Informational Rescaling of PCA Maps with Application to Genetic Distance
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913253787959296 |
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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 |