Next Article in Journal
Theory of Response to Perturbations in Non-Hermitian Systems Using Five-Hilbert-Space Reformulation of Unitary Quantum Mechanics
Previous Article in Journal
Detection of Hypoglycemia Using Measures of EEG Complexity in Type 1 Diabetes Patients
Previous Article in Special Issue
Learning the Macroscopic Flow Model of Short Fiber Suspensions from Fine-Scale Simulated Data
Open AccessReview

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

1
Department of Mathematics, University of Leicester, Leicester LE1 7RH, UK
2
Laboratory of Advanced Methods for High-Dimensional Data Analysis, Lobachevsky University, 603022 Nizhny Novgorod, Russia
3
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 / Revised: 2 January 2020 / Accepted: 6 January 2020 / 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. View Full-Text
Keywords: artificial intelligence; mistake correction; concentration of measure; discriminant; data mining; geometry artificial intelligence; mistake correction; concentration of measure; discriminant; data mining; geometry
Show Figures

Figure 1

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.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop