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# Philentropy: Information Theory and Distance Quantification with R

Drost, Hajk-Georg

Comparison is a fundamental method of scientific research leading to insights about the processes that generate similarity or dissimilarity. In statistical terms comparisons between probability functions are performed to infer connections, correlations, or relationships between objects or samples. Most quantification methods rely on distance or similarity measures, but the right choice for each individual application is not always clear and sometimes poorly explored. The reason for this is partly that diverse measures are either implemented in different R packages with very different notations or are not implemented at all. Thus, a comprehensive framework implementing the most common similarity and distance measures using a uniform notation is still missing. The R package Philentropy aims to fill this gap by implementing forty-six fundamental distance and similarity measures for comparing probability functions. These comparisons between probability functions have their foundations in a broad range of scientific disciplines from mathematics to ecology. The aim of this package is to provide a comprehensive and computationally optimized base framework for clustering, classification, statistical inference, goodness-of-fit, non-parametric statistics, information theory, and machine learning tasks that are based on comparing univariate or multivariate probability functions. All functions are written in C++ and are integrated into the R package using the Rcpp Application Programming Interface (API).

Together, this framework allows building new similarity or distance based (statistical) models and algorithms in R which are computationally efficient and scalable. The comprehensive availability of diverse metrics and measures furthermore enables a systematic assessment of choosing the most optimal similarity or distance measure for individual applications in diverse scientific disciplines.

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