Examination of the predictive value of structural magnetic resonance scans in bipolar disorder:a pattern classification approach

Background - Bipolar disorder (BD) is one of the leading causes of disability worldwide. Patients are further disadvantaged by delays in accurate diagnosis ranging between 5 and 10 years. We applied Gaussian process classifiers (GPCs) to structural magnetic resonance imaging (sMRI) data to evaluate the feasibility of using pattern recognition techniques for the diagnostic classification of patients with BD. Method - GPCs were applied to gray (GM) and white matter (WM) sMRI data derived from two independent samples of patients with BD (cohort 1: n = 26; cohort 2: n = 14). Within each cohort patients were matched on age, sex and IQ to an equal number of healthy controls. Results - The diagnostic accuracy of the GPC for GM was 73% in cohort 1 and 72% in cohort 2; the sensitivity and specificity of the GM classification were respectively 69% and 77% in cohort 1 and 64% and 99% in cohort 2. The diagnostic accuracy of the GPC for WM was 69% in cohort 1 and 78% in cohort 2; the sensitivity and specificity of the WM classification were both 69% in cohort 1 and 71% and 86% respectively in cohort 2. In both samples, GM and WM clusters discriminating between patients and controls were localized within cortical and subcortical structures implicated in BD. Conclusions - Our results demonstrate the predictive value of neuroanatomical data in discriminating patients with BD from healthy individuals. The overlap between discriminative networks and regions implicated in the pathophysiology of BD supports the biological plausibility of the classifiers.

Edge centrality via the Holevo quantity

In the study of complex networks, vertex centrality measures are used to identify the most important vertices within a graph. A related problem is that of measuring the centrality of an edge. In this paper, we propose a novel edge centrality index rooted in quantum information. More specifically, we measure the importance of an edge in terms of the contribution that it gives to the Von Neumann entropy of the graph. We show that this can be computed in terms of the Holevo quantity, a well known quantum information theoretical measure. While computing the Von Neumann entropy and hence the Holevo quantity requires computing the spectrum of the graph Laplacian, we show how to obtain a simplified measure through a quadratic approximation of the Shannon entropy. This in turns shows that the proposed centrality measure is strongly correlated with the negative degree centrality on the line graph. We evaluate our centrality measure through an extensive set of experiments on real-world as well as synthetic networks, and we compare it against commonly used alternative measures.

The average mixing matrix signature

Laplacian-based descriptors, such as the Heat Kernel Signature and the Wave Kernel Signature, allow one to embed the vertices of a graph onto a vectorial space, and have been successfully used to find the optimal matching between a pair of input graphs. While the HKS uses a heat di↵usion process to probe the local structure of a graph, the WKS attempts to do the same through wave propagation. In this paper, we propose an alternative structural descriptor that is based on continuoustime quantum walks. More specifically, we characterise the structure of a graph using its average mixing matrix. The average mixing matrix is a doubly-stochastic matrix that encodes the time-averaged behaviour of a continuous-time quantum walk on the graph. We propose to use the rows of the average mixing matrix for increasing stopping times to develop a novel signature, the Average Mixing Matrix Signature (AMMS). We perform an extensive range of experiments and we show that the proposed signature is robust under structural perturbations of the original graphs and it outperforms both the HKS and WKS when used as a node descriptor in a graph matching task.