Functional connectivity learning via Siamese-based SPD matrix representation of brain imaging data

Measurement of brain functional connectivity has become a dominant approach to explore the interaction dynamics between brain regions of subjects under examination. Conventional functional connectivity measures largely originate from deterministic models on empirical analysis, usually demanding application-specific settings (e.g., Pearson's Correlation and Mutual Information). To bridge the technical gap, this study proposes a Siamese-based Symmetric Positive Definite (SPD) Matrix Representation framework (SiameseSPD-MR) to derive the functional connectivity of brain imaging data (BID) such as Electroencephalography (EEG), thus the alternative application-independent measure (in the form of SPD matrix) can be automatically learnt: (1) SiameseSPD-MR first exploits graph convolution to extract the representative features of BID with the adjacency matrix computed considering the anatomical structure; (2) Adaptive Gaussian kernel function then applies to obtain the functional connectivity representations from the deep features followed by SPD matrix transformation to address the intrinsic functional characteristics; and (3) Two-branch (Siamese) networks are combined via an element-wise product followed by a dense layer to derive the similarity between the pairwise inputs. Experimental results on two EEG datasets (autism spectrum disorder, emotion) indicate that (1) SiameseSPD-MR can capture more significant differences in functional connectivity between neural states than the state-of-the-art counterparts do, and these findings properly highlight the typical EEG characteristics of ASD subjects, and (2) the obtained functional connectivity representations conforming to the proposed measure can act as meaningful markers for brain network analysis and ASD discrimination.