# Uniform Pooling for Graph Networks
## 4 Experiments
### Graph Classification on Brain Connectivity  
fMRI-based functional connectivity is an effective measure of brain function, which reflects the correlation of brain signals between brain regions [41]. Functional connectivity are often used as features for gender classification or diagnostic classification of brain disorders [42; 43; 44; 45]. However, in previous studies, the functional connectivity matrix was simply arranged as a vector ignoring the spatial information between brain regions. In fact, the brain regions were selected on the irregular brain cortex and the topological relationship between the brain regions is on non-Euclidean domains, which can be described by a graph structure. Therefore, in this experiment, we will perform pattern analysis on brain connectivity from a new perspective, i.e., GCN model with the global pooling architecture of UGPool. We selected two widely used publicly available fMRI datasets including Human Connectome Project (HCP) [46] and Autism Brain Imaging Data Exchange (ABIDE) [47] for gender classification and autism classification, respectively. HCP data consists of resting-state fMRI brain images from 500 males (1944 images) and 596 females (2289 images). ABIDE data consist of resting-state fMRI brain images from 1003 patients (1199 images) and 1166 healthy controls (1415 images). Please note that some subjects have multiple scans images. To increase the samples as much as possible, we used all the images for training and testing the models, and divided the training set and test set based on subjects rather than images to prevent the problem of peeking at samples. As shown in the illustration of the experiment in Figure 3, the steps for processing the fMRI data include data preprocessing, selecting the brain region template, extracting the time series of brain regions, calculating the functional connectivity graph, and classifying connectivity graphs using GCN with global UGPool architecture. The data preprocessing pipeline was the same as we did in our previous works [43; 48]. We used 808 ROIs as the brain template which was generated via spatially constrained spectral clustering [49]. [PERSON]'s correlation coefficients between pairs of ROI-based time series were calculated, resulting in an \(808\times 808\) symmetric connectivity matrix for each subject. We used a k-nn graph \(\mathcal{G}=(\
u,\varepsilon)\) to describe the brain connectivity graph, where its node \(v_{i}\in\
u\) represents a brain ROI, and functional connectivity of all the ROIs serve as node signals \(c_{s}i:v_{i}\)\(\rightarrow\)\(R^{N},s=1,\ldots,N.\) and the graph edge \(e_{i}\in\varepsilon\) represents the correlation distance between corresponding node signals. We calculated the average functional connectivity of training data to estimate the average adjacency matrix of the connectivity graph, which will be commonly applied to the GCN model for each subject. Please note that using the functional metric to represent the graph edges may capture more accurate brain functional architecture rather than using structural or spatial metrics [50]. Based on the connectivity graphs, we performed a GCN model with global UGPool architecture for gender classification and autism classification tasks, respectively. To make a comparison, we also evaluated the classification via the GCN model without the pooling method.