Feature selection is an important data-preprocessing technique in classification problems such as bioinformatics and signal processing. Generally, there are some situations where a user is interested in not only maximizing the classification performance but also minimizing the cost that may be associated with features. This kind of problem is called cost-based feature selection. However, most existing feature selection approaches treat this task as a single-objective optimization problem. This paper presents the first study of multi-objective particle swarm optimization (PSO) for cost-based feature selection problems. The task of this paper is to generate a Pareto front of nondominated solutions, that is, feature subsets, to meet different requirements of decision-makers in real-world applications. In order to enhance the search capability of the proposed algorithm, a probability-based encoding technology and an effective hybrid operator, together with the ideas of the crowding distance, the external archive, and the Pareto domination relationship, are applied to PSO. The proposed PSO-based multi-objective feature selection algorithm is compared with several multi-objective feature selection algorithms on five benchmark datasets. Experimental results show that the proposed algorithm can automatically evolve a set of nondominated solutions, and it is a highly competitive feature selection method for solving cost-based feature selection problems.

Evolutionary feature selection methods face the challenge of “curse of dimensionality" when dealing with high-dimensional data. Focusing on this challenge, this paper studies a variable-size cooperative coevolutionary particle swarm optimization algorithm (VS-CCPSO) for feature selection. The proposed algorithm employs the idea of “divide and conquer" in cooperative coevolutionary approach, but several new developed problem-guided operators/strategies make it more suitable for feature selection problems. Firstly, a space division strategy based on the feature importance is presented, which can classify relevant features into the same subspace with a low computational cost. Following that, an adaptive adjustment mechanism of sub-swarm size is developed to maintain an appropriate size for each sub-swarm, with the purpose of saving computational cost on evaluating particles. Moreover, a particle deletion strategy based on fitness-guided binary clustering, and a particle generation strategy based on feature importance and crossover both are designed to ensure the quality of particles in the sub-swarms. We apply VS-CCPSO to 12 typical datasets, and compare it with six state-of-the-art methods. Experimental results show that VS-CCPSO has the capability of obtaining good feature subsets, suggesting its competitiveness for tackling feature selection problems with high dimensionality.

The “curse of dimensionality” and the high computational cost have still limited the application of the evolutionary algorithm in high-dimensional feature selection (FS) problems. This article proposes a new three-phase hybrid FS algorithm based on correlation-guided clustering and particle swarm optimization (PSO) (HFS-C-P) to tackle the above two problems at the same time. To this end, three kinds of FS methods are effectively integrated into the proposed algorithm based on their respective advantages. In the first and second phases, a filter FS method and a feature clustering-based method with low computational cost are designed to reduce the search space used by the third phase. After that, the third phase applies oneself to finding an optimal feature subset by using an evolutionary algorithm with the global searchability. Moreover, a symmetric uncertainty-based feature deletion method, a fast correlation-guided feature clustering strategy, and an improved integer PSO are developed to improve the performance of the three phases, respectively. Finally, the proposed algorithm is validated on 18 publicly available real-world datasets in comparison with nine FS algorithms. Experimental results show that the proposed algorithm can obtain a good feature subset with the lowest computational cost.

Feature selection (FS) is an important data processing technique in the field of machine learning. There have been various FS methods, but all assume that the cost associated with a feature is precise, which restricts their real applications. Focusing on the FS problem with fuzzy cost, a fuzzy multiobjective FS method with particle swarm optimization, called PSOMOFS, is studied in this article. The proposed method develops a fuzzy dominance relationship to compare the goodness of candidate particles and defines a fuzzy crowding distance measure to prune the elitist archive and determine the global leader of particles. Also, a tolerance coefficient is introduced into the proposed method to ensure that the Pareto-optimal solutions obtained satisfy decision makers' preferences. The developed method is used to tackle a series of the UCI datasets and is compared with three fuzzy multiobjective evolutionary methods and three typical multiobjective FS methods. Experimental results show that the proposed method can achieve feature sets with superior performances in approximation, diversity, and feature cost.