Tumor classification based on microarray gene expression data is easy to fall into overfitting because such data are composed of many irrelevant, redundant, and noisy genes. Traditional gene selection methods cannot achieve satisfactory classification results. In this study, we propose a novel multi-target hybrid gene selection method named RMOGA (ReliefF Multi-Objective Genetic Algorithm), which aims to select a few genes and obtain good tumor recognition accuracy. RMOGA consists of two phases. Firstly, ReliefF is used to select the top 5% subset of genes from the original datasets. Secondly, a multi-objective genetic algorithm searches for the optimal gene subset from the gene subset obtained by the ReliefF method. To verify the validity of RMOGA, we conducted extensive experiments on 11 available microarray datasets and compared the proposed method with other previous methods. Two classical classifiers including Naive Bayes and Support Vector Machine were used to measure the classification performance of all comparison methods. Experimental results show that the RMOGA algorithm can yield significantly better results than previous state-of-the-art methods in terms of classification accuracy and the number of selected genes.

Feature selection is a preprocessing step that plays a crucial role in the domain of machine learning and data mining. Feature selection methods have been shown to be effective in removing redundant and irrelevant features, improving the learning algorithm’s prediction performance. Among the various methods of feature selection based on redundancy, the fast correlation-based filter (FCBF) is one of the most effective. In this paper, we developed a novel extension of FCBF, called resampling FCBF (RFCBF) that combines resampling technique to improve classification accuracy. We performed comprehensive experiments to compare the RFCBF with other state-of-the-art feature selection methods using three competitive classifiers (K-nearest neighbor, support vector machine, and logistic regression) on 12 publicly available datasets. The experimental results show that the RFCBF algorithm yields significantly better results than previous state-of-the-art methods in terms of classification accuracy and runtime.

Formalization of rough sets is a key issue in rough set theory. When rough sets are formalized by propositional logic, predicate logic, or modal propositional logic, it easily suffers from some problems. For instance, an incomplete system is obtained. The concepts of “ p r e c i s e” or “ r o u g h” of rough sets cannot be described. To tackle these issues, a new noncontingency axiomatic system is proposed for formalizing rough sets in this paper. First, a new concise accessibility relation is defined for the axiomatic system; then, two simpler axiom schemas of the axiomatic system are designed to replace the axiom schema K. This is helpful to prove the soundness and completeness theorems for the axiomatic system. Finally, rough sets can be perfectly formalized by our proposed axiomatic system. Theoretical analysis proves that a complete formal system is achieved. In addition, the concepts of “ p r e c i s e” or “ r o u g h” of rough sets can be described without the help of semantics functions of metalanguage.