Nonparametric learning of decision regions via the genetic algorithm

Leehter Yao

doi:10.1109/3477.485882

Nonparametric learning of decision regions via the genetic algorithm

Leehter Yao

Department of Electrical Engineering

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

A method for nonparametric (distribution-free) learning of complex decision regions in n-dimensional pattern space is introduced. Arbitrary n-dimensional decision regions are approximated by the union of a finite number of basic shapes. The primary example introduced in this paper are parallelepipeds and ellipsoids. By explicitly parameterizing these shapes, the decision region can be determined by estimating the parameters associated with each shape. A structural random search type algorithm called the genetic algorithm is applied to estimate these parameters. Two complex decision regions are examined in detail. One is linearly inseparable, nonconvex and disconnected. The other one is linearly inseparable, nonconvex and connected. The scheme is highly resilient to misclassification errors. The number of parameters to be estimated only grows linearly with the dimension of the pattern space for simple version of the scheme.

Original language	English
Pages (from-to)	313-321
Number of pages	9
Journal	IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Volume	26
Issue number	2
DOIs	https://doi.org/10.1109/3477.485882
State	Published - 1996

Bibliographical note

Funding Information:
Manuscript received Cctober 10, 1993; revised December 28, 1994. This work was supported in part by the National Science Council, Taiwan, R.O.C., under Grant NSC 82-01 13-027-033-T. The author is with the Department of Electrical Engineering, National Taipei Institute of Technology, Taipei 10643, Taiwan, R.O.C. Publisher Item Identifier S 1083-4419(96)02297-2.

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N2 - A method for nonparametric (distribution-free) learning of complex decision regions in n-dimensional pattern space is introduced. Arbitrary n-dimensional decision regions are approximated by the union of a finite number of basic shapes. The primary example introduced in this paper are parallelepipeds and ellipsoids. By explicitly parameterizing these shapes, the decision region can be determined by estimating the parameters associated with each shape. A structural random search type algorithm called the genetic algorithm is applied to estimate these parameters. Two complex decision regions are examined in detail. One is linearly inseparable, nonconvex and disconnected. The other one is linearly inseparable, nonconvex and connected. The scheme is highly resilient to misclassification errors. The number of parameters to be estimated only grows linearly with the dimension of the pattern space for simple version of the scheme.

AB - A method for nonparametric (distribution-free) learning of complex decision regions in n-dimensional pattern space is introduced. Arbitrary n-dimensional decision regions are approximated by the union of a finite number of basic shapes. The primary example introduced in this paper are parallelepipeds and ellipsoids. By explicitly parameterizing these shapes, the decision region can be determined by estimating the parameters associated with each shape. A structural random search type algorithm called the genetic algorithm is applied to estimate these parameters. Two complex decision regions are examined in detail. One is linearly inseparable, nonconvex and disconnected. The other one is linearly inseparable, nonconvex and connected. The scheme is highly resilient to misclassification errors. The number of parameters to be estimated only grows linearly with the dimension of the pattern space for simple version of the scheme.

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Nonparametric learning of decision regions via the genetic algorithm

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