Estimating Functional Connectivity Networks via Low-Rank Tensor Approximation with Applications to MCI Identification

Functional connectivity network (FCN) has become an increasingly important approach to gain a better understanding of the brain, as well as discover informative biomarkers for diagnosis of neurodegenerative diseases. Due to its importance, many FCN estimation methods have been developed in the past decades, including methods based on the classical Pearson's correlation, (regularized) partial correlation, and some higher-order variants. However, most of the existing methods estimate one FCN at a time, thus ignoring the possibly shared structure among FCNs from different subjects. Recently, researchers introduce group constraints (or population priors) into FCN estimation by assuming that FCNs are topologically identical across subjects. Obviously, such a constraint/prior is too strong to be satisfied in practice, especially when both patients and healthy subjects are involved simultaneously in the group. To address this problem, we propose a novel FCN estimation approach based on an assumption that the involved FCNs have similar but not necessarily identical topology. More specifically, we implement this idea under a two-step learning framework. First, we independently estimate FCNs based on traditional methods, such as Pearson's correltion and sparse representation, making sure that each FCN captures the specific properties of the corresponding subject. Then, we stack the estimated FCNs (in fact, their adjacency matrices) into a tensor, and refine the stacked FCNs via low-rank tensor approximation. Finally, we apply the improved FCNs to identify subjects with mild cognitive impairment (MCI) from healthy controls, and achieve a higher classification accuracy.