## 2 Methods
However, among them, there may exist highly correlated and relevant features. In what follows, we will remove those features obtained by SVMRFE-CA, and only retain the most discriminative features as the final optimal feature subset. **Step 2:** Feature selection based on F-score and the correlation score to form a new feature selection technique (FSCS)  
F-score is a simple and valid feature selection method to quantify the discernibility of a candidate feature [44]. The F-score of the \(i\)-th feature is defined as  
\[F_{score}(i)=\frac{(\mu_{i}^{P}-\mu_{i}^{N})^{2}}{(\sigma_{i}^{P})^{2}+(\sigma _{i}^{N})^{2}} \tag{4}\]  
where \(\mu_{i}^{P}\) and \(\mu_{i}^{N}\) are the means of the positive samples and the negative samples corresponding to the \(i\)-th feature, and \(\sigma_{i}^{P}\) and \(\sigma_{i}^{N}\) are the variances of them, respectively. In Equation (4), the numerator can be considered as an index of the distance between the centers of two data sets, which evaluates the ability of the \(i\)-th feature to distinguish between positive and negative sample sets. Since the variance of a data set indicates the degree of concentration, the denominator of Equation (4) represents the ability of the \(i\)-th feature to assemble samples. Therefore, the larger the \(F_{score}(i)\), the more distinguishable the feature \(i\) is between the two sample sets. In addition, we introduce the correlation score between the feature \(i\) and a feature set \(D\), which is defined as follows  
\[C_{score}(i,D)=\frac{1}{|D|}\sum_{j=1}^{|D|}c(i,j) \tag{5}\]  
where \(c(i,j)\) represents the Pearson correlation coefficient between features \(i\) and \(j\), and \(|D|\) denotes the feature size of \(D\). \(C_{score}(i,D)\) therefore measures the degree of correlation between feature \(i\) and feature set \(D\). In order to further select the most discriminative and non-redundant features from the feature subset obtained by SVMRFE-CA, we combine both F-score and the correlation score to form a new feature selection technique, i.e., FSCS. The evaluation criterion of it is defined as  
\[FSCS(i)=F_{score}(i)-C_{score}(i,D^{sel}) \tag{6}\]  
where \(D^{sel}\) is the current selected feature set. The definition suggests the greater the \(FSCS(i)\) is, the stronger distinguishing ability of the candidate feature \(i\), and meanwhile, the weaker the correlation between feature \(i\) and the features in \(D^{sel}\). The FSCS technique based on F-score and correlation score maximizes the discriminative power of feature \(i\) and simultaneously minimizes its overall correlation with other selected features, which can further optimize the features in the feature subset selected by SVMRFE-CA. **The Two-Step Feature Selection Method**  
In view of the above SVMRFE-CA as well as the FSCS method, we propose a two-step feature selection technique, and its flowchart is shown in Figure 1. In the first step, an integration of feature subsets is produced by multiple iterations of the SVMRFE-CA algorithm with random division of data. The frequency of each feature in these subsets is aggregated and sorted. The first \(n\) features with large frequency are retained, and they form an integrated feature subset which has a strong correlation with the classification performance. Based on this, the second step employs FSCS to further select features with the maximal discriminative abilities, while it has the minimal overall correlations with other candidate features. Therefore, using two-step feature selection, we can get the optimal feature subset. The two-step feature selection algorithm is described in Algorithm 1. Figure 1: The two-step feature selection method. In which SVMRFE-CA denotes support vector machine recursive feature elimination-classification accuracy, FSCS denotes F-score and the correlation score.