## 3 Results on Philadelphia Neuro Developmental Cohort (PNC) Data
### Comparison with Other Feature Selection Methods  
In order to show the advantages of the proposed two-step feature selection method, we compare it with SVM-RFE, FSCS and several other typical feature selection methods, i.e., maximum correlation minimum redundancy with mutual information difference (mRMR-MID), maximum correlation minimum redundancy with mutual information entropy (mRMR-MIQ), feature section with random forest by Gini index (RFFS-GINI), and feature section with random forest by out of bag data (RFFS-OOB) [55; 56]. Each feature selection method was repeated 20 times with random 70% training and 30% testing data. The performance of the classification accuracy rate (CAR) for different feature selection methods are shown in Figure 8. The two-step feature selection method achieves its optimal classification accuracy in a faster and more stable way than other methods. It is worth noting that for other methods, 600 or even more features (i.e., the differences of ICNs) are needed to get their best performances, while less than 200 features are sufficient for the proposed method to identify the the changes of brains' connectivity during development. This is consistent with the feature size selected in Section 3.3.  
Additionally, the redundant degree of a feature subset \(D\) can be calculated by  
\[C_{score}(D)=\frac{1}{|D|}\sum_{i,j=1}^{|D|}c(i,j) \tag{8}\]  
where \(c(i,j)\) represents the Pearson correlation coefficient of features \(i\) and \(j\), and \(|D|\) denotes the number of features in \(D\). By (8), the average redundant degree of both the two-step feature selection method and the SVM-RFE (with best performance) are 49.8423 and 138.6289, respectively, which strongly confirms the ability of the two-step feature selection method to effectively remove redundancy.  
In addition to CAR, the selected differences of ICNs can be further quantified by sensitivity (SS), specificity (SC), positive predictive value (PPV) and negative predictive value (NPV), which are defined as follows  
\[\begin{array}{rcl}SS&=&\frac{Corr_{p}}{Corr_{p}+InCorr_{n}}\\ SC&=&\frac{Corr_{n}}{Corr_{n}+InCorr_{p}}\\ PPV&=&\frac{Corr_{p}}{Corr_{p}+InCorr_{p}}\\ NPV&=&\frac{Corr_{n}}{Corr_{n}+InCorr_{n}}\\ CAR&=&\frac{Corr_{p}+Corr_{n}+InCorr_{n}+InCorr_{n}}\\ \end{array} \tag{9}\]  
\begin{table}
\begin{tabular}{l l} \hline
**Measure** & **Definition** \\ \hline \(Cc\): Clustering coefficient & \(Cc=\frac{1}{\pi}\sum_{i\in N}\frac{2i_{i}}{E_{i}(k-1)}\) \\  
where \(Corr_{p}\), \(InCorr_{p}\), \(Corr_{n}\) and \(InCorr_{n}\) denote the number of true positive, false positive, true negative and false negative samples, respectively. CAR, SS, SC, PPV and NPV provide five different assessments of the classifiers. CAR is the proportion of all samples that are correctly predicted, SS is the proportion of positive samples (here, the positive samples refer the children subjects) correctly predicted among all the predicted positive samples, SC is the proportion of negative samples (i.e., the young adults) correctly predicted among all the predicted negative samples, PPV is the proportion of correctly predicted positive samples among the true positive samples, and NPV is the proportion of negative samples correctly predicted among those true negative samples. We calculate the average classification performance when the