My watch list
my.chemeurope.com  
Login  

Entropy, Vol. 20, Pages 498: Assessing Information Transmission in Data Transformations with the Channel Multivariate Entropy Triangle

Entropy, Vol. 20, Pages 498: Assessing Information Transmission in Data Transformations with the Channel Multivariate Entropy Triangle

Entropy doi: 10.3390/e20070498

Authors: Francisco Valverde-Albacete Carmen Peláez-Moreno

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.

Authors:   Valverde-Albacete, Francisco J.; Peláez-Moreno, Carmen
Journal:   Entropy
Volume:   20
edition:   7
Year:   2018
Pages:   498
DOI:   10.3390/e20070498
Publication date:   27-Jun-2018
Facts, background information, dossiers
More about Molecular Diversity Preservation International
Your browser is not current. Microsoft Internet Explorer 6.0 does not support some functions on Chemie.DE