Characterization of Time Evolving Graph Using State-Space Modelling and its Application in Alzheimer's Disease Detection

Methods based on graph theoretical analysis of brain imaging data have been widely applied to detect various brain diseases like Alzheimer's disease (AD), autism spectrum disorder etc. But most of the conventional graph based methods assume the stationarity of the graph signals involved, neglecting the time varying nature of the associated graph connectivity. Recent studies involving the dynamic brain connectivity network revealed the altered brain connectivity dynamics in the disease state, thus making it a potential biomarker for the disease detection. In this paper, we propose a novel approach to characterize the dynamics of the time varying graph using the state-space representation of the graph signal, wherein the dynamic brain connectivity is modelled as a state of the system while the input graph signal serves as an observation. The dynamics of the time varying graph connectivity is then characterized by the state transition matrix which is obtained using the Kalman filtering algorithm. To detect AD using the altered brain connectivity dynamics, the SVM classifier is first trained using the state transition matrices of the training subjects, which is then used to classify a test subject as a normal control or having a mild cognitive impairment, the early stage of AD . The efficacy of the proposed model is verified using the resting state fMRI data from the ADNI dataset, wherein the proposed model outperformed state-of-the-art AD detection methods, possibly due to its ability to effectively characterize the brain connectivity dynamics.