High-Dimensional Brain in a High-Dimensional World: Blessing of Dimensionality
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Department of Mathematics, University of Leicester, Leicester LE1 7RH, UK
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Laboratory of Advanced Methods for High-Dimensional Data Analysis, Lobachevsky University, 603022 Nizhny Novgorod, Russia
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Instituto de Matemática Interdisciplinar, Faculty of Mathematics, Universidad Complutense de Madrid, Avda Complutense s/n, 28040 Madrid, Spain
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(1), 82; https://doi.org/10.3390/e22010082
Received: 9 December 2019
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Revised: 2 January 2020
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Accepted: 6 January 2020
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Published: 9 January 2020
(This article belongs to the Special Issue Entropies: Between Information Geometry and Kinetics)
High-dimensional data and high-dimensional representations of reality are inherent features of modern Artificial Intelligence systems and applications of machine learning. The well-known phenomenon of the “curse of dimensionality” states: many problems become exponentially difficult in high dimensions. Recently, the other side of the coin, the “blessing of dimensionality”, has attracted much attention. It turns out that generic high-dimensional datasets exhibit fairly simple geometric properties. Thus, there is a fundamental tradeoff between complexity and simplicity in high dimensional spaces. Here we present a brief explanatory review of recent ideas, results and hypotheses about the blessing of dimensionality and related simplifying effects relevant to machine learning and neuroscience.
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Keywords:
artificial intelligence; mistake correction; concentration of measure; discriminant; data mining; geometry
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MDPI and ACS Style
Gorban, A.N.; Makarov, V.A.; Tyukin, I.Y. High-Dimensional Brain in a High-Dimensional World: Blessing of Dimensionality. Entropy 2020, 22, 82. https://doi.org/10.3390/e22010082
AMA Style
Gorban AN, Makarov VA, Tyukin IY. High-Dimensional Brain in a High-Dimensional World: Blessing of Dimensionality. Entropy. 2020; 22(1):82. https://doi.org/10.3390/e22010082
Chicago/Turabian StyleGorban, Alexander N., Valery A. Makarov, and Ivan Y. Tyukin. 2020. "High-Dimensional Brain in a High-Dimensional World: Blessing of Dimensionality" Entropy 22, no. 1: 82. https://doi.org/10.3390/e22010082
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