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Pattern recognition with the help of quadratic discriminant functions

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Abstract

The problem of pattern recognition with the help of spherical and elliptic discriminant functions is studied; in so doing the pattern of an object is assumed to be a vector of its characters from a finite-dimensional Euclidean space. Using a conformal mapping of a punctured sphere onto the plane as well as the inversion transformation, a criterion for the error-free recognition of two sets containing a finite number of points of training samples is obtained with the help of spherical discriminant functions. An algorithm for solving approximately a problem of construction of an ellipsoid of the minimal volume containing a given finite set of points is described. Bibliography: 5 titles.

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Authors
  1. Yu. I. Petunin
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  2. B. V. Rublev
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Additional information

Translated fromObchyslyuval'na ta Prykladna Matematyka, No. 80, 1996, pp. 90–105.

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Petunin, Y.I., Rublev, B.V. Pattern recognition with the help of quadratic discriminant functions. J Math Sci 97, 3959–3967 (1999). https://doi.org/10.1007/BF02366387

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  • DOI: https://doi.org/10.1007/BF02366387

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