A New Separation Index and Classification Techniques Based on Shannon Entropy
Abstract The purpose is to use Shannon entropy measures to develop classification techniques and an index which estimates the separation of the groups in a finite mixture model. These measures can be applied to machine learning techniques such as discriminant analysis, cluster analysis, exploratory...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Navarro, Jorge [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2023 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s) 2023 |
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| Übergeordnetes Werk: |
Enthalten in: Methodology and computing in applied probability - Dordrecht [u.a.] : Springer Science + Business Media B.V, 1999, 25(2023), 4 vom: 22. Sept. |
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| Übergeordnetes Werk: |
volume:25 ; year:2023 ; number:4 ; day:22 ; month:09 |
| Links: |
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| DOI / URN: |
10.1007/s11009-023-10055-w |
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| Katalog-ID: |
SPR053163664 |
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| 100 | 1 | |a Navarro, Jorge |e verfasserin |0 (orcid)0000-0003-2822-915X |4 aut | |
| 245 | 1 | 2 | |a A New Separation Index and Classification Techniques Based on Shannon Entropy |
| 264 | 1 | |c 2023 | |
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| 520 | |a Abstract The purpose is to use Shannon entropy measures to develop classification techniques and an index which estimates the separation of the groups in a finite mixture model. These measures can be applied to machine learning techniques such as discriminant analysis, cluster analysis, exploratory data analysis, etc. If we know the number of groups and we have training samples from each group (supervised learning) the index is used to measure the separation of the groups. Here some entropy measures are used to classify new individuals in one of these groups. If we are not sure about the number of groups (unsupervised learning), the index can be used to determine the optimal number of groups from an entropy (information/uncertainty) criterion. It can also be used to determine the best variables in order to separate the groups. In all the cases we assume that we have absolutely continuous random variables and we use the Shannon entropy based on the probability density function. Theoretical, parametric and non-parametric techniques are proposed to get approximations of these entropy measures in practice. An application to gene selection in a colon cancer discrimination study with a lot of variables is provided as well. | ||
| 650 | 4 | |a Shannon entropy |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Discriminant analysis |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Cluster analysis |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Kernel density estimation |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Omic data |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Buono, Francesco |0 (orcid)0000-0002-3569-4052 |4 aut | |
| 700 | 1 | |a Arevalillo, Jorge M. |0 (orcid)0000-0003-1944-3699 |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Methodology and computing in applied probability |d Dordrecht [u.a.] : Springer Science + Business Media B.V, 1999 |g 25(2023), 4 vom: 22. Sept. |w (DE-627)320427412 |w (DE-600)2003336-9 |x 1573-7713 |7 nnns |
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| 856 | 4 | 0 | |u https://dx.doi.org/10.1007/s11009-023-10055-w |z kostenfrei |3 Volltext |
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10.1007/s11009-023-10055-w doi (DE-627)SPR053163664 (SPR)s11009-023-10055-w-e DE-627 ger DE-627 rakwb eng Navarro, Jorge verfasserin (orcid)0000-0003-2822-915X aut A New Separation Index and Classification Techniques Based on Shannon Entropy 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract The purpose is to use Shannon entropy measures to develop classification techniques and an index which estimates the separation of the groups in a finite mixture model. These measures can be applied to machine learning techniques such as discriminant analysis, cluster analysis, exploratory data analysis, etc. If we know the number of groups and we have training samples from each group (supervised learning) the index is used to measure the separation of the groups. Here some entropy measures are used to classify new individuals in one of these groups. If we are not sure about the number of groups (unsupervised learning), the index can be used to determine the optimal number of groups from an entropy (information/uncertainty) criterion. It can also be used to determine the best variables in order to separate the groups. In all the cases we assume that we have absolutely continuous random variables and we use the Shannon entropy based on the probability density function. Theoretical, parametric and non-parametric techniques are proposed to get approximations of these entropy measures in practice. An application to gene selection in a colon cancer discrimination study with a lot of variables is provided as well. Shannon entropy (dpeaa)DE-He213 Discriminant analysis (dpeaa)DE-He213 Cluster analysis (dpeaa)DE-He213 Kernel density estimation (dpeaa)DE-He213 Omic data (dpeaa)DE-He213 Buono, Francesco (orcid)0000-0002-3569-4052 aut Arevalillo, Jorge M. (orcid)0000-0003-1944-3699 aut Enthalten in Methodology and computing in applied probability Dordrecht [u.a.] : Springer Science + Business Media B.V, 1999 25(2023), 4 vom: 22. Sept. (DE-627)320427412 (DE-600)2003336-9 1573-7713 nnns volume:25 year:2023 number:4 day:22 month:09 https://dx.doi.org/10.1007/s11009-023-10055-w 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_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_152 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_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_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 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_2118 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_4126 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 25 2023 4 22 09 |
| spelling |
10.1007/s11009-023-10055-w doi (DE-627)SPR053163664 (SPR)s11009-023-10055-w-e DE-627 ger DE-627 rakwb eng Navarro, Jorge verfasserin (orcid)0000-0003-2822-915X aut A New Separation Index and Classification Techniques Based on Shannon Entropy 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract The purpose is to use Shannon entropy measures to develop classification techniques and an index which estimates the separation of the groups in a finite mixture model. These measures can be applied to machine learning techniques such as discriminant analysis, cluster analysis, exploratory data analysis, etc. If we know the number of groups and we have training samples from each group (supervised learning) the index is used to measure the separation of the groups. Here some entropy measures are used to classify new individuals in one of these groups. If we are not sure about the number of groups (unsupervised learning), the index can be used to determine the optimal number of groups from an entropy (information/uncertainty) criterion. It can also be used to determine the best variables in order to separate the groups. In all the cases we assume that we have absolutely continuous random variables and we use the Shannon entropy based on the probability density function. Theoretical, parametric and non-parametric techniques are proposed to get approximations of these entropy measures in practice. An application to gene selection in a colon cancer discrimination study with a lot of variables is provided as well. Shannon entropy (dpeaa)DE-He213 Discriminant analysis (dpeaa)DE-He213 Cluster analysis (dpeaa)DE-He213 Kernel density estimation (dpeaa)DE-He213 Omic data (dpeaa)DE-He213 Buono, Francesco (orcid)0000-0002-3569-4052 aut Arevalillo, Jorge M. (orcid)0000-0003-1944-3699 aut Enthalten in Methodology and computing in applied probability Dordrecht [u.a.] : Springer Science + Business Media B.V, 1999 25(2023), 4 vom: 22. Sept. (DE-627)320427412 (DE-600)2003336-9 1573-7713 nnns volume:25 year:2023 number:4 day:22 month:09 https://dx.doi.org/10.1007/s11009-023-10055-w 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_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_152 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_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_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 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_2118 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_4126 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 25 2023 4 22 09 |
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10.1007/s11009-023-10055-w doi (DE-627)SPR053163664 (SPR)s11009-023-10055-w-e DE-627 ger DE-627 rakwb eng Navarro, Jorge verfasserin (orcid)0000-0003-2822-915X aut A New Separation Index and Classification Techniques Based on Shannon Entropy 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract The purpose is to use Shannon entropy measures to develop classification techniques and an index which estimates the separation of the groups in a finite mixture model. These measures can be applied to machine learning techniques such as discriminant analysis, cluster analysis, exploratory data analysis, etc. If we know the number of groups and we have training samples from each group (supervised learning) the index is used to measure the separation of the groups. Here some entropy measures are used to classify new individuals in one of these groups. If we are not sure about the number of groups (unsupervised learning), the index can be used to determine the optimal number of groups from an entropy (information/uncertainty) criterion. It can also be used to determine the best variables in order to separate the groups. In all the cases we assume that we have absolutely continuous random variables and we use the Shannon entropy based on the probability density function. Theoretical, parametric and non-parametric techniques are proposed to get approximations of these entropy measures in practice. An application to gene selection in a colon cancer discrimination study with a lot of variables is provided as well. Shannon entropy (dpeaa)DE-He213 Discriminant analysis (dpeaa)DE-He213 Cluster analysis (dpeaa)DE-He213 Kernel density estimation (dpeaa)DE-He213 Omic data (dpeaa)DE-He213 Buono, Francesco (orcid)0000-0002-3569-4052 aut Arevalillo, Jorge M. (orcid)0000-0003-1944-3699 aut Enthalten in Methodology and computing in applied probability Dordrecht [u.a.] : Springer Science + Business Media B.V, 1999 25(2023), 4 vom: 22. Sept. (DE-627)320427412 (DE-600)2003336-9 1573-7713 nnns volume:25 year:2023 number:4 day:22 month:09 https://dx.doi.org/10.1007/s11009-023-10055-w 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_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_152 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_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_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 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_2118 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_4126 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 25 2023 4 22 09 |
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10.1007/s11009-023-10055-w doi (DE-627)SPR053163664 (SPR)s11009-023-10055-w-e DE-627 ger DE-627 rakwb eng Navarro, Jorge verfasserin (orcid)0000-0003-2822-915X aut A New Separation Index and Classification Techniques Based on Shannon Entropy 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract The purpose is to use Shannon entropy measures to develop classification techniques and an index which estimates the separation of the groups in a finite mixture model. These measures can be applied to machine learning techniques such as discriminant analysis, cluster analysis, exploratory data analysis, etc. If we know the number of groups and we have training samples from each group (supervised learning) the index is used to measure the separation of the groups. Here some entropy measures are used to classify new individuals in one of these groups. If we are not sure about the number of groups (unsupervised learning), the index can be used to determine the optimal number of groups from an entropy (information/uncertainty) criterion. It can also be used to determine the best variables in order to separate the groups. In all the cases we assume that we have absolutely continuous random variables and we use the Shannon entropy based on the probability density function. Theoretical, parametric and non-parametric techniques are proposed to get approximations of these entropy measures in practice. An application to gene selection in a colon cancer discrimination study with a lot of variables is provided as well. Shannon entropy (dpeaa)DE-He213 Discriminant analysis (dpeaa)DE-He213 Cluster analysis (dpeaa)DE-He213 Kernel density estimation (dpeaa)DE-He213 Omic data (dpeaa)DE-He213 Buono, Francesco (orcid)0000-0002-3569-4052 aut Arevalillo, Jorge M. (orcid)0000-0003-1944-3699 aut Enthalten in Methodology and computing in applied probability Dordrecht [u.a.] : Springer Science + Business Media B.V, 1999 25(2023), 4 vom: 22. Sept. (DE-627)320427412 (DE-600)2003336-9 1573-7713 nnns volume:25 year:2023 number:4 day:22 month:09 https://dx.doi.org/10.1007/s11009-023-10055-w 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_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_152 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_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_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 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_2118 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_4126 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 25 2023 4 22 09 |
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10.1007/s11009-023-10055-w doi (DE-627)SPR053163664 (SPR)s11009-023-10055-w-e DE-627 ger DE-627 rakwb eng Navarro, Jorge verfasserin (orcid)0000-0003-2822-915X aut A New Separation Index and Classification Techniques Based on Shannon Entropy 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract The purpose is to use Shannon entropy measures to develop classification techniques and an index which estimates the separation of the groups in a finite mixture model. These measures can be applied to machine learning techniques such as discriminant analysis, cluster analysis, exploratory data analysis, etc. If we know the number of groups and we have training samples from each group (supervised learning) the index is used to measure the separation of the groups. Here some entropy measures are used to classify new individuals in one of these groups. If we are not sure about the number of groups (unsupervised learning), the index can be used to determine the optimal number of groups from an entropy (information/uncertainty) criterion. It can also be used to determine the best variables in order to separate the groups. In all the cases we assume that we have absolutely continuous random variables and we use the Shannon entropy based on the probability density function. Theoretical, parametric and non-parametric techniques are proposed to get approximations of these entropy measures in practice. An application to gene selection in a colon cancer discrimination study with a lot of variables is provided as well. Shannon entropy (dpeaa)DE-He213 Discriminant analysis (dpeaa)DE-He213 Cluster analysis (dpeaa)DE-He213 Kernel density estimation (dpeaa)DE-He213 Omic data (dpeaa)DE-He213 Buono, Francesco (orcid)0000-0002-3569-4052 aut Arevalillo, Jorge M. (orcid)0000-0003-1944-3699 aut Enthalten in Methodology and computing in applied probability Dordrecht [u.a.] : Springer Science + Business Media B.V, 1999 25(2023), 4 vom: 22. Sept. (DE-627)320427412 (DE-600)2003336-9 1573-7713 nnns volume:25 year:2023 number:4 day:22 month:09 https://dx.doi.org/10.1007/s11009-023-10055-w 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_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_152 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_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_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 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_2118 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_4126 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 25 2023 4 22 09 |
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Navarro, Jorge |
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Navarro, Jorge misc Shannon entropy misc Discriminant analysis misc Cluster analysis misc Kernel density estimation misc Omic data A New Separation Index and Classification Techniques Based on Shannon Entropy |
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A New Separation Index and Classification Techniques Based on Shannon Entropy Shannon entropy (dpeaa)DE-He213 Discriminant analysis (dpeaa)DE-He213 Cluster analysis (dpeaa)DE-He213 Kernel density estimation (dpeaa)DE-He213 Omic data (dpeaa)DE-He213 |
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A New Separation Index and Classification Techniques Based on Shannon Entropy |
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new separation index and classification techniques based on shannon entropy |
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A New Separation Index and Classification Techniques Based on Shannon Entropy |
| abstract |
Abstract The purpose is to use Shannon entropy measures to develop classification techniques and an index which estimates the separation of the groups in a finite mixture model. These measures can be applied to machine learning techniques such as discriminant analysis, cluster analysis, exploratory data analysis, etc. If we know the number of groups and we have training samples from each group (supervised learning) the index is used to measure the separation of the groups. Here some entropy measures are used to classify new individuals in one of these groups. If we are not sure about the number of groups (unsupervised learning), the index can be used to determine the optimal number of groups from an entropy (information/uncertainty) criterion. It can also be used to determine the best variables in order to separate the groups. In all the cases we assume that we have absolutely continuous random variables and we use the Shannon entropy based on the probability density function. Theoretical, parametric and non-parametric techniques are proposed to get approximations of these entropy measures in practice. An application to gene selection in a colon cancer discrimination study with a lot of variables is provided as well. © The Author(s) 2023 |
| abstractGer |
Abstract The purpose is to use Shannon entropy measures to develop classification techniques and an index which estimates the separation of the groups in a finite mixture model. These measures can be applied to machine learning techniques such as discriminant analysis, cluster analysis, exploratory data analysis, etc. If we know the number of groups and we have training samples from each group (supervised learning) the index is used to measure the separation of the groups. Here some entropy measures are used to classify new individuals in one of these groups. If we are not sure about the number of groups (unsupervised learning), the index can be used to determine the optimal number of groups from an entropy (information/uncertainty) criterion. It can also be used to determine the best variables in order to separate the groups. In all the cases we assume that we have absolutely continuous random variables and we use the Shannon entropy based on the probability density function. Theoretical, parametric and non-parametric techniques are proposed to get approximations of these entropy measures in practice. An application to gene selection in a colon cancer discrimination study with a lot of variables is provided as well. © The Author(s) 2023 |
| abstract_unstemmed |
Abstract The purpose is to use Shannon entropy measures to develop classification techniques and an index which estimates the separation of the groups in a finite mixture model. These measures can be applied to machine learning techniques such as discriminant analysis, cluster analysis, exploratory data analysis, etc. If we know the number of groups and we have training samples from each group (supervised learning) the index is used to measure the separation of the groups. Here some entropy measures are used to classify new individuals in one of these groups. If we are not sure about the number of groups (unsupervised learning), the index can be used to determine the optimal number of groups from an entropy (information/uncertainty) criterion. It can also be used to determine the best variables in order to separate the groups. In all the cases we assume that we have absolutely continuous random variables and we use the Shannon entropy based on the probability density function. Theoretical, parametric and non-parametric techniques are proposed to get approximations of these entropy measures in practice. An application to gene selection in a colon cancer discrimination study with a lot of variables is provided as well. © The Author(s) 2023 |
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| title_short |
A New Separation Index and Classification Techniques Based on Shannon Entropy |
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https://dx.doi.org/10.1007/s11009-023-10055-w |
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Buono, Francesco Arevalillo, Jorge M. |
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| doi_str |
10.1007/s11009-023-10055-w |
| up_date |
2024-07-03T17:31:34.902Z |
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