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High-Dimensional Brain in a High-Dimensional World: Blessing of Dimensionality

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Gorban, Alexander N. and Makarov, Valeri A. and Tyukin, Ivan Y. (2020) High-Dimensional Brain in a High-Dimensional World: Blessing of Dimensionality. Entropy, 22 (1). p. 82. ISSN 1099-4300

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Official URL: https://doi.org/10.3390/e22010082




Abstract

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.


Item Type:Article
Uncontrolled Keywords:Artificial intelligence, Mistake correction, Concentration of measure, Discriminant, Data mining; geometry
Subjects:Sciences > Computer science > Artificial intelligence
Sciences > Mathematics > Cybernetics
Sciences > Mathematics > Geometry
Sciences > Mathematics > Operations research
ID Code:63012
Deposited On:10 Nov 2020 18:21
Last Modified:11 Nov 2020 09:14

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