Logratio approach to distributional modeling


Statistical learning
Logratio approach to distributional modeling
Friday 20th January 2017
Menafoglio, A.; Hron, K.; Filzmoser, P.
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Symbolic data analysis (SDA) provides a unified approach to analyze distributional data, resulting from capturing intrinsic variability of groups of individuals as input observations. In parallel to the SDA approach, a concise methodology has been developed since the early 1980s to deal with compositional data — i.e., data carrying only relative information — through the logratios of their parts. Most methods in compositional data analysis aims to treat multivariate observations which can be identified with probability functions of discrete distributions. Nevertheless, a methodology to capture the specific features of continuous distributions (densities) has been recently introduced. The aim of this work is to describe a general setting that includes both the discrete and the continuous setting, and to provide specific details to both frameworks focusing on the implications on SDA. The theoretical developments are illustrated with real-world case studies.
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In review for pubblication in "Analysis of Distributional Data", edited by P. Brito, CRC Press.