{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/assessing-information-transmission-in-data","title":"Assessing Information Transmission in Data Transformations with the Channel Multivariate Entropy Triangle","arxiv_id":"1711.11510","date":"2017-11-30","proceeding":null,"authors":["Francisco J. Valverde-Albacete","Carmen Peláez-Moreno"],"abstract":"Data transformation, e.g. feature transformation and selection, is an\nintegral part of any machine learning procedure. In this paper we introduce an\ninformation-theoretic model and tools to assess the quality of data\ntransformations in machine learning tasks. In an unsupervised fashion, we\nanalyze the transfer of information of the transformation of a discrete,\nmultivariate source of information X into a discrete, multivariate sink of\ninformation Y related by a distribution PXY . The first contribution is a\ndecomposition of the maximal potential entropy of (X, Y) that we call a balance\nequation, into its a) non-transferable, b) transferable but not transferred and\nc) transferred parts. Such balance equations can be represented in (de Finetti)\nentropy diagrams, our second set of contributions. The most important of these,\nthe aggregate Channel Multivariate Entropy Triangle is a visual exploratory\ntool to assess the effectiveness of multivariate data transformations in\ntransferring information from input to output variables. We also show how these\ndecomposition and balance equation also apply to the entropies of X and Y\nrespectively and generate entropy triangles for them. As an example, we present\nthe application of these tools to the assessment of information transfer\nefficiency for PCA and ICA as unsupervised feature transformation and selection\nprocedures in supervised classification tasks.","url_abs":"http://arxiv.org/abs/1711.11510v2","url_pdf":"http://arxiv.org/pdf/1711.11510v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"assessing-information-transmission-in-data","repo_url":"https://github.com/FJValverde/entropies","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"machine-learning","task_name":"BIG-bench Machine Learning"}],"methods":[{"method_slug":"ica","method_name":"ICA"},{"method_slug":"pca","method_name":"PCA"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}