INTRODUCTION

There has been success with deep learning in fMRI analysis, where fMRI data are considered on structured grids and spatial features within Euclidean neighbors are extracted through convolutional neural networks (CNNs). Meanwhile, graphs, as a ubiquitous data structure in many applications, have been widely applied for ROI-based fMRI data analysis, in which functional connectivity (FC) between all pairs of regions is thoroughly considered. Inspired by the remarkable performance of recently introduced CNNs on graph data, we define graphs based on FC and introduce a connectivity-based graph convolution network (cGCN) architecture for fMRI data analysis. This architecture allows us to extract spatial features within connectivity-based neighborhood from each frame and capture the temporal dynamics of fMRI data.

METHODS

We considered fMRI data analysis as a spatiotemporal feature extraction task, where spatial patterns were extracted from each frame, and temporal evolution was obtained between frames based on existing spatial features. For each frame of fMRI data, ROI-based fMRI data were represented in the form of graphs, in which ROIs acted as nodes with intensity values and the edge weight between any two ROIs was given by their Pearson’s correlation coefficient. In order to reduce the computational complexity, a k-nearest neighbor (k-NN) graph was defined by taking the top-k neighbors for each node with the highest correlation. In this way, the community information was also reserved in the k-NN graph. Different values (3, 5, 10 and 20) of k, the only hyperparameter related to the graph structure and similar to the size of the convolution kernel, were tested in our study. Stacking convolutional layers generated spatial features with the shared k-NN graph, and latent representations were obtained by a recurrent neural network (RNN) and followed by a softmax layer for classification. The architecture of cGCN is shown in Fig.1.

We trained and tested our cGCN architecture to realize individual identification on 100 subjects with resting-state fMRI data from the Human Connectome Project (54 females, mean age = 29.1 ± 3.7, TR = 0.72 s)¹. Two scans on the 1^st day were used for training and other two scans on the 2^nd day were used for validation and testing. Each scan has 1200 frames in total. During training and validation, input data were divided into 100-frame segments. The final identification accuracy was reported as the average performance on the testing dataset with different number of frames as inputs. In order to validate the contribution of connectivity-based neighborhood for convolutions, we compared the cGCN performance with the FC-based k-NN graph and a random graph.

RESULTS

In Fig.2, we show the individual identification performance on the testing dataset with different number of frames (from 1200 frames to a single frame) as input data. In general, cGCN achieved better performance with increasing number of frames and its performance leveled off with over 100 frames. In terms of the k value, cGCN achieved highest identification accuracy on average when k=10, compared with other k values (3, 5, and 20). Compared to the traditional CNN model², cGCN showed substantial performance improvement with fewer than 100 frames. For cGCN models with the random k-NN graph, the classification accuracy was always lower than cGCNs, however, they still outperformed the conventional CNN significantly, especially when k=3 and 5.

DISCUSSION

fMRI data can be represented on graphs with top connectivity-based neighborhood being directly connected. Instead of considering fMRI data as grid data and performing convolutions within neighbors on the grid in Euclidean space, we conducted convolutions within top connectomic neighbors for spatial features. In such a way, the spatial pattern related to FC can be extracted by stacking convolutional layers within multi-hop neighborhood for the enlarged receptive field. Our cGCN achieved better individual identification than traditional CNNs, which performed convolution on the list of ROIs without considering appropriate neighborhood. Our results also demonstrated that cGCN model with k=10 achieved the highest identification accuracy. One possible reason is that increasing the number of convolutional neighbors can utilize more connectomic neighbors for complex feature extraction. However, convolutions on too many nodes could fail to generate local generalizable features. For this application, the k value of 10 is a good compromise between these opposing factors, although the optimal value of k will depend on the application.

CONCLUSION

We introduced a graph convolutional neural network with neighborhood defined based on FC, cGCN, for resting-state fMRI data analysis. Our cGCN was evaluated on HCP data with varying number of neighborhoods. The experimental results indicate that 1) the new architecture outperforms existing approaches and 2) a neighborhood size of 10 is optimal for individual identification. The new approach provides a robust alternative for analyzing resting-state fMRI data.

Acknowledgements

Thanks to Alexandra Reardon for proofreading.