# Principal Subspace of Dynamic Functional Connectivity for Diagnosis of Autism Spectrum Disorder
## 3 Material and Method
### Selection of the Most Significant ASD-Related Functional Connectivity
#### 3.3.2 ANOVA-SVM and Correlation Analysis  
In the first step to find the most discriminative FC related to ASD, the ANOVA-SVM algorithm is applied to the WCF feature vector. The size of the WCF matrix is the total number of subjects \(\times\) 4005. ANOVA-SVM is a supervised learning algorithm that uses a heuristic search strategy to identify which of the 4005 connectivity features significantly contribute to the identification of ASD-FC patterns. A detailed description of the ANOVA-SVM steps can be found in Algorithm 1. Here, the \(p\)-value is the threshold used to control the size of subsets of FC. In our experiment, five subsets were determined by setting the \(p\)-value in the range (0.01:0.01:0.05). Then, each subset of the FC network is evaluated in terms of 10-fold CV classification accuracy by using the SVM classifier. The top subset of ASD FC is selected based on the highest classification scores for input to the correlation analysis stage. After that, correlation analysis is applied between the top subset of the FC network and the SRS scores to determine the significant connectivity features that correlate positively and negatively with ASD symptoms.  
Figure 3: Method of selecting the most significant brain-node pairs from wavelet coherence using WCF, ANOVA-SVM and correlation analysis between WCF and SRS.  
Previous studies have shown that correlation analysis between FC features and clinical symptoms of ASD is helpful in discovering discriminative FC patterns for ASD patients [21; 39; 40]. In this study, correlation analysis between DFC measured using the WCF and clinical symptoms scores is conducted to find the subset of most significant FCs related to ASD. Clinical symptoms are represented by the Social Responsiveness Scale (SRS), with details given in Table 2 (Appendix A). The SRS is a tool used to assess the severity of autism symptoms. It consists of 65 items divided into five content-areas of social deficits: awareness (AWA), cognition (COG), communication (COM), motivation (MOT) and mannerism (MAN) [41].  
It should be noted that by using PCC, each subject will generate a single 90 \(\times\) 90 PCC matrix. The size of the 2D matrix generated by PCC is relatively small compared to the WC analysis. Therefore, the PCC undergoes only ANOVA-SVM. In addition, by comparing the accuracy results of PCC and WC from ANOVA-SVM, as covered in Table 3, it is clear that the WC method is superior to PCC. Hence, correlation analysis with SRS is not applied to PCC but only to WCF.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **ASD Mean (SD)** & **NC Mean (SD)** & **F-Test** & \(p\)**-Value** \\ \hline No. of subjects & 29 (26M/3F) & 33 (28M/5F) & - & - \\ Age (years) & 17.7 (0.9) & 18.3 (0.8) & 0.9 & 0.5 \\ SRS\_AWA & 7.8 (0.6) & 7.4 (0.8) & 0.4 & 0.02 \\ SRS\_COG & 10.2 (1.1) & 10.4 (1.6) & 0.4 & 0.00 \\ SRS\_COM & 18.6 (1.7) & 16.7 (2.8) & 0.3 & 0.00 \\ SRS\_MOT & 10.9 (1.1) & 10.4 (1.5) & 0.4 & 0.01 \\ SRS\_MAN & 9.7 (1.0) & 8.6 (1.4) & 0.5 & 0.02 \\ SRS\_TOT & 56.8 (4.9) & 53.6 (7.8) & 0.3 & 0.00 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Demographic and mean value \(\pm\) standard deviation (SD) of clinical diagnostic SRS scores of LEUVEN dataset.