## 2 Methods  
In this paper, we propose a two-step feature selection strategy to select features without redundancy, with the potential to improve the accuracy of prediction and identification of sparse ICN changes. **Step 1:** Feature selection based on SVMRFE-CA  
SVM-RFE is a wrapper feature selection algorithm that avoids overfitting when the data is of high dimension. It can remove insignificant features in order to achieve higher classification performance. SVM-RFE was first proposed for gene selection [39], and has been widely applied to many other fields [40; 41; 42]. Suppose that in the training set \(\{(\mathbf{x}_{i},y_{i})\}_{i=1}^{N}\), \(\mathbf{x}_{i}\in R^{D}\) is the \(i\)-th sample, \(y_{i}\in\{+1,-1\}\) is the label of \(\mathbf{x}_{i}\), \(N\) is the sample size, and \(D\) is the dimension of each sample (thus the original dimension of the feature data is also \(D\)). Finding the optimal classification hyperplane of SVM is equivalent to minimizing the objective function \(J\)  
\[ \begin{array}{l}J=\frac{1}{2}\|\boldsymbol{\omega}\|^{2}+C\sum_{i}\xi_{i}\\ s.t.\quad y_{i}(\boldsymbol{\omega}^{T}\mathbf{x}_{i}+b)\geq 1-\xi_{i},\ \xi_{i}\geq 0 \end{array}  \tag{1}\]where \(\frac{2}{\|\mathbf{\omega}\|}\) is defined as the margin, \(\xi_{i}\) is the slack variable related with training errors, and \(C\) is the penalty coefficient used as a trade-off between the maximum margin and the minimum training errors. By the Lagrange multiplier method, the optimal solution of (1) is  
\[\mathbf{\omega}=\sum_{i}\alpha_{i}y_{i}\mathbf{x}_{i},\alpha_{i}\geq 0 \tag{2}\]  
where \(\alpha_{i}\) is the Lagrange multiplier. Let \(\mathbf{\omega}=(\omega_{1},\omega_{2},\cdots,\omega_{D})^{T}\). In the SVM-RFE algorithm, each \(\omega_{i}\) is defined as the weight of feature \(i\)[39]. In [40], it was proven that \(\omega_{i}^{2}\approx|J-J_{i}|\), where \(J_{i}\) represents the value of the objective function after feature \(i\) is removed; i.e., \(\omega_{i}^{2}\) is an approximation of the change of the objective function when feature \(i\) is eliminated. Therefore, eliminating features with small weights will not have a big impact on the objective function of the optimization problem, which is just the essence of the SVM-RFE algorithm. Since \(|\omega_{i}|\) and \(\omega_{i}^{2}\) are consistent in values, the importance of feature \(i\) can be evaluated by  
\[Score(i)=|\omega_{i}|\quad\text{or}\quad Score(i)=\omega_{i}^{2}. \tag{3}\]  
For SVM-RFE, the importance of each feature of the training data is calculated by (3), and the feature with the smallest score is deleted [43]. The SVM is trained again with the remaining features, and the iterations are conducted until the stopping criterion is reached. In the SVM-RFE algorithm, if a feature is eliminated, it will not be considered again in the subsequent process, which may however have some discriminative ability. This happens especially in the case that the data set is small but with high dimensions. In order to improve the performance of SVM-RFE, we divide the training data into two parts: one for feature selection and the other for validation. The classification accuracy (CA) on the validation set is regarded as the evaluation criterion of the candidate feature subset. Then, by combining with backward deletion, the optimal feature subset can be finally obtained. Specifically, if one feature with small weight is picked, while the corresponding CA on the validation set decreases after its removal, then this feature should be reconsidered. Additionally, multiple subsampling strategies on the training data are utilized and a series of feature selection processes are performed to avoid mistakenly removing such features. Finally, such obtained series of feature subsets form one optimal feature subset. The improved method of SVM-RFE is denoted as SVMRFE-CA. For SVMRFE-CA, the selected features are evaluated by their classification performances, so the features in the optimal feature subset are beneficial to the discrimination.