A Tri-Objective Method for Bi-Objective Feature Selection in Classification

Minimizing the number of selected features and maximizing the classification performance are two main objectives in feature selection, which can be formulated as a bi-objective optimization problem. Due to the complex interactions between features, a solution (i.e., feature subset) with poor objective values does not mean that all the features it selects are useless, as some of them combined with other complementary features can greatly improve the classification performance. Thus, it is necessary to consider not only the performance of feature subsets in the objective space, but also their differences in the search space, to explore more promising feature combinations. To this end, this paper proposes a tri-objective method for bi-objective feature selection in classification, which solves a bi-objective feature selection problem as a tri-objective problem by considering the diversity (differences) between feature subsets in the search space as the third objective. The selection based on the converted tri-objective method can maintain a balance between minimizing the number of selected features, maximizing the classification performance, and exploring more promising feature subsets. Furthermore, a novel initialization strategy and an offspring reproduction operator are proposed to promote the diversity of feature subsets in the objective space and improve the search ability, respectively. The proposed algorithm is compared with five multiobjective-based feature selection methods, six typical feature selection methods, and two peer methods with diversity as a helper objective. Experimental results on 20 real-world classification datasets suggest that the proposed method outperforms the compared methods in most scenarios.