Feature selection schema based on game theory and biology migration algorithm for regression problems

Many real-world datasets nowadays are of regression type, while only a few dimensionality reduction methods have been developed for regression problems. On the other hand, most existing regression methods are based on the computation of the covariance matrix, rendering them inefficient in the reduction process. Therefore, a BMA-based multi-objective feature selection method, GBMA, is introduced by incorporating the Nash equilibrium approach. GBMA is intended to maximize model accuracy and minimize the number of features through a less complex procedure. The proposed method is composed of four steps. The first step involves defining three players, each of which is trying to improve its objective function (i.e., model error, number of features, and precision adjustment). The second step includes clustering features based on the correlation therebetween and detecting the most appropriate ordering of features to enhance cluster efficiency. The third step comprises extracting a new feature from each cluster based on various weighting methods (i.e., moderate, strict, and hybrid). Finally, the fourth step encompasses updating players based on stochastic search operators. The proposed GBMA strategy explores the search space and finds optimal solutions in an acceptable amount of time without examining every possible solution. The experimental results and statistical tests based on ten well-known datasets from the UCI repository proved the high performance of GBMA in selecting features for solving regression problems.