Alexander N. Gorban

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University of Leicester

Chair in Applied Mathematics, University of Leicester, UK

Coloring panchromatic nighttime satellite images: Elastic maps vs. kernel smoothing and multivariate regression approach

Artificial light-at-night (ALAN), emitted from the ground and visible fr...
08/21/2020 ∙ by N. Rybnikova, et al. ∙ 0 ∙ share

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Correction of AI systems by linear discriminants: Probabilistic foundations

Artificial Intelligence (AI) systems sometimes make errors and will make...
11/11/2018 ∙ by Alexander N. Gorban, et al. ∙ 0 ∙ share

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The unreasonable effectiveness of small neural ensembles in high-dimensional brain

Despite the widely-spread consensus on the brain complexity, sprouts of ...
09/20/2018 ∙ by Alexander N. Gorban, et al. ∙ 14 ∙ share

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How deep should be the depth of convolutional neural networks: a backyard dog case study

We present a straightforward non-iterative method for shallowing of deep...
05/03/2018 ∙ by Alexander N. Gorban, et al. ∙ 0 ∙ share

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Blessing of dimensionality: mathematical foundations of the statistical physics of data

The concentration of measure phenomena were discovered as the mathematic...
01/10/2018 ∙ by Alexander N. Gorban, et al. ∙ 0 ∙ share

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Piece-wise quadratic approximations of arbitrary error functions for fast and robust machine learning

Most of machine learning approaches have stemmed from the application of...
05/20/2016 ∙ by Alexander N. Gorban, et al. ∙ 0 ∙ share

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Grasping Complexity

The century of complexity has come. The face of science has changed. Sur...
03/15/2013 ∙ by Alexander N. Gorban, et al. ∙ 0 ∙ share

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Geometrical complexity of data approximators

There are many methods developed to approximate a cloud of vectors embed...
02/11/2013 ∙ by E. M. Mirkes, et al. ∙ 0 ∙ share

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Nonlinear Quality of Life Index

We present details of the analysis of the nonlinear quality of life inde...
08/24/2010 ∙ by A. Zinovyev, et al. ∙ 0 ∙ share

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Principal manifolds and graphs in practice: from molecular biology to dynamical systems

We present several applications of non-linear data modeling, using princ...
01/07/2010 ∙ by Alexander N. Gorban, et al. ∙ 0 ∙ share

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Principal Graphs and Manifolds

In many physical, statistical, biological and other investigations it is...
09/02/2008 ∙ by Alexander N. Gorban, et al. ∙ 0 ∙ share

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Topological Grammars for Data Approximation

A method of topological grammars is proposed for multidimensional data ...
03/22/2006 ∙ by Alexander N. Gorban, et al. ∙ 0 ∙ share

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Generation of Explicit Knowledge from Empirical Data through Pruning of Trainable Neural Networks

This paper presents a generalized technology of extraction of explicit k...
07/03/2003 ∙ by Alexander N. Gorban, et al. ∙ 0 ∙ share

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Seven clusters in genomic triplet distributions

In several recent papers new gene-detection algorithms were proposed for...
05/29/2003 ∙ by Alexander N. Gorban, et al. ∙ 0 ∙ share

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Back-propagation of accuracy

In this paper we solve the problem: how to determine maximal allowable e...
05/22/2003 ∙ by M. Yu. Senashova, et al. ∙ 0 ∙ share

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Neural network modeling of data with gaps: method of principal curves, Carleman's formula, and other

A method of modeling data with gaps by a sequence of curves has been dev...
05/21/2003 ∙ by Alexander N. Gorban, et al. ∙ 0 ∙ share

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Alexander N. Gorban

Featured Co-authors

E. M. Mirkes

A. Zinovyev

I. Y. Tyukin

A. Y. Zinovyev

D. C. Wunsch II

G. S. Yablonsky

N. R. Sumner

I. Y. Tukin

A. A. Rossiev

N. Rybnikova

B. A. Portnov

Coloring panchromatic nighttime satellite images: Elastic maps vs. kernel smoothing and multivariate regression approach

Correction of AI systems by linear discriminants: Probabilistic foundations

The unreasonable effectiveness of small neural ensembles in high-dimensional brain

How deep should be the depth of convolutional neural networks: a backyard dog case study

Blessing of dimensionality: mathematical foundations of the statistical physics of data

Piece-wise quadratic approximations of arbitrary error functions for fast and robust machine learning

Grasping Complexity

Geometrical complexity of data approximators

Nonlinear Quality of Life Index

Principal manifolds and graphs in practice: from molecular biology to dynamical systems

Principal Graphs and Manifolds

Topological Grammars for Data Approximation

Generation of Explicit Knowledge from Empirical Data through Pruning of Trainable Neural Networks

Seven clusters in genomic triplet distributions

Back-propagation of accuracy

Neural network modeling of data with gaps: method of principal curves, Carleman's formula, and other