2017/11/30 by Francisco J. Valverde-Albacete, Carmen Peláez-Moreno
Computer Science · Mathematics · Neuroscience · #Algorithm #Artificial intelligence #Blind Source Separation Techniques #Computer science #Data mining #Entropy (arrow of time) #Feature selection #Information theory #Machine learning #Mathematics #Multivariate statistics #Mutual information #Neural Networks and Applications #Neural dynamics and brain function #Pattern recognition (psychology) #Principal component analysis #Principle of maximum entropy #Statistics #Transfer entropy #Transformation (genetics) #cs.IT #math.IT #stat.ML
paper · pdf · doi:10.3390/e20070498
published as Entropy 2018, 20(7), 498 · 21 pages, 7 figures and 1 table
openalex publication_date 2018/06/27 · openalex created_date 2018/07/10 · arxiv created 2018/10/10 · arxiv updated 2018/10/11 · openalex updated_date 2026/08/05
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.