## 4 Conclusions and Discussion  
The goal of the present study was to apply an adversarial neural network to the case study of ASD and perform classification using multi-site functional connectivity data. The second objective was to compare this approach of multi-site data harmonization to the analytical and more commonly used one based on the NeuroHarmonize tool. This latter approach was carried out in the study by [PERSON] et al. [25]. In their paper, working on the ABIDE I dataset, and parcellating the brain with a different atlas called CC200, they obtained, after data harmonization, AUC values of 0.66 and 0.8 depending on the classifier employed for the analysis. In the recent paper by [PERSON] et al. [26], the authors proposed a different approach to the analysis of timeseries and subsequent classification of data from the ABIDE I dataset. The authors used a long short-term memory (LSTM) network to extract correlations and features from cerebral ROIs, and then they classified these features with a deep neural network after applying data augmentation techniques. They also compared their approach to the standard analytical method based on Pearson's correlation coefficients between the timeseries and dimensionality reduction with PCA. Their approach differs from ours in the use of an LSTM network and PCA. Furthermore, unlike our paper, their study did not address the multi-site harmonization problem. Remarkably, despite their quite different approach from ours, [PERSON] et al. achieved similar results to ours, obtaining an AUC of 72% on non-harmonized data in a cross-validation scheme. In our study, the two different approaches to multi-site data harmonization illustrated above lead us to consistent results on the whole ABIDE (I and II) dataset, namely AUC = 0.71 \(\pm\) 0.01 for the DNN analysis of harmonized data and AUC = 0.70 \(\pm\) 0.03 with the adversarial network. We are prone to consider the second one as a more promising strategy since it is completely data-driven and does not need any data preparation before inputting them to a machine learning algorithm. However, a possible drawback of using this type of network with data such as these is the possible confusion in the weights updating introduced by the huge number of sites and the limited dimension of the dataset from each site, which does not allow for an accurate training of the network. In different papers, domain-adversarial neural networks outperform different domain adaptation techniques; however, so far, these networks have only been tested on two domains [11; 12; 13]. In the article, [PERSON] et al. [11], who first designed this network, tested their algorithm on different datasets, which include two different domains, each one containing labeled or unlabeled data. In this way, they were able to test the domain adaptability of their network and, depending on the analyzed dataset, they achieved improvements in accuracy of up to 20%. In the study by [PERSON] et al. [12], a DNN was used for the analysis of text datasets. This approach outperforms other \"domain adaptation\" techniques, leading to an improvement of 2-7% accuracy. In the work of [PERSON] et al. [13], an improvement in accuracy using a DNN of more than 8% compared to other techniques was reported. In all these papers, the so-called _domains_ are the equivalent of our _sites_. However, in our data, we dealt with 36 different sites. Even if the site-predictor branch is encouraged to learn site-distinctive traits, it is not always able to distinguish among so many different sites. This is mainly due to the small size of some sites, and can cause confusion during the back-propagation on the update of weights related to the feature extractor branch. Also taking into account the previously described limitations, the ad-DNN approach obtained comparable performances with the analytical harmonization of connectivity measures followed by a DNN. The advantage of the former approach is that it is completely data-driven, with no need for preliminary data processing.