spaces Employing Wirtinger's Subgradients
URI	https://ieeexplore.ieee.org/document/6126047 https://www.ncbi.nlm.nih.gov/pubmed/24808549 https://www.proquest.com/docview/923926848 https://www.proquest.com/docview/1019655186 https://www.proquest.com/docview/1523406049
Volume	23
WOSCitedRecordID	wos000302705100005&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText	1
inHoldings	1
isFullTextHit
isPrint
journalDatabaseRights	– providerCode: PRVIEE databaseName: IEEE Electronic Library (IEL) customDbUrl: eissn: 2162-2388 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0000605649 issn: 2162-237X databaseCode: RIE dateStart: 20120101 isFulltext: true titleUrlDefault: https://ieeexplore.ieee.org/ providerName: IEEE
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1Ri9QwEA53hw--eOqpV0-XCIIPWq9N0qR5PMTjwGMR7tR9K0kzWRaW7tJ2xZ9vJu1WBT2wD6UkU9JkMs2XZPINIa95gCCF8j5VRbgJbbLUcC1Tq8F5x7iRkaz667Waz8vFQn8-IO-mszAAEJ3P4D0-xr18t6l3uFR2HkZjmQl1SA6VksNZrWk9JQu4XEa0y3LJUsbVYn9GJtPnt_P59c1A2MmQoivHCHBMlAFwIIvmb0NSjLGCHpKmC43kh-gW_4afcRi6PP6_CjwkD0a4SS-G_vGIHEDzmBzvQznQ0bJPiLlwZot_PjoSri7pqqEot4YfNKD0SAyLyZ-gbWBNr1ZIjtXTmy36dNEhcDDmf1shL8ES2jcdDX-lZRt9yvruCfly-fH2w1U6Rl9Ia6F0n9aeS-u0l9rZgknufQ4qM9pbx7UpwEvIIMzLtcgc-opaJ4Cb0opw4bFM_pQcNZsGTgktS62MDYmZtyI0gS5Lw2plwbHcOuMTku8VUNUjNTlGyFhXcYqS6Srqr0L9VaP-EvJ2emc7EHPcKX2C2pgkR0UkZPaHnqd8hrBSCJ2Qs73iq9G4uypgYo0kOWVCXk25wSpxq8U0sNl16DinJZLdyTtkCsYFcheFUp4NfepX-WPXfP737z4j90Pt2OAL94Ic9e0OXpJ79fd-1bWzYB6LchbN4ycZ7gn-
linkProvider	IEEE
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3fi9QwEB7OU9AXTz1_1NMzguCD1kuTNG0eD_FYuXURbtV9K2mTLAtLd2m74p9vJu1WBT2wD6UkU9JkMs2XZPINwCvuIUiaORdnqb8JpWmsuZJxqaxxhnEtA1n112k2m-WLhfp8AG_HszDW2uB8Zt_hY9jLN5tqh0tlZ340llRkN-BmKgSj_WmtcUWFemQuA95liWQx49lif0qGqrP5bDa96ik7GZJ0JRgDjoncQw7k0fxtUApRVtBHUre-mVwf3-LfADQMRBdH_1eFe3B3AJzkvO8h9-HA1g_gaB_MgQy2fQz63Ogt_vvIQLm6JKuaoNza_iAepwdqWEy-tE1t12SyQnqsjlxt0auL9KGDMf_bCpkJlrZ53RL_X1o2wausax_Cl4sP8_eTeIi_EFciU11cOS5Lo5xUpkyZ5M4lNqNaudJwpVPrpKXWz8yVoAa9RUsjLNd5KfyFBzP5IzisN7V9AiTPVaZLn0hdKXwTqDzXrMpKa1hSGu0iSPYKKKqBnBxjZKyLMEmhqgj6K1B_xaC_CN6M72x7ao5rpY9RG6PkoIgITv_Q85jPEFgKoSI42Su-GMy7LTwqVkiTk0fwcsz1dombLbq2m12LrnNKIt2dvEYmZVwge5Ev5XHfp36VP3TNp3__7hdwezL_NC2mH2eXJ3DH15T1nnHP4LBrdvY53Kq-d6u2OQ1G8hPJVwxd
openUrl	ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Adaptive+Learning+in+Complex+Reproducing+Kernel+Hilbert+Spaces+Employing+Wirtinger%27s+Subgradients&rft.jtitle=IEEE+transaction+on+neural+networks+and+learning+systems&rft.au=Bouboulis%2C+Pantelis&rft.au=Slavakis%2C+Konstantinos&rft.au=Theodoridis%2C+Sergios&rft.date=2012-03-01&rft.issn=2162-237X&rft.eissn=2162-2388&rft.volume=23&rft.issue=3&rft.spage=425&rft.epage=438&rft_id=info:doi/10.1109%2FTNNLS.2011.2179810&rft.externalDBID=NO_FULL_TEXT
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2162-237X&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2162-237X&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2162-237X&client=summon