## 2 Materials and Methods  
### Data Selection  
For this study, we used rs-fMRI data from the multicenter ABIDE dataset [20]. The dataset comprises two collections: ABIDE I and ABIDE II. ABIDE I includes scans of 1112 subjects, evenly distributed between ASD and TD, collected from 17 different sites. ABIDE II includes scans of 1114 subjects, evenly distributed between ASD and TD, collected from 19 different sites. In addition to the scan images, ABIDE also provides phenotypic information, such as age, sex, eye status at scan, and additional clinical information.  
Although some sites in ABIDE II may be the same as those in ABIDE I, the pipeline and acquisition parameters may have been modified between the two datasets. For this reason, they will be considered as distinct acquisition sites. Furthermore, even within a single collection, such as ABIDE II, there are sites that have released two different data samples. For this reason, some of these samples are labeled with a subscription number (e.g., 1 or 2). Subjects from the ABIDE II collection will have the prefix \"ABIDE II\" before the site name. If this prefix is missing, the collection belongs to ABIDE I.  
We selected 1001 male subjects, aged between 5 and 40 years, with eyes open during acquisition. The data of these subjects are collected from 23 different sites. Male subjects were chosen because the male sample is larger than the females one since males have a higher probability of being affected by ASD than females [21]. Moreover, the female dataset was insufficiently populated to allow for statistically significant studies. The choice of the condition with open eyes was made to avoid including subjects who were potentially sleeping during the examination. The dataset is evenly divided between ASD and TD, containing 506 TD and 495 ASD subjects. Figure 1 shows the distribution of ASD/TD for each site and Table 1 provides information on age distribution for each of the 23 sites.  
Figure 1: Dataset composition. Sites without a prefix belong to the ABIDE I collection.  
\begin{table}
\begin{tabular}{c c c c} \hline
**SITE** & **Mean\_Age**\(\pm\)**Standard\_Deviation** & **Min\_Age** & **Max\_Age** \\ \hline ABIDEII-TCD\_1 & \(15\pm 3\) & 10 & 20 \\ \hline ABIDEII-SDSU\_1 & \(13\pm 3\) & 8 & 18 \\ \hline ABIDEII-GU\_1 & \(11\pm 2\) & 8 & 14 \\ \hline ABIDEII-NYU\_1 & \(9\pm 4\) & 5 & 27 \\ \hline ABIDEII-OHSU\_1 & \(11\pm 2\) & 7 & 15 \\ \hline ABIDEII-USM\_1 & \(21\pm 7\) & 9 & 36 \\ \hline ABIDEII-IU\_1 & \(23\pm 5\) & 17 & 34 \\ \hline ABIDEII-KKI\_1 & \(10\pm 1\) & 8 & 13 \\ \hline ABIDEII-ETH\_1 & \(23\pm 4\) & 14 & 31 \\ \hline ABIDEII-OILH\_2 & \(23\pm 3\) & 18 & 28 \\ \hline YALE & \(12\pm 3\) & 7 & 18 \\ \hline USM & \(21\pm 7\) & 9 & 39 \\ \hline OLIN & \(16\pm 3\) & 10 & 23 \\ \hline NYU & \(15\pm 6\) & 7 & 39 \\ \hline UM\_2 & \(16\pm 3\) & 13 & 29 \\ \hline UCLA\_2 & \(12\pm 1\) & 10 & 15 \\ \hline UM\_1 & \(13\pm 3\) & 8 & 19 \\ \hline SDSU & \(14\pm 1\) & 12 & 17 \\ \hline KKI & \(10\pm 1\) & 8 & 13 \\ \hline UCLA\_1 & \(13\pm 2\) & 9 & 18 \\ \hline MAX\_MUN & \(10\pm 2\) & 7 & 13 \\ \hline LEUVEN\_1 & \(23\pm 3\) & 18 & 32 \\ \hline OHSU & \(10\pm 2\) & 8 & 14 \\ \hline \end{tabular}
\end{table}
Table 1: Information about the mean \(\pm\) standard deviation, the minimum and the maximum value of age, in years, across each of the 23 considered sites.