# A Multi-Site Anti-Interference Neural Network for ASD Classification
## 2 Materials and Methods
### Representation Learning  
The input of the representation learning module is the functional connection matrix, and the physiological meaning is the brain functional network. There are obvious differences between the data structure and the picture, mainly reflected in the fact that the functional connection matrix is a non-Euclidean space and the picture is a Euclidean space. In the Euclidean space of the picture, the neighbors of a pixel are the surrounding pixels in space, so the convolution nuclear energy in the two-dimensional form gathers the information in the neighborhood domain. However, in the functional connection matrix, the neighbor nodes of the target node are not always adjacent in space, so the convolution kernel in two-dimensional form cannot guarantee that all the gathered information comes from the neighbor domain of the target node. This can lead to a mixture of features from different brain regions, which is not conducive to the analysis of important brain regions. The topology of the functional connection matrix is characterized by the fact that each row in the matrix represents the correlation between the brain region corresponding to that row and all the other brain regions. When the functional connection matrix is regarded as a brain functional network, a row in the matrix can also be used as the correlation between the target node and its neighbor node. Therefore, we designed the CNN (1D) representation learning module. The convolution kernel is one-dimensional and contains the same number of weights as the number of brain regions, so that the receptive field of the convolution kernel is exactly a row of the functional connection matrix, which can imitate the interaction between the target brain region and all other brain regions in the row. In this way, each convolution operation gathers the information of the neighbor domain of the target brain region, and the convolution results of each brain region are not mixed with each other, which is conducive to the final analysis of important brain regions. The CNN (1D) consists of two convolutional layers and one fully connected layer, as shown in Figure 4.  
The first layer uses the horizontal convolution kernel in the form of 64@1 \(\times\) 200, where 1 \(\times\) 200 represents the shape of the convolution kernel, 200 represents the number of brain regions, and 64 represents the number of channels. Since each row in the matrix represents the correlation between a certain brain region and all other brain regions, the convolution kernel in the form of 1 \(\times\) 200 ensures that each operation is carried out between the target brain region and its adjacent brain regions, and the convolution result can be regarded as a feature of the target brain region. The feature form obtained after the first layer of convolution operation is 64 \(\times\) 200 \(\times\) 1, meaning 64 feature maps extracted from 200 brain regions. The second layer of convolution uses vertical convolution kernel to extract whole brain features from brain region features. The convolution kernel in the form of 128@200 \(\times\) 1200 \(\times\) 1 forms the feature convolution operation of 200 brain regions to form the feature of the whole brain, and the dimension is 128. In this process, the features of brain regions are mapped to the features of the whole brain, and the weight of convolutional nuclei corresponds to the weight of brain regions. Therefore, the absolute values can be used to represent the importance degrees of different brain regions, so as to analyze the interpretability of the model. Finally, the feature is further extracted through a full-connection layer to better complete the classification task. Pooling layer is not used in the model mainly because each convolution is independent of each other based on the unit of brain region, there is no overlap in the receptive field, and the redundancy of extracted features is small. On the contrary, some key features may be lost in the downsampling of the pooling layer.