Breeding policies in evolutionary approximation of optimal subspace

Abstract

In very high dimension variable space (e.g. 30 or more), huge computations evenly hinder investigators to conduct any direct meaningful analysis. A traditional trick is firstly to conduct single variable analysis, then combine several top most single-fittest variables to approximate the optimal subspace. In this investigation, an evolutionary method for optimal subspace approximation is proposed. The breeding policies of this evolutionary approximation, its scalability and generalization have been intensively investigated. The studied object is a 30-D variable space which contains 6000 artificial individuals. In this data, except for 3 variables containing two donut-type data distributions, each with 3000 individuals, the remaining 27 variables only contain quasi-random data with the same value range as the donut data distributions. The donut distribution consist of two toroidal distributions (classes) which are interlocked like links in a chain. The cross-section of each distribution is a Gaussian function distributed with standard deviation delta. Even the Donut problem which possesses a variety of pathological traits can invalidate many non-complex analyses for classification. The goal of this investigation was to find the 3 donut variables within the optimal subspace of 30-D variable space in which most quasi-random variables emerge as noise variables. In order to reach this goal, various breeding policies were implemented and compared. Although no perfect solution for the approximation was found, various breeding policies and their impact on decreasing the error were studied. These were found to be relatively usable for reference and might be improved when used in a practical application.