Network analysis of human brain connectivity is critically important for understanding brain function and disease states. Embedding a brain network as a whole graph instance into a meaningful low-dimensional representation can be used to investigate disease mechanisms and inform therapeutic interventions. Moreover, by exploiting information from multiple neuroimaging modalities or views, we are able to obtain an embedding that is more useful than the embedding learned from an individual view. Therefore, multi-view multi-graph embedding becomes a crucial task. Currently, only a few studies have been devoted to this topic, and most of them focus on the vector-based strategy which will cause structural information contained in the original graphs lost. As a novel attempt to tackle this problem, we propose Multi-view Multi-graph Embedding (M2E) by stacking multi-graphs into multiple partially-symmetric tensors and using tensor techniques to simultaneously leverage the dependencies and correlations among multi-view and multi-graph brain networks. Extensive experiments on real HIV and bipolar disorder brain network datasets demonstrate the superior performance of M2E on clustering brain networks by leveraging the multi-view multi-graph interactions.
Brain Network Embedding makes characterization of brain disorders at a whole-brain connectivity level possible, thus providing a new direction for brain disease clustering. The goal of graph embedding is to find low-dimensional representations of nodes that can preserve the important structure and properties of graphs @cite_7 . In particular, @cite_1 proposed a graph embedding algorithm based on Laplacian-type operator on manifold, which can apply to recover the geometry of data and extend a function on new data points. Recently, @cite_21 established a general formulation of high-order proximity measurements, and then applied it with generalized SVD for graph embedding. In the field of brain network neuroscience, most of the existing works aim to learn the structure from a specific kind of brain networks @cite_0 @cite_11 . In contrast to the node embedding on single graph, we aim at learning an effective graph embedding approach on multi-view multi-graph brain networks, such as fMRI brain network together with DTI brain network.
@cite_7 @cite_21 @cite_1 @cite_0 @cite_11
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Learning from graph data has been attracting much attention recently due to its importance in many scientific applications, where objects are represented as graphs. In this paper, we study the problem of multi-graph clustering i.e., clustering multiple graphs. We propose a multi-graph clustering approach MGCT based on the interior-node topology of graphs. Specifically, we extract the interior-node topological structure of each graph through a sparsity-inducing interior-node clustering. We merge the interior-node clustering stage and the multi-graph clustering stage into a unified iterative framework, where the multi-graph clustering will influence the interior-node clustering and the updated interior-node clustering results will be further exerted on multi-graph clustering. We apply MGCT on two real brain network data sets i.e., ADHD and HIV. Experimental results demonstrate the superior performance of the proposed model on multi-graph clustering. Graph embedding algorithms embed a graph into a vector space where the structure and the inherent properties of the graph are preserved. The existing graph embedding methods cannot preserve the asymmetric transitivity well, which is a critical property of directed graphs. Asymmetric transitivity depicts the correlation among directed edges, that is, if there is a directed path from u to v, then there is likely a directed edge from u to v. Asymmetric transitivity can help in capturing structures of graphs and recovering from partially observed graphs. To tackle this challenge, we propose the idea of preserving asymmetric transitivity by approximating high-order proximity which are based on asymmetric transitivity. In particular, we develop a novel graph embedding algorithm, High-Order Proximity preserved Embedding (HOPE for short), which is scalable to preserve high-order proximities of large scale graphs and capable of capturing the asymmetric transitivity. More specifically, we first derive a general formulation that cover multiple popular high-order proximity measurements, then propose a scalable embedding algorithm to approximate the high-order proximity measurements based on their general formulation. Moreover, we provide a theoretical upper bound on the RMSE (Root Mean Squared Error) of the approximation. Our empirical experiments on a synthetic dataset and three real-world datasets demonstrate that HOPE can approximate the high-order proximities significantly better than the state-of-art algorithms and outperform the state-of-art algorithms in tasks of reconstruction, link prediction and vertex recommendation. In this paper, we propose a novel technique for finding the graph embedding and function extension for directed graphs. We assume that the data points are sampled from a manifold and the similarity between the points is given by an asymmetric kernel. We provide a graph embedding algorithm which is motivated by Laplacian type operator on manifold. We also introduce a Nystrom type eigenfunctions extension which is used both for extending the embedding to new data points and to extend an empirical function on new data set. For extending the eigenfunctions to new points, we assume that only the distances of the new points from the labelled data are given. Simulation results demonstrate the performance of the proposed method in recovering the geometry of data and extending a function on new data points. HighlightsA novel technique for finding the graph embedding and function extension for directed graphs is proposed.The data points are assumed to be sampled from a manifold and the similarity between the points is given by an asymmetric kernel.A graph embedding algorithm motivated by Laplacian type operator on manifold is proposed.A Nystrom type eigenfunctions extension for extending the embedding an empirical function on new data set is proposed.In extension phase, we assume that only the distances of the new points to the labelled data are given. Following the recent advances in neuroimaging technology, the research on brain network analysis becomes an emerging area in data mining community. Brain network data pose many unique challenges for data mining research. For example, in brain networks, the nodes (i.e., the brain regions) and edges (i.e., relationships between brain regions) are usually not given, but should be derived from the neuroimaging data. The network structure can be very noisy and uncertain. Therefore, innovative methods are required for brain network analysis. Many research efforts have been devoted to this area. They have achieved great success in various applications, such as brain network extraction, graph mining, neuroimaging data analysis. In this paper, we review some recent data mining methods which are used in the literature for mining brain network data. The analysis of data represented as graphs is common having wide scale applications from social networks to medical imaging. A popular analysis is to cut the graph so that the disjoint subgraphs can represent communities (for social network) or background and foreground cognitive activity (for medical imaging). An emerging setting is when multiple data sets (graphs) exist which opens up the opportunity for many new questions. In this paper we study two such questions: i) For a collection of graphs find a single cut that is good for all the graphs and ii) For two collections of graphs find a single cut that is good for one collection but poor for the other. We show that existing formulations of multiview, consensus and alternative clustering cannot address these questions and instead we provide novel formulations in the spectral clustering framework. We evaluate our approaches on functional magnetic resonance imaging (fMRI) data to address questions such as: "What common cognitive network does this group of individuals have?" and "What are the differences in the cognitive networks for these two groups?" We obtain useful results without the need for strong domain knowledge.