## 4 Discussion  
The methods based on machine learning pay more attention to the classification accuracy, but the statistical methods emphasize the correlation between feature and label, which explains the essential difference between the two approaches. Comparing the significant subsets selected by these two approaches, it is clear that most of the biomarkers in these two subsets were same, and this means that despite the emphasis of the two approaches being different, both of them did find the significant features. Further, by integrating the significant subset of these two approaches, the significant features can be double checked and obtained finally by the hybrid method proposed in this article. For example, for the data before feature selection, the \(p\)-value of characteristic path length, which is referred to as \(L\) in the above section, was \(5.02\times 10^{-3}\). The \(p\)-value of \(L\) for the optimal subset I, which was obtained by machine learning methods, the \(p\)-value of \(L\) for the optimal subset II, which was obtained by statistic methods, and the \(p\)-value of \(L\) for the optimal subset by the proposed hybrid method were \(9.40\times 10^{-6}\), \(2.82\times 10^{-5}\) and \(3.41\times 10^{-6}\) respectively. The results show that the HCs and SZ became obviously distinguishable after feature selection; specially, our method was more significant than machine learning, as well as statistical methods. In summary, the hybrid method can combine the strength of both machine learning and statistic methods to improve the accuracy of the results, and the results of network evaluation also confirmed this point. Our findings are quite consistent with those reports that the grey matter volume of CG, PCUN and CAU is significantly reduced in SZ [26; 27; 52; 53]. The CG is considered to be a brain region closely related to task attention, memory and affection, which has been reported to be destroyed in SZ [54]. The PCUN is the portion of the superior parietal lobule on the medial surface of each brain hemisphere, and it is often considered to be a brain region that plays an important role in the pathogenesis of SZ [55]. Given that the Behavioural Inhibition System (BIS) activity and Cloninger's Temperamental Dimension Harm Avoidance (HA) are mainly bound up with the study of the anxiety trait [56; 57] and the research results show that the BIS-sensitively as well as HA are negatively correlated with the regional gray matter volume at the CG and PCUN, the SZ may be accompanied by anxiety trait due to the reduction of the gray matter volume at these two regions [58]. The CAU is one of the structures that makes up the dorsal striatum, which is a component of the basal ganglia. It can affect the cognitive function of patients, resulting in decreased memory ability, and may be the cause of cognitive dysfunction in SZ [59]. In our findings, most of the brain connectivity in SZ was significantly reduced, which had been generally accepted as the fact that the functional connectivity reduces significantly in SZ and the reduction may cause the damage of information integration [60]. Among these abnormal connectivities, CAU, INS and ROL were the most connected regions. The INS mainly participates in the formation of aversion, the regulation of pain, the production of depression, the regulation of cardiac activity and the planning of language [61], and these may be the cause of affective symptoms in SZ. Moreover, many studies have found that the connectivity in the INS decreased, which may cause the disrupted functional integration of the brain [30]. The ROL is mainly involved in language, and [PERSON] et al. suggested that the reduction of connectivity of ROL improves the vulnerability of speech recognition to speech masking [62]. Not only that, the work also showed that the ROL is bound up with hallucination [63].