Real-coded Crossovers as a Role of Kernel Density Estimator Proposal of Crossover Kernels based on Unimordal Normal Distribution Crossover

Abstract

This paper presents a kernel density estimation method by means of real-coded crossovers. Functions of real-coded crossover operators are composed of probabilistic density estimation from parental populations and sampling from estimated models. Real-coded Genetic Algorithm (RCGA) does not explicitly estimate probabilistic distributions, however, probabilistic model estimation is implicitly included in algorithms of real-coded crossovers. Based on this understanding, we exploit the implicit estimation of probabilistic distribution of crossovers as a kernel density estimator. We also propose an application of crossover kernels to Expectation-Maximization estimation (EM) of Gaussian mixtures. The effectiveness of our method is tested by classification problems of artificially generated data sets and data sets in real world problems. It is shown that the proposed method is superior in generalization errors especially in high dimensionality in the comparison with conventional EM estimation. keywords: real-coded GA, crossover, kernel, density estimation, classification, mixture model, expectation maximization, Gaussian mixture. © 2007, The Japanese Society for Artificial Intelligence. All rights reserved.