## 3 Experiments
### Locating the Abnormalities in Brains for SZ
#### 3.2.3 Feature Selection Results Based on a Hybrid Method  
By both machine learning and statistical methods, the key candidate features for SZ were selected, and the dataset were quite similar. We adopted the intersection of them as the final selected feature subset, and thus, the abnormal brain regions from the SBM data (see Figure 8) and the abnormal functional connectivity from the FNC data (see Figure 9) can be obtained. Figure 5: The results obtained by the Kendall correlation coefficient. The \(x\) axis corresponds to the features, and the \(y\) axis is the absolute value of the Kendall tau correlation coefficient. Figure 6: The results of hypothesis test for both two-sample \(t\)-tests and the permutation test. The \(x\) axis corresponds to the features, and the \(y\) axis is the significance level \((-log_{2}P)\). The red and green lines show the significance levels of 0.05 and 0.01, respectively. The features with \(-log_{2}P\) values above the lines have significant differences, and they are the candidates of abnormal regions or connections. Figure 7: Feature selection results based on statistical methods. Figure 8 shows the brain regions selected by our method that differed from healthy controls in SZ, and these abnormal brain regions were mainly distributed in supramarginal gyrus (SMG), cingulate gyrus (CG), middle frontal gyrus (MFG), precuneus (PCUN), superior frontal gyrus (SFG) and caudate (CAU). Compared with the HC group, the SZ group had significantly reduced grey matter volumes in the CG, PCUN and CAU and significantly increased grey matter volume of brain regions including SMG, MFG and SFG. Figure 9 shows the abnormal functional connections of brains with SZ. In this figure, the left table lists the selected abnormal functional connections of the regions of interest (the relationships of the regions and the labels are shown in Figure A2), in which ML refers to machine learning methods and SM refers to statistical methods. The circular connectivity graph in the middle is a schematic map of the selected functional connections, which are listed in the fourth column of the left table. The labels in this graph correspond to the regions of interest, and the corresponding spatial maps of these regions (see [48]) are also shown in this graph. The right graph depicts the locations and their connections of the selected brain regions by the BrainNet Viewer toolbox [49]. Figure 8: The selected abnormal brain regions of SZ by the hybrid method. [PERSON] et al. presented the relationships between the cortical maps and the brain regions described by the SBM features [47]. Figure 9: The abnormal functional connections of brains with SZ. In this figure, the left table lists the selected abnormal functional connections of the regions of interest (the relationships of the regions and the labels are shown in Figure A2), in which ML refers to machine learning methods and SM refers to statistical methods. The circular connectivity graph in the middle is a schematic map of the selected functional connections, which are listed in the fourth column of the left table. The labels in this graph correspond to the regions of interest, and the corresponding spatial maps of these regions (see [48]) are also shown in this graph. The right graph depicts the locations and their connections of the selected brain regions by the BrainNet Viewer toolbox [49]. Figure 9 shows that by the hybrid feature selection method proposed here, 17 abnormal functional connections between the SZ group and HC group can be discovered. Furthermore, by combining with the relationship between the connections and the regions shown in Figure A2, six connections are related to the caudate nucleus (CAU), including rolandic operculum (ROL), insula (INS), supramarginal gyrus (SMG), superior occipital gyrus (SOG), precuneus (PCUN) and median cingulate and paracingulate gyri.