# Principal Subspace of Dynamic Functional Connectivity for Diagnosis of Autism Spectrum Disorder
## 4 Results and Discussion
### Correlation Analysis between WCF and SRS Scores  
In this section, using the 212 FCs obtained using the ANOVA-SVM algorithm as described in the previous section, correlation analysis between WCF of the 212 FCs and SRS is conducted. This allows us to select the most important brain connections from the 212 connections that are more indicative of being ASD biomarkers. The results of thecorrelation analysis are given in Table 14. Clearly, out of 212 connections, 35 connections are highly correlated with ASD symptoms. The criteria for selecting highly correlated pairwise WCFs are high correlation at >95% confidence level and SRS scores higher than four. Accordingly, there are five pairwise positive correlations and six pairwise negative correlations with ASD symptoms, as given in Table 14 in the Appendix A.  
Plots of the main connections that positively and negatively correlate with SRS scores in the left and right hemispheres and all four lobes of the brain are shown in Figure 5(a),b, respectively. These include the frontal lobe (MFG, SFGmed, SFGdor, ORBsup and ROL), the parietal lobe (SPG, PCUN and SMG), the occipital lobe (SOG and CAL) and the temporal lobe (STG, TPOmid, THA, HIP and OLF). For further validation, we compare the selected connections with the results of previous neuroscience studies [45; 46; 47]. It is noteworthy that the abnormality in FCs between MFG-HIP and THA-TPOmid is consistent with the results of [45; 46]. In addition, [PERSON] et al. [47] confirmed the presence of abnormalities in the functional connectivity of regions in the parietal lobe that correlate with performance of social skills of ASD subjects. According to these results, the selected autistic neural patterns based on WCF analysis can be used as biomarkers to better understand the dynamic neural mechanisms of ASD.  
Classification Evaluation Using PWC Matrices Reconstructed by Increasing Number of Principal Components  
In this section, we present the results of an experiment to verify that the first principal component of a WC matrix is the one that carries the most important feature and provides the best classification accuracy. The FC matrix from the PWC block as illustrated in Figure 4 is WC, but it is reconstructed using only the first component, as in Equation (9). The performance of the 3L-CNN using WCs reconstructed using the first principal component through the first ten principal components is given in Figure 7.  
It can be seen in Figure 7 that the classification accuracy decreases significantly as the number of principal components increases. It is clear that the first principal subspace, spanned by the first, leftmost eigenvector, senses the maximal oriented energy of the images, a concept that was highly discussed in [48]. It is then expected that the first principal component yields better accuracy than subsets with more than one of the leftmost eigenvectors. This trend is clearly evident from the plot of accuracy vs. number of principal components, i.e., the number of the leftmost eigenvectors, as shown in Figure 7.  
Figure 6: Brain nodes with (**a**) positive and (**b**) negative correlation with autism severity symptoms (SRS score) as listed in Table 14.