Improved method for correcting sample Mahalanobis distance without estimating population eigenvalues or eigenvectors of covariance matrix

Abstract The recognition performance of the sample Mahalanobis distance (SMD) deteriorates as the number of learning samples decreases. Therefore, it is important to correct the SMD for a population Mahalanobis distance (PMD) such that it becomes equivalent to the case of infinite learning samples....
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Kobayashi, Yasuyuki [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2019

Schlagwörter:	Sample Mahalanobis distance Correction method Sample eigenvalues and eigenvectors Delta method Lawley’s bias estimation Gaussian mixture model

Übergeordnetes Werk:	Enthalten in: International journal of data science and analytics - Cham, Switzerland : Springer International Publishing, 2016, 10(2019), 2 vom: 07. Dez., Seite 121-134
Übergeordnetes Werk:	volume:10 ; year:2019 ; number:2 ; day:07 ; month:12 ; pages:121-134

Links:	Volltext

DOI / URN:	10.1007/s41060-019-00201-4

Katalog-ID:	SPR040377792

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245	1	0	\|a Improved method for correcting sample Mahalanobis distance without estimating population eigenvalues or eigenvectors of covariance matrix
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520			\|a Abstract The recognition performance of the sample Mahalanobis distance (SMD) deteriorates as the number of learning samples decreases. Therefore, it is important to correct the SMD for a population Mahalanobis distance (PMD) such that it becomes equivalent to the case of infinite learning samples. In order to reduce the computation time and cost for this main purpose, this paper presents a correction method that does not require the estimation of the population eigenvalues or eigenvectors of the covariance matrix. In short, this method only requires the sample eigenvalues of the covariance matrix, number of learning samples, and dimensionality to correct the SMD for the PMD. This method involves the summation of the SMD’s principal components (each of which is divided by its expectation obtained using the delta method), Lawley’s bias estimation, and the variances of the sample eigenvectors. A numerical experiment demonstrates that this method works well for various cases of learning sample number, dimensionality, population eigenvalues sequence, and non-centrality. The application of this method also shows improved performance of estimating a Gaussian mixture model using the expectation–maximization algorithm.
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650		4	\|a Correction method \|7 (dpeaa)DE-He213
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650		4	\|a Delta method \|7 (dpeaa)DE-He213
650		4	\|a Lawley’s bias estimation \|7 (dpeaa)DE-He213
650		4	\|a Gaussian mixture model \|7 (dpeaa)DE-He213
773	0	8	\|i Enthalten in \|t International journal of data science and analytics \|d Cham, Switzerland : Springer International Publishing, 2016 \|g 10(2019), 2 vom: 07. Dez., Seite 121-134 \|w (DE-627)84425083X \|w (DE-600)2843078-5 \|x 2364-4168 \|7 nnns
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allfields	10.1007/s41060-019-00201-4 doi (DE-627)SPR040377792 (SPR)s41060-019-00201-4-e DE-627 ger DE-627 rakwb eng 004 ASE 004 ASE Kobayashi, Yasuyuki verfasserin aut Improved method for correcting sample Mahalanobis distance without estimating population eigenvalues or eigenvectors of covariance matrix 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The recognition performance of the sample Mahalanobis distance (SMD) deteriorates as the number of learning samples decreases. Therefore, it is important to correct the SMD for a population Mahalanobis distance (PMD) such that it becomes equivalent to the case of infinite learning samples. In order to reduce the computation time and cost for this main purpose, this paper presents a correction method that does not require the estimation of the population eigenvalues or eigenvectors of the covariance matrix. In short, this method only requires the sample eigenvalues of the covariance matrix, number of learning samples, and dimensionality to correct the SMD for the PMD. This method involves the summation of the SMD’s principal components (each of which is divided by its expectation obtained using the delta method), Lawley’s bias estimation, and the variances of the sample eigenvectors. A numerical experiment demonstrates that this method works well for various cases of learning sample number, dimensionality, population eigenvalues sequence, and non-centrality. The application of this method also shows improved performance of estimating a Gaussian mixture model using the expectation–maximization algorithm. Sample Mahalanobis distance (dpeaa)DE-He213 Correction method (dpeaa)DE-He213 Sample eigenvalues and eigenvectors (dpeaa)DE-He213 Delta method (dpeaa)DE-He213 Lawley’s bias estimation (dpeaa)DE-He213 Gaussian mixture model (dpeaa)DE-He213 Enthalten in International journal of data science and analytics Cham, Switzerland : Springer International Publishing, 2016 10(2019), 2 vom: 07. Dez., Seite 121-134 (DE-627)84425083X (DE-600)2843078-5 2364-4168 nnns volume:10 year:2019 number:2 day:07 month:12 pages:121-134 https://dx.doi.org/10.1007/s41060-019-00201-4 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 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_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_266 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 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_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 10 2019 2 07 12 121-134
spelling	10.1007/s41060-019-00201-4 doi (DE-627)SPR040377792 (SPR)s41060-019-00201-4-e DE-627 ger DE-627 rakwb eng 004 ASE 004 ASE Kobayashi, Yasuyuki verfasserin aut Improved method for correcting sample Mahalanobis distance without estimating population eigenvalues or eigenvectors of covariance matrix 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The recognition performance of the sample Mahalanobis distance (SMD) deteriorates as the number of learning samples decreases. Therefore, it is important to correct the SMD for a population Mahalanobis distance (PMD) such that it becomes equivalent to the case of infinite learning samples. In order to reduce the computation time and cost for this main purpose, this paper presents a correction method that does not require the estimation of the population eigenvalues or eigenvectors of the covariance matrix. In short, this method only requires the sample eigenvalues of the covariance matrix, number of learning samples, and dimensionality to correct the SMD for the PMD. This method involves the summation of the SMD’s principal components (each of which is divided by its expectation obtained using the delta method), Lawley’s bias estimation, and the variances of the sample eigenvectors. A numerical experiment demonstrates that this method works well for various cases of learning sample number, dimensionality, population eigenvalues sequence, and non-centrality. The application of this method also shows improved performance of estimating a Gaussian mixture model using the expectation–maximization algorithm. Sample Mahalanobis distance (dpeaa)DE-He213 Correction method (dpeaa)DE-He213 Sample eigenvalues and eigenvectors (dpeaa)DE-He213 Delta method (dpeaa)DE-He213 Lawley’s bias estimation (dpeaa)DE-He213 Gaussian mixture model (dpeaa)DE-He213 Enthalten in International journal of data science and analytics Cham, Switzerland : Springer International Publishing, 2016 10(2019), 2 vom: 07. Dez., Seite 121-134 (DE-627)84425083X (DE-600)2843078-5 2364-4168 nnns volume:10 year:2019 number:2 day:07 month:12 pages:121-134 https://dx.doi.org/10.1007/s41060-019-00201-4 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 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_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_266 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 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_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 10 2019 2 07 12 121-134
allfields_unstemmed	10.1007/s41060-019-00201-4 doi (DE-627)SPR040377792 (SPR)s41060-019-00201-4-e DE-627 ger DE-627 rakwb eng 004 ASE 004 ASE Kobayashi, Yasuyuki verfasserin aut Improved method for correcting sample Mahalanobis distance without estimating population eigenvalues or eigenvectors of covariance matrix 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The recognition performance of the sample Mahalanobis distance (SMD) deteriorates as the number of learning samples decreases. Therefore, it is important to correct the SMD for a population Mahalanobis distance (PMD) such that it becomes equivalent to the case of infinite learning samples. In order to reduce the computation time and cost for this main purpose, this paper presents a correction method that does not require the estimation of the population eigenvalues or eigenvectors of the covariance matrix. In short, this method only requires the sample eigenvalues of the covariance matrix, number of learning samples, and dimensionality to correct the SMD for the PMD. This method involves the summation of the SMD’s principal components (each of which is divided by its expectation obtained using the delta method), Lawley’s bias estimation, and the variances of the sample eigenvectors. A numerical experiment demonstrates that this method works well for various cases of learning sample number, dimensionality, population eigenvalues sequence, and non-centrality. The application of this method also shows improved performance of estimating a Gaussian mixture model using the expectation–maximization algorithm. Sample Mahalanobis distance (dpeaa)DE-He213 Correction method (dpeaa)DE-He213 Sample eigenvalues and eigenvectors (dpeaa)DE-He213 Delta method (dpeaa)DE-He213 Lawley’s bias estimation (dpeaa)DE-He213 Gaussian mixture model (dpeaa)DE-He213 Enthalten in International journal of data science and analytics Cham, Switzerland : Springer International Publishing, 2016 10(2019), 2 vom: 07. Dez., Seite 121-134 (DE-627)84425083X (DE-600)2843078-5 2364-4168 nnns volume:10 year:2019 number:2 day:07 month:12 pages:121-134 https://dx.doi.org/10.1007/s41060-019-00201-4 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 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_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_266 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 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_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 10 2019 2 07 12 121-134
allfieldsGer	10.1007/s41060-019-00201-4 doi (DE-627)SPR040377792 (SPR)s41060-019-00201-4-e DE-627 ger DE-627 rakwb eng 004 ASE 004 ASE Kobayashi, Yasuyuki verfasserin aut Improved method for correcting sample Mahalanobis distance without estimating population eigenvalues or eigenvectors of covariance matrix 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The recognition performance of the sample Mahalanobis distance (SMD) deteriorates as the number of learning samples decreases. Therefore, it is important to correct the SMD for a population Mahalanobis distance (PMD) such that it becomes equivalent to the case of infinite learning samples. In order to reduce the computation time and cost for this main purpose, this paper presents a correction method that does not require the estimation of the population eigenvalues or eigenvectors of the covariance matrix. In short, this method only requires the sample eigenvalues of the covariance matrix, number of learning samples, and dimensionality to correct the SMD for the PMD. This method involves the summation of the SMD’s principal components (each of which is divided by its expectation obtained using the delta method), Lawley’s bias estimation, and the variances of the sample eigenvectors. A numerical experiment demonstrates that this method works well for various cases of learning sample number, dimensionality, population eigenvalues sequence, and non-centrality. The application of this method also shows improved performance of estimating a Gaussian mixture model using the expectation–maximization algorithm. Sample Mahalanobis distance (dpeaa)DE-He213 Correction method (dpeaa)DE-He213 Sample eigenvalues and eigenvectors (dpeaa)DE-He213 Delta method (dpeaa)DE-He213 Lawley’s bias estimation (dpeaa)DE-He213 Gaussian mixture model (dpeaa)DE-He213 Enthalten in International journal of data science and analytics Cham, Switzerland : Springer International Publishing, 2016 10(2019), 2 vom: 07. Dez., Seite 121-134 (DE-627)84425083X (DE-600)2843078-5 2364-4168 nnns volume:10 year:2019 number:2 day:07 month:12 pages:121-134 https://dx.doi.org/10.1007/s41060-019-00201-4 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 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_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_266 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 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_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 10 2019 2 07 12 121-134
allfieldsSound	10.1007/s41060-019-00201-4 doi (DE-627)SPR040377792 (SPR)s41060-019-00201-4-e DE-627 ger DE-627 rakwb eng 004 ASE 004 ASE Kobayashi, Yasuyuki verfasserin aut Improved method for correcting sample Mahalanobis distance without estimating population eigenvalues or eigenvectors of covariance matrix 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The recognition performance of the sample Mahalanobis distance (SMD) deteriorates as the number of learning samples decreases. Therefore, it is important to correct the SMD for a population Mahalanobis distance (PMD) such that it becomes equivalent to the case of infinite learning samples. In order to reduce the computation time and cost for this main purpose, this paper presents a correction method that does not require the estimation of the population eigenvalues or eigenvectors of the covariance matrix. In short, this method only requires the sample eigenvalues of the covariance matrix, number of learning samples, and dimensionality to correct the SMD for the PMD. This method involves the summation of the SMD’s principal components (each of which is divided by its expectation obtained using the delta method), Lawley’s bias estimation, and the variances of the sample eigenvectors. A numerical experiment demonstrates that this method works well for various cases of learning sample number, dimensionality, population eigenvalues sequence, and non-centrality. The application of this method also shows improved performance of estimating a Gaussian mixture model using the expectation–maximization algorithm. Sample Mahalanobis distance (dpeaa)DE-He213 Correction method (dpeaa)DE-He213 Sample eigenvalues and eigenvectors (dpeaa)DE-He213 Delta method (dpeaa)DE-He213 Lawley’s bias estimation (dpeaa)DE-He213 Gaussian mixture model (dpeaa)DE-He213 Enthalten in International journal of data science and analytics Cham, Switzerland : Springer International Publishing, 2016 10(2019), 2 vom: 07. Dez., Seite 121-134 (DE-627)84425083X (DE-600)2843078-5 2364-4168 nnns volume:10 year:2019 number:2 day:07 month:12 pages:121-134 https://dx.doi.org/10.1007/s41060-019-00201-4 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 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_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_266 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 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_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 10 2019 2 07 12 121-134
language	English
source	Enthalten in International journal of data science and analytics 10(2019), 2 vom: 07. Dez., Seite 121-134 volume:10 year:2019 number:2 day:07 month:12 pages:121-134
sourceStr	Enthalten in International journal of data science and analytics 10(2019), 2 vom: 07. Dez., Seite 121-134 volume:10 year:2019 number:2 day:07 month:12 pages:121-134
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Sample Mahalanobis distance Correction method Sample eigenvalues and eigenvectors Delta method Lawley’s bias estimation Gaussian mixture model
dewey-raw	004
isfreeaccess_bool	true
container_title	International journal of data science and analytics
authorswithroles_txt_mv	Kobayashi, Yasuyuki @@aut@@
publishDateDaySort_date	2019-12-07T00:00:00Z
hierarchy_top_id	84425083X
dewey-sort	14
id	SPR040377792
language_de	englisch
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author	Kobayashi, Yasuyuki
spellingShingle	Kobayashi, Yasuyuki ddc 004 misc Sample Mahalanobis distance misc Correction method misc Sample eigenvalues and eigenvectors misc Delta method misc Lawley’s bias estimation misc Gaussian mixture model Improved method for correcting sample Mahalanobis distance without estimating population eigenvalues or eigenvectors of covariance matrix
authorStr	Kobayashi, Yasuyuki
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topic_title	004 ASE Improved method for correcting sample Mahalanobis distance without estimating population eigenvalues or eigenvectors of covariance matrix Sample Mahalanobis distance (dpeaa)DE-He213 Correction method (dpeaa)DE-He213 Sample eigenvalues and eigenvectors (dpeaa)DE-He213 Delta method (dpeaa)DE-He213 Lawley’s bias estimation (dpeaa)DE-He213 Gaussian mixture model (dpeaa)DE-He213
topic	ddc 004 misc Sample Mahalanobis distance misc Correction method misc Sample eigenvalues and eigenvectors misc Delta method misc Lawley’s bias estimation misc Gaussian mixture model
topic_unstemmed	ddc 004 misc Sample Mahalanobis distance misc Correction method misc Sample eigenvalues and eigenvectors misc Delta method misc Lawley’s bias estimation misc Gaussian mixture model
topic_browse	ddc 004 misc Sample Mahalanobis distance misc Correction method misc Sample eigenvalues and eigenvectors misc Delta method misc Lawley’s bias estimation misc Gaussian mixture model
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title	Improved method for correcting sample Mahalanobis distance without estimating population eigenvalues or eigenvectors of covariance matrix
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title_full	Improved method for correcting sample Mahalanobis distance without estimating population eigenvalues or eigenvectors of covariance matrix
author_sort	Kobayashi, Yasuyuki
journal	International journal of data science and analytics
journalStr	International journal of data science and analytics
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author-letter	Kobayashi, Yasuyuki
doi_str_mv	10.1007/s41060-019-00201-4
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title_sort	improved method for correcting sample mahalanobis distance without estimating population eigenvalues or eigenvectors of covariance matrix
title_auth	Improved method for correcting sample Mahalanobis distance without estimating population eigenvalues or eigenvectors of covariance matrix
abstract	Abstract The recognition performance of the sample Mahalanobis distance (SMD) deteriorates as the number of learning samples decreases. Therefore, it is important to correct the SMD for a population Mahalanobis distance (PMD) such that it becomes equivalent to the case of infinite learning samples. In order to reduce the computation time and cost for this main purpose, this paper presents a correction method that does not require the estimation of the population eigenvalues or eigenvectors of the covariance matrix. In short, this method only requires the sample eigenvalues of the covariance matrix, number of learning samples, and dimensionality to correct the SMD for the PMD. This method involves the summation of the SMD’s principal components (each of which is divided by its expectation obtained using the delta method), Lawley’s bias estimation, and the variances of the sample eigenvectors. A numerical experiment demonstrates that this method works well for various cases of learning sample number, dimensionality, population eigenvalues sequence, and non-centrality. The application of this method also shows improved performance of estimating a Gaussian mixture model using the expectation–maximization algorithm.
abstractGer	Abstract The recognition performance of the sample Mahalanobis distance (SMD) deteriorates as the number of learning samples decreases. Therefore, it is important to correct the SMD for a population Mahalanobis distance (PMD) such that it becomes equivalent to the case of infinite learning samples. In order to reduce the computation time and cost for this main purpose, this paper presents a correction method that does not require the estimation of the population eigenvalues or eigenvectors of the covariance matrix. In short, this method only requires the sample eigenvalues of the covariance matrix, number of learning samples, and dimensionality to correct the SMD for the PMD. This method involves the summation of the SMD’s principal components (each of which is divided by its expectation obtained using the delta method), Lawley’s bias estimation, and the variances of the sample eigenvectors. A numerical experiment demonstrates that this method works well for various cases of learning sample number, dimensionality, population eigenvalues sequence, and non-centrality. The application of this method also shows improved performance of estimating a Gaussian mixture model using the expectation–maximization algorithm.
abstract_unstemmed	Abstract The recognition performance of the sample Mahalanobis distance (SMD) deteriorates as the number of learning samples decreases. Therefore, it is important to correct the SMD for a population Mahalanobis distance (PMD) such that it becomes equivalent to the case of infinite learning samples. In order to reduce the computation time and cost for this main purpose, this paper presents a correction method that does not require the estimation of the population eigenvalues or eigenvectors of the covariance matrix. In short, this method only requires the sample eigenvalues of the covariance matrix, number of learning samples, and dimensionality to correct the SMD for the PMD. This method involves the summation of the SMD’s principal components (each of which is divided by its expectation obtained using the delta method), Lawley’s bias estimation, and the variances of the sample eigenvectors. A numerical experiment demonstrates that this method works well for various cases of learning sample number, dimensionality, population eigenvalues sequence, and non-centrality. The application of this method also shows improved performance of estimating a Gaussian mixture model using the expectation–maximization algorithm.
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title_short	Improved method for correcting sample Mahalanobis distance without estimating population eigenvalues or eigenvectors of covariance matrix
url	https://dx.doi.org/10.1007/s41060-019-00201-4
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doi_str	10.1007/s41060-019-00201-4
up_date	2024-07-03T15:36:00.128Z
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Improved method for correcting sample Mahalanobis distance without estimating population eigenvalues or eigenvectors of covariance matrix

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