Published on Tue Jan 14 2020

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

Alexander N. Gorban, Valery A. Makarov, Ivan Y. Tyukin

High-dimensional data and high-dimensional representations of reality are inherent features of modern Artificial Intelligence systems and applications of machine learning. There is a fundamental tradeoff between complexity and simplicity in high dimensional spaces.

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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.