Paper: Informational Rescaling of PCA Maps with Application to Genetic Distance

Abstract

Principal Component Analysis (PCA) is a powerful multivariate tool allowing the projection of data in low-dimensional representations. Nevertheless, datapoint distances on these low-dimensional projections are challenging to interpret. Here, we propose a computationally simple heuristic to transform a map based on standard PCA (when the variables are asymptotically Gaussian) into an entropy-based map where distances are based on mutual information (MI). Moreover, we show that in certain instances our proposed scaled PCA can improve cluster identification. Rescaling principal component-based distances using MI results in 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), quantifies relative distances into information units, such as “bits”. We illustrate the effect of this rescaling using genomics data derived from world populations and describe how the interpretation of results are impacted.

Link to Paper – www.sciencedirect.com/science/article/pii/S2001037024004136

[X] Foreword to a textbook on Antifragility by Jeffrey West et al.

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Catch Nassim Nicholas Taleb and Fintan O’Toole at Kilkenomics 2024: Power, Corruption, and Lies

Nassim Nicholas Taleb, author of The Black Swan, joins award-winning journalist Fintan O’Toole for a one-hour discussion on Power, Corruption, and Lies at Kilkenomics 2024. Taking place at the Watergate Theatre in Kilkenny on November 8th, 2024, this event is part of the world’s only economics and comedy festival.

  • Date: November 8th, 2024, 17:00
  • Venue: Watergate Theatre, Kilkenny, Ireland
  • Tickets: €29.00 full price | €27.00 concession (+ €1.50 fees)

Book now: kilkenomics.ticketsolve.com/ticketbooth/shows/873665809