Graph-to-Signal Transformation Based Classification of Functional Connectivity Brain Networks

Abstract

Complex network theory has been successful at unveiling the topology of the brain and showing alterations to the network structure due to brain disease, cognitive function and behavior. Functional connectivity networks (FCNs) represent different brain regions as the nodes and the connectivity between them as the edges of a graph. Graph theoretic measures provide a way to extract features from these networks enabling subsequent characterization and discrimination of networks across conditions. However, these measures are constrained mostly to binary networks and highly dependent on the network size. In this paper, we propose a novel graph-to-signal transform that overcomes these shortcomings to extract features from functional connectivity networks. The proposed transformation is based on classical multidimensional scaling (CMDS) theory and transforms a graph into signals such that the Euclidean distance between the nodes of the network is preserved. In this paper, we propose to use the resistance distance matrix for transforming weighted functional connectivity networks into signals. Our results illustrate how well-known network structures transform into distinct signals using the proposed graph-to-signal transformation. We then compute well-known signal features on the extracted graph signals to discriminate between FCNs constructed across different experimental conditions. Based on our results, the signals obtained from the graph-to-signal transformation allow for the characterization of functional connectivity networks, and the corresponding features are more discriminative compared to graph theoretic measures. Introduction 1The human brain is a highly interconnected network. While early studies of 2 neurophysiological and neuroimaging data focused on the analysis of isolated regions, i.e. 3 univariate analysis, most of the recent work indicates that the network organization of 4 the brain fundamentally shapes its function [1]. Thus, generating comprehensive maps 5 of brain connectivity, also known as connectomes, and characterizing these networks has 6 become a major goal of neuroscience [2,3]. Complex network theory has contributed 7 significantly to the characterization of the topology of FCNs, in particular in the 8 assessment of functional integration and segregation [4,5]. Specifically, graph theoretic 9 measures such as the path length and clustering coefficient have helped to characterize 10 small-world brain networks [6][7][8], and the degree distribution has been utilized to 11 characterize scale-free networks [9]. Over the last decade, the study of FCNs through 12 complex network theory has provided new means for discriminating between different 13 neural dysfunctions such as epilepsy [10,11], depression [12, 13], Alzheimer's 14 Disease [14, 15], and Parkinson's Disease [16]. 15 Although graph theoretical approaches provide an elegant way to describe the 16 topology of functional brain networks, these measures suffer from several major 17 shortcomings. First, most network measures are optimally suit...