Estimating High-order Functional Networks With Applications To The Early Diagnosis Of Brain Disorders

Brain functional connectivity network(FCN) has been becoming an increasingly useful tool for understanding the cerebral working mechanism and mining sensitive biomarkers for neural/mental disease diagnosis.However,the extreme complexity of brain makes it a great challenge to estimate an ideal FCN.FCN is usually based on resting state functional magnetic resonance imaging technique,where the nodes correspond to regions-of-interest(ROIs) and the edges correspond to the statistical dependency between these ROIs.Currently,researchers have proposed many FCN modeling methods,including Pearson correlation,partial correlation and regularized partial correlation,to name a few.Though these methods are well applied in practice,they mainly capture the second-order statistical information by calculating the low-order correlations between the brain regions.Meanwhile,the recently proposed high-order FCN methods are mostly constructed intuitively and heuristically without support of any theoretical basis.As such,we focus on the estimation methods of high-order FCN and the research achievements are listed as follows:1.Based on the matrix variate normal distribution(MVND),we put forward a novel high-order FCN estimation method that can achieve both low-and high-order networks simultaneously and provide a clear theoretical explanation.In particular,a sliding window approach is first used to generate a sequence of overlapping time subseries.For each subseries,the traditional low-order FCN is constructed by Pearson correlation.Then,the so-constructed FCN are used as samples to estimate the final low-and high-order FCNs by maximizing the likelihood estimation(MLE) function of MVND.The experimental results of mild cognitive impairment(MCI) classification task have verified the effectiveness of the proposed methods.2.Based on a regularized learning framework,we propose to improve the MLE-based high-order FCN,since it may contain noisy connections.In order to improve the sparsity of MLE-based high-order FCN,an optimal neighborhood network of initially estimated network is learnt to meet the sparsity and modularity regularizers,respectively.We evaluate the proposed methods with applications to MCI and autism spectrum disorder(ASD) identification tasks,and the results show that the improved high-order FCN with modularity prior performs best.3.We propose a new high-order FCN in Bayesian framework.We first reformulate Pearson correlation in Bayesian view with a normal distribution prior,and then,following this framework,we reformulate correlation's correlation with a prior that FCN follows the MVND.Based on this model,we have a clear probabilistic explanation for high-order FCN,and develop a new method that can automatically learn low-and high-order FCNs from data.The proposed methods are used to classify ASDs from normal controls,and they perform better than baseline methods.