IJPAM: Volume 108, No. 2 (2016)

RECOGNITION OF A MIXTURE OF
MULTIPLE GAUSSIAN PATTERNS

A.C. Mkolesia$^1$, C.R. Kikawa$^2$, M.Y. Shatalov$^3$, B.M. Kalema$^4$
$^{1,2,3}$Department of Mathematics and Statistics
Tshwane University of Technology
175 Nelson Mandela Drive, Pretoria, 0001, RSA
$^4$Department of Informatics
Tshwane University of Technology
2 College Road, Block L, Pretoria North, 0116, RSA

Abstract. In this paper a methodology for the recognition of multiple Gaussian patterns by estimating sufficient parameters of a finite mixture model (FMM) is proposed. Regular methods of FMM identification require initial guess values (IGVs) that may result in high computation time, slow convergence and or even fail to converge if the provided IGVs are far from the optimal solution. The FMM is firstly decomposed into it's even and odd parts, which are linearised through differential techniques. Secondly the ordinary least squares (OLS) method is employed to estimate the unknown parameters in the linearised models. A Monte Carlo simulation is done to evaluate the performance of the proposed method (PM). It is shown that numerical results of the PM compare well with the simulated values. The study indicates that (i) the PM can be used symbiotically with the regular methods to compute IGVs; and (ii) can be used to estimate a general $n$-component Gaussian model.

Received: April 4, 2016

Revised: April 4, 2016

Published: October 1, 2016

AMS Subject Classification: 62F15, 62C10

Key Words and Phrases: finite mixture models, Gaussian distributions, parameter estimation, ordinary least squares, ordinary differential equation
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DOI: 10.12732/ijpam.v108i2.8 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 108
Issue: 2
Pages: 307 - 326


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