Metrics for Graph Comparison: A Practitioner's Guide

Comparison of graph structure is a ubiquitous task in data analysis and machine learning, with diverse applications in fields such as neuroscience, cyber security, social network analysis, and bioinformatics, among others. Discovery and comparison of structures such as modular communities, rich clubs, hubs, and trees in data in these fields yields insight into the generative mechanisms and functional properties of the graph. Often, two graphs are compared via a pairwise distance measure, with a small distance indicating structural similarity and vice versa. Common choices include spectral distances (also known as $\lambda$ distances) and distances based on node affinities. However, there has of yet been no comparative study of the efficacy of these distance measures in discerning between common graph topologies and different structural scales. In this work, we compare commonly used graph metrics and distance measures, and demonstrate their ability to discern between common topological features found in both random graph models and empirical datasets. We put forward a multi-scale picture of graph structure, in which the effect of global and local structure upon the distance measures is considered. We make recommendations on the applicability of different distance measures to empirical graph data problem based on this multi-scale view. Finally, we introduce the Python library NetComp which implements the graph distances used in this work

Graph analysis of functional brain networks: practical issues in translational neuroscience

The brain can be regarded as a network: a connected system where nodes, or units, represent different specialized regions and links, or connections, represent communication pathways. From a functional perspective communication is coded by temporal dependence between the activities of different brain areas. In the last decade, the abstract representation of the brain as a graph has allowed to visualize functional brain networks and describe their non-trivial topological properties in a compact and objective way. Nowadays, the use of graph analysis in translational neuroscience has become essential to quantify brain dysfunctions in terms of aberrant reconfiguration of functional brain networks. Despite its evident impact, graph analysis of functional brain networks is not a simple toolbox that can be blindly applied to brain signals. On the one hand, it requires a know-how of all the methodological steps of the processing pipeline that manipulates the input brain signals and extract the functional network properties. On the other hand, a knowledge of the neural phenomenon under study is required to perform physiological-relevant analysis. The aim of this review is to provide practical indications to make sense of brain network analysis and contrast counterproductive attitudes

Estimation of gender-specific connectional brain templates using joint multi-view cortical morphological network integration

The estimation of a connectional brain template (CBT) integrating a population of brain networks while capturing shared and differential connectional patterns across individuals remains unexplored in gender fingerprinting. This paper presents the first study to estimate gender-specific CBTs using multi-view cortical morphological networks (CMNs) estimated from conventional T1-weighted magnetic resonance imaging (MRI). Specifically, each CMN view is derived from a specific cortical attribute (e.g. thickness), encoded in a network quantifying the dissimilarity in morphology between pairs of cortical brain regions. To this aim, we propose Multi-View Clustering and Fusion Network (MVCF-Net), a novel multi-view network fusion method, which can jointly identify consistent and differential clusters of multi-view datasets in order to capture simultaneously similar and distinct connectional traits of samples. Our MVCF-Net method estimates a representative and well-centered CBTs for male and female populations, independently, to eventually identify their fingerprinting regions of interest (ROIs) in four main steps. First, we perform multi-view network clustering model based on manifold optimization which groups CMNs into shared and differential clusters while preserving their alignment across views. Second, for each view, we linearly fuse CMNs belonging to each cluster, producing local CBTs. Third, for each cluster, we non-linearly integrate the local CBTs across views, producing a cluster-specific CBT. Finally, by linearly fusing the cluster-specific centers we estimate a final CBT of the input population. MVCF-Net produced the most centered and representative CBTs for male and female populations and identified the most discriminative ROIs marking gender differences. The most two gender-discriminative ROIs involved the lateral occipital cortex and pars opercularis in the left hemisphere and the middle temporal gyrus and lingual gyrus in the right hemisphere.</p

Hyper-connectivity of functional networks for brain disease diagnosis

Exploring structural and functional interactions among various brain regions enables better understanding of pathological underpinnings of neurological disorders. Brain connectivity network, as a simplified representation of those structural and functional interactions, has been widely used for diagnosis and classification of neurodegenerative diseases, especially for Alzheimer’s disease (AD) and its early stage - mild cognitive impairment (MCI). However, the conventional functional connectivity network is usually constructed based on the pairwise correlation among different brain regions and thus ignores their higher-order relationships. Such loss of high-order information could be important for disease diagnosis, since neurologically a brain region predominantly interacts with more than one other brain regions. Accordingly, in this paper, we propose a novel framework for estimating the hyper-connectivity network of brain functions and then use this hyper-network for brain disease diagnosis. Here, the functional connectivity hyper-network denotes a network where each of its edges representing the interactions among multiple brain regions (i.e., an edge can connect with more than two brain regions), which can be naturally represented by a hyper-graph. Specifically, we first construct connectivity hyper-networks from the resting-state fMRI (R-fMRI) time series by using sparse representation. Then, we extract three sets of brain-region specific features from the connectivity hyper-networks, and further exploit a manifold regularized multi-task feature selection method to jointly select the most discriminative features. Finally, we use multi-kernel support vector machine (SVM) for classification. The experimental results on both MCI dataset and attention deficit hyperactivity disorder (ADHD) dataset demonstrate that, compared with the conventional connectivity network-based methods, the proposed method can not only improve the classification performance, but also help discover disease-related biomarkers important for disease diagnosis

Latent Factor Analysis of High-Dimensional Brain Imaging Data

Recent advances in neuroimaging study, especially functional magnetic resonance imaging (fMRI), has become an important tool in understanding the human brain. Human cognitive functions can be mapped with the brain functional organization through the high-resolution fMRI scans. However, the high-dimensional data with the increasing number of scanning tasks and subjects pose a challenge to existing methods that wasn’t optimized for high-dimensional imaging data. In this thesis, I develop advanced data-driven methods to help utilize more available sources of information in order to reveal more robust brain-behavior relationship. In the first chapter, I provide an overview of the current related research in fMRI and my contributions to the field. In the second chapter, I propose two extensions to the connectome-based predictive modeling (CPM) method that is able to combine multiple connectomes when building predictive models. The two extensions are both able to generate higher prediction accuracy than using the single connectome or the average of multiple connectomes, suggesting the advantage of incorporating multiple sources of information in predictive modeling. In the third chapter, I improve CPM from the target behavioral measure’s perspective. I propose another two extensions for CPM that are able to combine multiple available behavioral measures into a composite measure for CPM to predict. The derived composite measures are shown to be predicted more accurately than any other single behavioral measure, suggesting a more robust brainbehavior relationship. In the fourth chapter, I propose a nonlinear dimensionality reduction framework to embed fMRI data from multiple tasks into a low-dimensional space. This framework helps reveal the common brain state in the multiple available tasks while also help discover the differences among these tasks. The results also provide valuable insights into the various prediction performance based on connectomes from different tasks. In the fifth chapter, I propose an another hyerbolic geometry-based brain graph edge embedding framework. The framework is based on Poincar´e embedding and is able to more accurately represent edges in the brain graph in a low-dimensional space than traditional Euclidean geometry-based embedding. Utilizing the embedding, we are able to cluster edges of the brain graph into disjoint clusters. The edge clusters can then be used to define overlapping brain networks and the derived metrics like network overlapping number can be used to investigate functional flexibility of each brain region. Overall, these work provide rich data-driven methods that help understand the brain-behavioral relationship through predictive modeling and low-dimensional data representation

Deep Learning Architectures for Novel Problems

With convolutional neural networks revolutionizing the computer vision field it is important to extend the capabilities of neural-based systems to dynamic and unrestricted data like graphs. Doing so not only expands the applications of such systems, but also provide more insight into improvements to neural-based systems. Currently most implementations of graph neural networks are based on vertex filtering on fixed adjacency matrices. Although important for a lot of applications, vertex filtering restricts the applications to vertex focused graphs and cannot be efficiently extended to edge focused graphs like social networks. Applications of current systems are mostly limited to images and document references. Beyond the graph applications, this work also explored the usage of convolutional neural networks for intelligent character recognition in a novel way. Most systems define Intelligent Character Recognition as either a recurrent classification problem or image classification. This achieves great performance in a limited environment but does not generalize well on real world applications. This work defines intelligent Character Recognition as a segmentation problem which we show to provide many benefits. The goal of this work was to explore alternatives to current graph neural networks implementations as well as exploring new applications of such system. This work also focused on improving Intelligent Character Recognition techniques on isolated words using deep learning techniques. Due to the contrast between these to contributions this documents was divided into Part I focusing on the graph work, and Part II focusing on the intelligent character recognition work