Informational Rescaling of PCA Maps with Application to Genetic Distance

Fuente: arXiv
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Main Authors: Taleb, Nassim Nicholas, Zalloua, Pierre, Elbassioni, Khaled, Henschel, Andreas, Platt, Daniel E.
Format: Preprint
Published: 2023
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author Taleb, Nassim Nicholas
Zalloua, Pierre
Elbassioni, Khaled
Henschel, Andreas
Platt, Daniel E.
author_facet Taleb, Nassim Nicholas
Zalloua, Pierre
Elbassioni, Khaled
Henschel, Andreas
Platt, Daniel E.
contents We discuss the inadequacy of covariances/correlations and other measures in L2 as relative distance metrics under some conditions. We propose a computationally simple heuristic to transform a map based on standard principal component analysis (PCA) (when the variables are asymptotically Gaussian) into an entropy-based map where distances are based on mutual information (MI). Rescaling Principal Component based distances using MI allows a representation of relative statistical associations when, as in genetics, it is applied on bit measurements between individuals' genomic mutual information. This entropy rescaled PCA, while preserving order relationships (along a dimension), changes the relative distances to make them linear to information. We show the effect on the entire world population and some subsamples, which leads to significant differences with the results of current research.
format Preprint
id arxiv_https___arxiv_org_abs_2303_12654
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Informational Rescaling of PCA Maps with Application to Genetic Distance
Taleb, Nassim Nicholas
Zalloua, Pierre
Elbassioni, Khaled
Henschel, Andreas
Platt, Daniel E.
Information Theory
Populations and Evolution
We discuss the inadequacy of covariances/correlations and other measures in L2 as relative distance metrics under some conditions. We propose a computationally simple heuristic to transform a map based on standard principal component analysis (PCA) (when the variables are asymptotically Gaussian) into an entropy-based map where distances are based on mutual information (MI). Rescaling Principal Component based distances using MI allows a representation of relative statistical associations when, as in genetics, it is applied on bit measurements between individuals' genomic mutual information. This entropy rescaled PCA, while preserving order relationships (along a dimension), changes the relative distances to make them linear to information. We show the effect on the entire world population and some subsamples, which leads to significant differences with the results of current research.
title Informational Rescaling of PCA Maps with Application to Genetic Distance
topic Information Theory
Populations and Evolution
url https://arxiv.org/abs/2303.12654