# Machine Learning and rs-fMRI to Identify Potential Brain Regions Associated with Autism Severity
## 2 Methodology
### SVC Classifying Algorithm  
We used a supervised learning method, support vector machine (SVM), specifically the C-Support Vector Classification (SVC), to check the differences between ASD sub-classes. This method has three steps: training, validation, and test [43; 44]. Based on an in-depth systematic review and meta-analysis available in [21], we selected SVM as our ML method. SVM was the most used AI tool for solving ASD classification problems, showing some reliable results when applied in similar situations [18; 20; 37; 45; 46]. The second most used method was the artificial neural network (ANN) [21]. Both approaches have similar results in the literature, with SVM slightly better in terms of sensitivity [21]. As our goal was to find potential regions of a biomarker, and due to the complexity of the problem, we decided to adopt SVM given its more direct comparison, facilitating the interpretability of the results. We used the SVM from the scikit-learn library available at [47]. SVM creates a multidimensional plane, where each object (in our case, each subject) will be positioned according to the selected features' value. First, the sample part used for training will determine a curve to split the plane, as shown in Figure 1, where each area corresponds to one class. Then, the validation sample part will verify the accuracy of the curve, and this process will be repeated until the SVM reaches the best angle given \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Group** & **AVG** & **MAX** & **MIN** & **Standard Deviation** \\ \hline
**ASD** & 108.35 & 132.0 & 76.0 & 13.66 \\ \hline
**Auistic** & 104.81 & 148.0 & 65.0 & 16.76 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: FIQ distribution. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Set** & **ROIs** & **Set** & **ROIs** & **Set** & **ROIs** & **Set** & **ROIs** \\
**ID** & **IDs** & **ID** & **IDs** & **ID** & **IDs** & **ID** & **IDs** \\ \hline
**0** & [0, 1] & **9** & [26; 27] & **18** & [48,...,53] & **27** & [72; 73] \\ \hline
**1** & [2,..., 5] & **10** & [28; 29] & **19** & [54; 55] & **28** & [74; 75] \\ \hline  
the features, training sample, and validation sample. After this, the test sample is used to measure the SVM generalization. We hypothesized that higher accuracy would reflect the existence of an interpretative way to differ each class. In other words, SoRs with higher accuracy potentially contain the regions where classes are more distinct regarding the features used. These findings can highlight the areas to consider for further investigations on functional brain activity and ASD severity. As the main goal was to find regions where there is a functional brain difference in the ASD severity level, and there is a lack of data about SVM setups in previews works on fMRI related to ASD investigations, as observed in [21], we chose a few educated-guess setups in our experiment. The setup was related to the variables _gamma_, _coef0_, _kernel_, _class_weight_, _degree_, and _max_iter_. The _gamma_ delimitates how close the final classification should be regarding the training sample, with more significant values given to more rigid solutions and lower values to given more flexible solutions. The _coef0_ is an independent value related to the scale of the sample. Meanwhile, the _kernel_ is the mathematical equation used to solve the problem, and the ones available from [47] are _linear_, _poly_, _rbf_, _sigmoid_. The _class_weight_ option considers the size of each class in the training step, adjusting the weight accordingly. For example, regarding training, if Class 1 has three subjects and Class 2 has nine subjects, Class 1 will weigh three while Class 2 will weigh one. This process is meant to avoid the algorithm taking into account only the dominant class from training, which can jeopardize the SVM's generalization capacity. The _degree_ will define the curve degree of the equation that splits the SVM classification plane.