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A. Zinovyev

  1. Nonlinear Quality of Life Index.

    Wed, 08/25/2010 - 15:01 — SomNambul
    Authors: A. Zinovyev, A.N. Gorban
    Subjects: Neural and Evolutionary Computation
    Abstract

    This paper includes supplementary material for the paper [A.N. Gorban, A.
    Zinovyev, Principal manifolds and graphs in practice: from molecular biology to
    dynamical systems, International Journal of Neural Systems 20 (3) (2010),
    219-232. E-print: arXiv:1001.1122 [cs.NE]]. We present details of the analysis
    of the nonlinear quality of life index for 162 countries. This index is based
    on four indicators: GDP per capita, Life expectancy at birth, Infant mortality
    rate, and Tuberculosis incidence.

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

    Fri, 01/08/2010 - 16:01 — SomNambul
    Authors: A. N. Gorban, A. Zinovyev
    Subjects: Neural and Evolutionary Computation
    Abstract

    We present several applications of non-linear data modeling, using principal
    manifolds and principal graphs constructed using the metaphor of elasticity
    (elastic principal graph approach). These approaches are generalizations of the
    Kohonen's self-organizing maps, a class of artificial neural networks. On
    several examples we show advantages of using non-linear objects for data
    approximation in comparison to the linear ones. We propose four numerical
    criteria for comparing linear and non-linear mappings of datasets into the
    spaces of lower dimension.

Math-arch

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