Assessing Information Transmission in Data Transformations with the Channel Multivariate Entropy Triangle
Data transformation, e.g., feature transformation and selection, is an integral part of any machine learning procedure. In this paper, we introduce an information-theoretic model and tools to assess the quality of data transformations in machine learning tasks. In an unsupervised fashion, we analyze...
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-06-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/20/7/498 |
| _version_ | 1818007965488119808 |
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| author | Francisco J. Valverde-Albacete Carmen Peláez-Moreno |
| author_facet | Francisco J. Valverde-Albacete Carmen Peláez-Moreno |
| author_sort | Francisco J. Valverde-Albacete |
| collection | DOAJ |
| description | Data transformation, e.g., feature transformation and selection, is an integral part of any machine learning procedure. In this paper, we introduce an information-theoretic model and tools to assess the quality of data transformations in machine learning tasks. In an unsupervised fashion, we analyze the transformation of a discrete, multivariate source of information X¯ into a discrete, multivariate sink of information Y¯ related by a distribution PX¯Y¯. The first contribution is a decomposition of the maximal potential entropy of (X¯,Y¯), which we call a balance equation, into its (a) non-transferable, (b) transferable, but not transferred, and (c) transferred parts. Such balance equations can be represented in (de Finetti) entropy diagrams, our second set of contributions. The most important of these, the aggregate channel multivariate entropy triangle, is a visual exploratory tool to assess the effectiveness of multivariate data transformations in transferring information from input to output variables. We also show how these decomposition and balance equations also apply to the entropies of X¯ and Y¯, respectively, and generate entropy triangles for them. As an example, we present the application of these tools to the assessment of information transfer efficiency for Principal Component Analysis and Independent Component Analysis as unsupervised feature transformation and selection procedures in supervised classification tasks. |
| first_indexed | 2024-04-14T05:22:35Z |
| format | Article |
| id | doaj.art-86b5550402eb44e981bd5fa219f1d292 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-14T05:22:35Z |
| publishDate | 2018-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-86b5550402eb44e981bd5fa219f1d2922022-12-22T02:10:08ZengMDPI AGEntropy1099-43002018-06-0120749810.3390/e20070498e20070498Assessing Information Transmission in Data Transformations with the Channel Multivariate Entropy TriangleFrancisco J. Valverde-Albacete0Carmen Peláez-Moreno1Department of Signal Theory and Communications, Universidad Carlos III de Madrid, Leganés 28911, SpainDepartment of Signal Theory and Communications, Universidad Carlos III de Madrid, Leganés 28911, SpainData transformation, e.g., feature transformation and selection, is an integral part of any machine learning procedure. In this paper, we introduce an information-theoretic model and tools to assess the quality of data transformations in machine learning tasks. In an unsupervised fashion, we analyze the transformation of a discrete, multivariate source of information X¯ into a discrete, multivariate sink of information Y¯ related by a distribution PX¯Y¯. The first contribution is a decomposition of the maximal potential entropy of (X¯,Y¯), which we call a balance equation, into its (a) non-transferable, (b) transferable, but not transferred, and (c) transferred parts. Such balance equations can be represented in (de Finetti) entropy diagrams, our second set of contributions. The most important of these, the aggregate channel multivariate entropy triangle, is a visual exploratory tool to assess the effectiveness of multivariate data transformations in transferring information from input to output variables. We also show how these decomposition and balance equations also apply to the entropies of X¯ and Y¯, respectively, and generate entropy triangles for them. As an example, we present the application of these tools to the assessment of information transfer efficiency for Principal Component Analysis and Independent Component Analysis as unsupervised feature transformation and selection procedures in supervised classification tasks.http://www.mdpi.com/1099-4300/20/7/498entropy, entropy visualizationentropy balance equationShannon-type relationsmultivariate analysismachine learning evaluationdata transformation |
| spellingShingle | Francisco J. Valverde-Albacete Carmen Peláez-Moreno Assessing Information Transmission in Data Transformations with the Channel Multivariate Entropy Triangle Entropy entropy, entropy visualization entropy balance equation Shannon-type relations multivariate analysis machine learning evaluation data transformation |
| title | Assessing Information Transmission in Data Transformations with the Channel Multivariate Entropy Triangle |
| title_full | Assessing Information Transmission in Data Transformations with the Channel Multivariate Entropy Triangle |
| title_fullStr | Assessing Information Transmission in Data Transformations with the Channel Multivariate Entropy Triangle |
| title_full_unstemmed | Assessing Information Transmission in Data Transformations with the Channel Multivariate Entropy Triangle |
| title_short | Assessing Information Transmission in Data Transformations with the Channel Multivariate Entropy Triangle |
| title_sort | assessing information transmission in data transformations with the channel multivariate entropy triangle |
| topic | entropy, entropy visualization entropy balance equation Shannon-type relations multivariate analysis machine learning evaluation data transformation |
| url | http://www.mdpi.com/1099-4300/20/7/498 |
| work_keys_str_mv | AT franciscojvalverdealbacete assessinginformationtransmissionindatatransformationswiththechannelmultivariateentropytriangle AT carmenpelaezmoreno assessinginformationtransmissionindatatransformationswiththechannelmultivariateentropytriangle |