A class of multidimensional NIPALS algorithms for quaternion and tensor partial least squares regression

Quaternion and tensor-based signal processing benefits from exploiting higher dimensional structure in data to outperform the corresponding approaches using multivariate real algebras. Along with the extended range of processing options, these methods produce opportunities for a physically-meaningfu...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Stott, Alexander E. [verfasserIn] Scalzo Dees, Bruno [verfasserIn] Kisil, Ilia [verfasserIn] Mandic, Danilo P. [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2019

Schlagwörter:	Multidimensional signal processing Partial least squares Component analysis Latent variables Matrix factorisation

Übergeordnetes Werk:	Enthalten in: Signal processing - Amsterdam [u.a.] : Elsevier, 1979, 160, Seite 316-327
Übergeordnetes Werk:	volume:160 ; pages:316-327

DOI / URN:	10.1016/j.sigpro.2019.03.002

Katalog-ID:	ELV001937928

Internformat


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100	1		\|a Stott, Alexander E. \|e verfasserin \|0 (orcid)0000-0001-6121-705X \|4 aut
245	1	0	\|a A class of multidimensional NIPALS algorithms for quaternion and tensor partial least squares regression
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520			\|a Quaternion and tensor-based signal processing benefits from exploiting higher dimensional structure in data to outperform the corresponding approaches using multivariate real algebras. Along with the extended range of processing options, these methods produce opportunities for a physically-meaningful interpretation. In this paper, we propose a class of novel partial least squares (PLS) algorithms for tensor- and quaternion-valued data, the widely linear quaternion PLS (WL-QPLS), the higher order nonlinear iterative PLS (HONIPALS) and the generalised higher order PLS (GHOPLS). This enables a regularised regression solution along with a latent variable decomposition of the original data based on the mutual information in the input and output block. The performance of the proposed algorithms is verified through analysis, together with a detailed comparison between quaternions and tensors and their application for image classification.
650		4	\|a Multidimensional signal processing
650		4	\|a Partial least squares
650		4	\|a Component analysis
650		4	\|a Latent variables
650		4	\|a Matrix factorisation
700	1		\|a Scalzo Dees, Bruno \|e verfasserin \|4 aut
700	1		\|a Kisil, Ilia \|e verfasserin \|4 aut
700	1		\|a Mandic, Danilo P. \|e verfasserin \|4 aut
773	0	8	\|i Enthalten in \|t Signal processing \|d Amsterdam [u.a.] : Elsevier, 1979 \|g 160, Seite 316-327 \|h Online-Ressource \|w (DE-627)265784166 \|w (DE-600)1466346-6 \|w (DE-576)074891022 \|7 nnns
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912			\|a GBV_ILN_32
912			\|a GBV_ILN_40
912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_63
912			\|a GBV_ILN_65
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_74
912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_101
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_224
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2006
912			\|a GBV_ILN_2008
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2056
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2147
912			\|a GBV_ILN_2148
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2470
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_2522
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4126
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4251
912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4313
912			\|a GBV_ILN_4322
912			\|a GBV_ILN_4323
912			\|a GBV_ILN_4324
912			\|a GBV_ILN_4325
912			\|a GBV_ILN_4326
912			\|a GBV_ILN_4333
912			\|a GBV_ILN_4334
912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4393
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Indexfelder

author_variant	a e s ae aes d b s db dbs i k ik d p m dp dpm
matchkey_str	stottalexanderescalzodeesbrunokisililiam:2019----:casfutdmninliasloihsoqaenoadesrat
hierarchy_sort_str	2019
bklnumber	53.73
publishDate	2019
allfields	10.1016/j.sigpro.2019.03.002 doi (DE-627)ELV001937928 (ELSEVIER)S0165-1684(19)30089-1 DE-627 ger DE-627 rda eng 004 000 DE-600 53.73 bkl Stott, Alexander E. verfasserin (orcid)0000-0001-6121-705X aut A class of multidimensional NIPALS algorithms for quaternion and tensor partial least squares regression 2019 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Quaternion and tensor-based signal processing benefits from exploiting higher dimensional structure in data to outperform the corresponding approaches using multivariate real algebras. Along with the extended range of processing options, these methods produce opportunities for a physically-meaningful interpretation. In this paper, we propose a class of novel partial least squares (PLS) algorithms for tensor- and quaternion-valued data, the widely linear quaternion PLS (WL-QPLS), the higher order nonlinear iterative PLS (HONIPALS) and the generalised higher order PLS (GHOPLS). This enables a regularised regression solution along with a latent variable decomposition of the original data based on the mutual information in the input and output block. The performance of the proposed algorithms is verified through analysis, together with a detailed comparison between quaternions and tensors and their application for image classification. Multidimensional signal processing Partial least squares Component analysis Latent variables Matrix factorisation Scalzo Dees, Bruno verfasserin aut Kisil, Ilia verfasserin aut Mandic, Danilo P. verfasserin aut Enthalten in Signal processing Amsterdam [u.a.] : Elsevier, 1979 160, Seite 316-327 Online-Ressource (DE-627)265784166 (DE-600)1466346-6 (DE-576)074891022 nnns volume:160 pages:316-327 GBV_USEFLAG_U SYSFLAG_U GBV_ELV GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 53.73 Nachrichtenübertragung AR 160 316-327
spelling	10.1016/j.sigpro.2019.03.002 doi (DE-627)ELV001937928 (ELSEVIER)S0165-1684(19)30089-1 DE-627 ger DE-627 rda eng 004 000 DE-600 53.73 bkl Stott, Alexander E. verfasserin (orcid)0000-0001-6121-705X aut A class of multidimensional NIPALS algorithms for quaternion and tensor partial least squares regression 2019 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Quaternion and tensor-based signal processing benefits from exploiting higher dimensional structure in data to outperform the corresponding approaches using multivariate real algebras. Along with the extended range of processing options, these methods produce opportunities for a physically-meaningful interpretation. In this paper, we propose a class of novel partial least squares (PLS) algorithms for tensor- and quaternion-valued data, the widely linear quaternion PLS (WL-QPLS), the higher order nonlinear iterative PLS (HONIPALS) and the generalised higher order PLS (GHOPLS). This enables a regularised regression solution along with a latent variable decomposition of the original data based on the mutual information in the input and output block. The performance of the proposed algorithms is verified through analysis, together with a detailed comparison between quaternions and tensors and their application for image classification. Multidimensional signal processing Partial least squares Component analysis Latent variables Matrix factorisation Scalzo Dees, Bruno verfasserin aut Kisil, Ilia verfasserin aut Mandic, Danilo P. verfasserin aut Enthalten in Signal processing Amsterdam [u.a.] : Elsevier, 1979 160, Seite 316-327 Online-Ressource (DE-627)265784166 (DE-600)1466346-6 (DE-576)074891022 nnns volume:160 pages:316-327 GBV_USEFLAG_U SYSFLAG_U GBV_ELV GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 53.73 Nachrichtenübertragung AR 160 316-327
allfields_unstemmed	10.1016/j.sigpro.2019.03.002 doi (DE-627)ELV001937928 (ELSEVIER)S0165-1684(19)30089-1 DE-627 ger DE-627 rda eng 004 000 DE-600 53.73 bkl Stott, Alexander E. verfasserin (orcid)0000-0001-6121-705X aut A class of multidimensional NIPALS algorithms for quaternion and tensor partial least squares regression 2019 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Quaternion and tensor-based signal processing benefits from exploiting higher dimensional structure in data to outperform the corresponding approaches using multivariate real algebras. Along with the extended range of processing options, these methods produce opportunities for a physically-meaningful interpretation. In this paper, we propose a class of novel partial least squares (PLS) algorithms for tensor- and quaternion-valued data, the widely linear quaternion PLS (WL-QPLS), the higher order nonlinear iterative PLS (HONIPALS) and the generalised higher order PLS (GHOPLS). This enables a regularised regression solution along with a latent variable decomposition of the original data based on the mutual information in the input and output block. The performance of the proposed algorithms is verified through analysis, together with a detailed comparison between quaternions and tensors and their application for image classification. Multidimensional signal processing Partial least squares Component analysis Latent variables Matrix factorisation Scalzo Dees, Bruno verfasserin aut Kisil, Ilia verfasserin aut Mandic, Danilo P. verfasserin aut Enthalten in Signal processing Amsterdam [u.a.] : Elsevier, 1979 160, Seite 316-327 Online-Ressource (DE-627)265784166 (DE-600)1466346-6 (DE-576)074891022 nnns volume:160 pages:316-327 GBV_USEFLAG_U SYSFLAG_U GBV_ELV GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 53.73 Nachrichtenübertragung AR 160 316-327
allfieldsGer	10.1016/j.sigpro.2019.03.002 doi (DE-627)ELV001937928 (ELSEVIER)S0165-1684(19)30089-1 DE-627 ger DE-627 rda eng 004 000 DE-600 53.73 bkl Stott, Alexander E. verfasserin (orcid)0000-0001-6121-705X aut A class of multidimensional NIPALS algorithms for quaternion and tensor partial least squares regression 2019 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Quaternion and tensor-based signal processing benefits from exploiting higher dimensional structure in data to outperform the corresponding approaches using multivariate real algebras. Along with the extended range of processing options, these methods produce opportunities for a physically-meaningful interpretation. In this paper, we propose a class of novel partial least squares (PLS) algorithms for tensor- and quaternion-valued data, the widely linear quaternion PLS (WL-QPLS), the higher order nonlinear iterative PLS (HONIPALS) and the generalised higher order PLS (GHOPLS). This enables a regularised regression solution along with a latent variable decomposition of the original data based on the mutual information in the input and output block. The performance of the proposed algorithms is verified through analysis, together with a detailed comparison between quaternions and tensors and their application for image classification. Multidimensional signal processing Partial least squares Component analysis Latent variables Matrix factorisation Scalzo Dees, Bruno verfasserin aut Kisil, Ilia verfasserin aut Mandic, Danilo P. verfasserin aut Enthalten in Signal processing Amsterdam [u.a.] : Elsevier, 1979 160, Seite 316-327 Online-Ressource (DE-627)265784166 (DE-600)1466346-6 (DE-576)074891022 nnns volume:160 pages:316-327 GBV_USEFLAG_U SYSFLAG_U GBV_ELV GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 53.73 Nachrichtenübertragung AR 160 316-327
allfieldsSound	10.1016/j.sigpro.2019.03.002 doi (DE-627)ELV001937928 (ELSEVIER)S0165-1684(19)30089-1 DE-627 ger DE-627 rda eng 004 000 DE-600 53.73 bkl Stott, Alexander E. verfasserin (orcid)0000-0001-6121-705X aut A class of multidimensional NIPALS algorithms for quaternion and tensor partial least squares regression 2019 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Quaternion and tensor-based signal processing benefits from exploiting higher dimensional structure in data to outperform the corresponding approaches using multivariate real algebras. Along with the extended range of processing options, these methods produce opportunities for a physically-meaningful interpretation. In this paper, we propose a class of novel partial least squares (PLS) algorithms for tensor- and quaternion-valued data, the widely linear quaternion PLS (WL-QPLS), the higher order nonlinear iterative PLS (HONIPALS) and the generalised higher order PLS (GHOPLS). This enables a regularised regression solution along with a latent variable decomposition of the original data based on the mutual information in the input and output block. The performance of the proposed algorithms is verified through analysis, together with a detailed comparison between quaternions and tensors and their application for image classification. Multidimensional signal processing Partial least squares Component analysis Latent variables Matrix factorisation Scalzo Dees, Bruno verfasserin aut Kisil, Ilia verfasserin aut Mandic, Danilo P. verfasserin aut Enthalten in Signal processing Amsterdam [u.a.] : Elsevier, 1979 160, Seite 316-327 Online-Ressource (DE-627)265784166 (DE-600)1466346-6 (DE-576)074891022 nnns volume:160 pages:316-327 GBV_USEFLAG_U SYSFLAG_U GBV_ELV GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 53.73 Nachrichtenübertragung AR 160 316-327
language	English
source	Enthalten in Signal processing 160, Seite 316-327 volume:160 pages:316-327
sourceStr	Enthalten in Signal processing 160, Seite 316-327 volume:160 pages:316-327
format_phy_str_mv	Article
bklname	Nachrichtenübertragung
institution	findex.gbv.de
topic_facet	Multidimensional signal processing Partial least squares Component analysis Latent variables Matrix factorisation
dewey-raw	004
isfreeaccess_bool	false
container_title	Signal processing
authorswithroles_txt_mv	Stott, Alexander E. @@aut@@ Scalzo Dees, Bruno @@aut@@ Kisil, Ilia @@aut@@ Mandic, Danilo P. @@aut@@
publishDateDaySort_date	2019-01-01T00:00:00Z
hierarchy_top_id	265784166
dewey-sort	14
id	ELV001937928
language_de	englisch
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author	Stott, Alexander E.
spellingShingle	Stott, Alexander E. ddc 004 bkl 53.73 misc Multidimensional signal processing misc Partial least squares misc Component analysis misc Latent variables misc Matrix factorisation A class of multidimensional NIPALS algorithms for quaternion and tensor partial least squares regression
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topic_title	004 000 DE-600 53.73 bkl A class of multidimensional NIPALS algorithms for quaternion and tensor partial least squares regression Multidimensional signal processing Partial least squares Component analysis Latent variables Matrix factorisation
topic	ddc 004 bkl 53.73 misc Multidimensional signal processing misc Partial least squares misc Component analysis misc Latent variables misc Matrix factorisation
topic_unstemmed	ddc 004 bkl 53.73 misc Multidimensional signal processing misc Partial least squares misc Component analysis misc Latent variables misc Matrix factorisation
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title	A class of multidimensional NIPALS algorithms for quaternion and tensor partial least squares regression
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title_full	A class of multidimensional NIPALS algorithms for quaternion and tensor partial least squares regression
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title_sort	a class of multidimensional nipals algorithms for quaternion and tensor partial least squares regression
title_auth	A class of multidimensional NIPALS algorithms for quaternion and tensor partial least squares regression
abstract	Quaternion and tensor-based signal processing benefits from exploiting higher dimensional structure in data to outperform the corresponding approaches using multivariate real algebras. Along with the extended range of processing options, these methods produce opportunities for a physically-meaningful interpretation. In this paper, we propose a class of novel partial least squares (PLS) algorithms for tensor- and quaternion-valued data, the widely linear quaternion PLS (WL-QPLS), the higher order nonlinear iterative PLS (HONIPALS) and the generalised higher order PLS (GHOPLS). This enables a regularised regression solution along with a latent variable decomposition of the original data based on the mutual information in the input and output block. The performance of the proposed algorithms is verified through analysis, together with a detailed comparison between quaternions and tensors and their application for image classification.
abstractGer	Quaternion and tensor-based signal processing benefits from exploiting higher dimensional structure in data to outperform the corresponding approaches using multivariate real algebras. Along with the extended range of processing options, these methods produce opportunities for a physically-meaningful interpretation. In this paper, we propose a class of novel partial least squares (PLS) algorithms for tensor- and quaternion-valued data, the widely linear quaternion PLS (WL-QPLS), the higher order nonlinear iterative PLS (HONIPALS) and the generalised higher order PLS (GHOPLS). This enables a regularised regression solution along with a latent variable decomposition of the original data based on the mutual information in the input and output block. The performance of the proposed algorithms is verified through analysis, together with a detailed comparison between quaternions and tensors and their application for image classification.
abstract_unstemmed	Quaternion and tensor-based signal processing benefits from exploiting higher dimensional structure in data to outperform the corresponding approaches using multivariate real algebras. Along with the extended range of processing options, these methods produce opportunities for a physically-meaningful interpretation. In this paper, we propose a class of novel partial least squares (PLS) algorithms for tensor- and quaternion-valued data, the widely linear quaternion PLS (WL-QPLS), the higher order nonlinear iterative PLS (HONIPALS) and the generalised higher order PLS (GHOPLS). This enables a regularised regression solution along with a latent variable decomposition of the original data based on the mutual information in the input and output block. The performance of the proposed algorithms is verified through analysis, together with a detailed comparison between quaternions and tensors and their application for image classification.
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title_short	A class of multidimensional NIPALS algorithms for quaternion and tensor partial least squares regression
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up_date	2024-07-06T23:04:39.081Z
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A class of multidimensional NIPALS algorithms for quaternion and tensor partial least squares regression

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