Comprehensive study of feature selection methods to solve multicollinearity problem according to evaluation criteria

Abstract

This paper provides a new approach to feature selection based on the concept of feature filters, so that feature selection is independent of the prediction model. Data fitting is stated as a single-objective optimization problem, where the objective function indicates the error of approximating the target vector as some function of given features. Linear dependence between features induces the multicollinearity problem and leads to instability of the model and redundancy of the feature set. This paper introduces a feature selection method based on quadratic programming. This approach takes into account the mutual dependence of the features and the target vector, and selects features according to relevance and similarity measures defined according to the specific problem. The main idea is to minimize mutual dependence and maximize approximation quality by varying a binary vector that indicates the presence of features. The selected model is less redundant and more stable. To evaluate the quality of the proposed feature selection method and compare it with others, we use several criteria to measure instability and redundancy. In our experiments, we compare the proposed approach with several other feature selection methods, and show that the quadratic programming approach gives superior results according to the criteria considered for the test and real data sets.