We propose a framework of Siamese community-preserving graph convolutional network (SCP-GCN) to learn the structural and functional joint embedding of brain networks. Specifically, we use graph convolutions to learn the structural and functional joint embedding, where the graph structure is defined with structural connectivity and node features are from the functional connectivity. Moreover, we propose to preserve the community structure of brain networks in the graph convolutions by considering the intra-community and inter-community properties in the learning process. Furthermore, we use Siamese architecture which models the pair-wise similarity learning to guide the learning process. To evaluate the proposed approach, we conduct extensive experiments on two real brain network datasets. The experimental results demonstrate the superior performance of the proposed approach in structural and functional joint embedding for neurological disorder analysis, indicating its promising value for clinical applications.

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 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.

Multi-view clustering has become a widely studied problem in the area of unsupervised learning. It aims to integrate multiple views by taking advantages of the consensus and complimentary information from multiple views. Most of the existing works in multi-view clustering utilize the vector-based representation for features in each view. However, in many real-world applications, instances are represented by graphs, where those vector-based models cannot fully capture the structure of the graphs from each view. To solve this problem, in this paper we propose a Multi-view Clustering framework on graph instances with Graph Embedding (MCGE). Specifically, we model the multi-view graph data as tensors and apply tensor factorization to learn the multi-view graph embeddings, thereby capturing the local structure of graphs. We build an iterative framework by incorporating multi-view graph embedding into the multi-view clustering task on graph instances, jointly performing multi-view clustering and multi-view graph embedding simultaneously. The multi-view clustering results are used for refining the multi-view graph embedding, and the updated multi-view graph embedding results further improve the multi-view clustering. Extensive experiments on two real brain network datasets (i.e., HIV and Bipolar) demonstrate the superior performance of the proposed MCGE approach in multi-view connectome analysis for clinical investigation and application.

Owing to prominence as a diagnostic tool for probing the neural correlates of cognition, neuroimaging tensor data has been the focus of intense investigation. Although many supervised tensor learning approaches have been proposed, they either cannot capture the nonlinear relationships of tensor data or cannot preserve the complex multi-way structural information. In this paper, we propose a Multi-way Multi-level Kernel (MMK) model that can extract discriminative, nonlinear and structural preserving representations of tensor data. Specifically, we introduce a kernelized CP tensor factorization technique, which is equivalent to performing the low-rank tensor factorization in a possibly much higher dimensional space that is implicitly defined by the kernel function. We further employ a multi-way nonlinear feature mapping to derive the dual structural preserving kernels, which are used in conjunction with kernel machines (e.g., SVM). Extensive experiments on real-world neuroimages demonstrate that the proposed MMK method can effectively boost the classification performance on diverse brain disorders (i.e., Alzheimers disease, ADHD, and HIV).

Multi-view graph embedding and hub detection have both become widely studied problems in the area of graph learning. Both graph embedding and hub detection relate to the node clustering structure of graphs. The multi-view graph embedding usually implies the node clustering structure of the graph based on the multiple views, while hubs are the boundary-spanning nodes across different node clusters in the graph and thus may potentially influence the clustering structure of the graph. However, none of the existing works considered joint learning the multi-view embeddings and the hubs from multi-view graph data. In this paper, we propose to incorporate the hub detection task into the multi-view graph embedding framework so that the two tasks could benefit from each other. Specifically, we propose an auto-weighted framework of Multi-view Graph Embedding with Hub Detection (MVGE-HD) for brain network analysis. The MVGE-HD framework learns a unified graph embedding across all the views while reducing the potential influence of the hubs on blurring the boundaries between node clusters in the graph, thus leading to a clear and discriminative node clustering structure for the graph. We apply MVGE-HD on two real multi-view brain network datasets (i.e., HIV and Bipolar). The experimental results demonstrate the superior performance of the proposed framework in brain network analysis for clinical investigation and application.

In the context of supervised tensor learning, preserving the structural information and exploiting the discriminative nonlinear relationships of tensor data are crucial for improving the performance of learning tasks. Based on tensor factorization theory and kernel methods, we propose a novel Kernelized Support Tensor Machine (KSTM) which integrates kernelized tensor factorization with maximum-margin criterion. Specifically, the kernelized factorization technique is introduced to approximate the tensor data in kernel space such that the complex nonlinear relationships within tensor data can be explored. Further, dual structural preserving kernels are devised to learn the nonlinear boundary between tensor data. As a result of joint optimization, the kernels obtained in KSTM exhibit better generalization power to discriminative analysis. The experimental results on real-world neuroimaging datasets show the superiority of KSTM over the state-of-the-art techniques.

Mining from neuroimaging data is becoming increasingly popular in the field of healthcare and bioinformatics, due to its potential to discover clinically meaningful structure patterns that could facilitate the understanding and diagnosis of neurological and neuropsychiatric disorders. Most recent research concentrates on applying subgraph mining techniques to discover connected subgraph patterns in the brain network. However, the underlying brain network structure is complicated. As a shallow linear model, subgraph mining cannot capture the highly non-linear structures, resulting in sub-optimal patterns. Therefore, how to learn representations that can capture the highly non-linearity of brain networks and preserve the underlying structures is a critical problem.

The analysis of brain imaging data has attracted much attention recently. A popular analysis is to discover a network representation of brain from the neuroimaging data, where each node denotes a brain region and each edge represents a functional association or structural connection between two brain regions. Motivated by the multi-subject and multi-collection settings in neuroimaging studies, in this paper, we consider brain network discovery under two novel settings: 1) unified setting: Given a collection of subjects, discover a single network that is good for all subjects. 2) contrasting setting: Given two collections of subjects, discover a single network that best discriminates two collections. We show that the existing formulation of graphical Lasso (GLasso) cannot address above problems properly. Two novel models, UGLasso (Unified Graphical Lasso) and CGLasso(Contrasting Graphical Lasso), are proposed to address these two problems respectively. We evaluate our methods on synthetic data and two real-world functional magnetic resonance imaging (fMRI) datasets. Empirical results demonstrate the effectiveness of the proposed methods.

Owing to prominence as a research and diagnostic tool in human brain mapping, whole-brain fMRI image analysis has been the focus of intense investigation. Conventionally, input fMRI brain images are converted into vectors or matrices and adapted in kernel based classifiers. fMRI data, however, are inherently coupled with sophisticated spatio-temporal tensor structure (i.e., 3D space × time). Valuable structural information will be lost if the tensors are converted into vectors. Furthermore, time series fMRI data are noisy, involving time shift and low temporal resolution. To address these analytic challenges, more compact and discriminative representations for kernel modeling are needed. In this paper, we propose a novel spatio-temporal tensor kernel (STTK) approach for whole-brain fMRI image analysis. Specifically, we design a volumetric time series extraction approach to model the temporal data, and propose a spatio-temporal tensor based factorization for feature extraction. We further leverage the tensor structure to encode prior knowledge in the kernel. Extensive experiments using real-world datasets demonstrate that our proposed approach effectively boosts the fMRI classification performance in diverse brain disorders (i.e., Alzheimer's disease, ADHD and HIV).

There is considerable interest in mining neuroimage data to discover clinically meaningful connectivity patterns to inform an understanding of neurological and neuropsychiatric disorders. Subgraph mining models have been used to discover connected subgraph patterns. However, it is difficult to capture the complicated interplay among patterns. As a result, classification performance based on these results may not be satisfactory. To address this issue, we propose to learn non-linear representations of brain connectivity patterns from deep learning architectures. This is non-trivial, due to the limited subjects and the high costs of acquiring the data. Fortunately, auxiliary information from multiple side views such as clinical, serologic, immunologic, cognitive and other diagnostic testing also characterizes the states of subjects from different perspectives. In this paper, we present a novel Multi-side-View guided AutoEncoder (MVAE) that incorporates multiple side views into the process of deep learning to tackle the bias in the construction of connectivity patterns caused by the scarce clinical data. Extensive experiments show that MVAE not only captures discriminative connectivity patterns for classification, but also discovers meaningful information for clinical interpretation.

Mining discriminative subgraph patterns from graph data has attracted great interest in recent years. It has a wide variety of applications in disease diagnosis, neuroimaging, etc. Most research on subgraph mining focuses on the graph representation alone. However, in many real-world applications, the side information is available along with the graph data. For example, for neurological disorder identification, in addition to the brain networks derived from neuroimaging data, hundreds of clinical, immunologic, serologic and cognitive measures may also be documented for each subject. These measures compose multiple side views encoding a tremendous amount of supplemental information for diagnostic purposes, yet are often ignored. In this paper, we study the problem of discriminative subgraph selection using multiple side views and propose a novel solution to find an optimal set of subgraph features for graph classification by exploring a plurality of side views. We derive a feature evaluation criterion, named gSide, to estimate the usefulness of subgraph patterns based upon side views. Then we develop a branch-and-bound algorithm, called gMSV, to efficiently search for optimal subgraph features by integrating the subgraph mining process and the procedure of discriminative feature selection. Empirical studies on graph classification tasks for neurological disorders using brain networks demonstrate that subgraph patterns selected by the multi-side-view guided subgraph selection approach can effectively boost graph classification performances and are relevant to disease diagnosis.

In the era of big data, we can easily access information from multiple views which may be obtained from different sources or feature subsets. Generally, different views provide complementary information for learning tasks. Thus, multi-view learning can facilitate the learning process and is prevalent in a wide range of application domains. For example, in medical science, measurements from a series of medical examinations are documented for each subject, including clinical, imaging, immunologic, serologic and cognitive measures which are obtained from multiple sources. Specifically, for brain diagnosis, we can have different quantitative analysis which can be seen as different feature subsets of a subject. It is desirable to combine all these features in an effective way for disease diagnosis. However, some measurements from less relevant medical examinations can introduce irrelevant information which can even be exaggerated after view combinations. Feature selection should therefore be incorporated in the process of multi-view learning. In this paper, we explore tensor product to bring different views together in a joint space, and present a dual method of tensor-based multi-view feature selection (dual-Tmfs) based on the idea of support vector machine recursive feature elimination. Experiments conducted on datasets derived from neurological disorder demonstrate the features selected by our proposed method yield better classification performance and are relevant to disease diagnosis.

With advances in data collection technologies, tensor data is assuming increasing prominence in many applications and the problem of supervised tensor learning has emerged as a topic of critical significance in the data mining and machine learning community. Conventional methods for supervised tensor learning mainly focus on learning kernels by flattening the tensor into vectors or matrices, however structural information within the tensors will be lost. In this paper, we introduce a new scheme to design structure-preserving kernels for supervised tensor learning. Specifically, we demonstrate how to leverage the naturally available structure within the tensorial representation to encode prior knowledge in the kernel. We proposed a tensor kernel that can preserve tensor structures based upon dual-tensorial mapping. The dual-tensorial mapping function can map each tensor instance in the input space to another tensor in the feature space while preserving the tensorial structure. Theoretically, our approach is an extension of the conventional kernels in the vector space to tensor space. We applied our novel kernel in conjunction with SVM to real-world tensor classification problems including brain fMRI classification for three different diseases (i.e., Alzheimer's disease, ADHD and brain damage by HIV). Extensive empirical studies demonstrate that our proposed approach can effectively boost tensor classification performances, particularly with small sample sizes.

Mining discriminative features for graph data has attracted much attention in recent years due to its important role in constructing graph classifiers, generating graph indices, etc. Most measurement of interestingness of discriminative subgraph features are defined on certain graphs, where the structure of graph objects are certain, and the binary edges within each graph represent the “presence” of linkages among the nodes. In many real-world applications, however, the linkage structure of the graphs is inherently uncertain. Therefore, existing measurements of interestingness based upon certain graphs are unable to capture the structural uncertainty in these applications effectively. In this paper, we study the problem of discriminative subgraph feature selection from uncertain graphs. This problem is challenging and different from conventional subgraph mining problems because both the structure of the graph objects and the discrimination score of each subgraph feature are uncertain. To address these challenges, we propose a novel discriminative subgraph feature selection method, DUG, which can find discriminative subgraph features in uncertain graphs based upon different statistical measures including expectation, median, mode and φ-probability. We first compute the probability distribution of the discrimination scores for each subgraph feature based on dynamic programming. Then a branch-and-bound algorithm is proposed to search for discriminative subgraphs efficiently. Extensive experiments on various neuroimaging applications (i.e., Alzheimers Disease, ADHD and HIV) have been performed to analyze the gain in performance by taking into account structural uncertainties in identifying discriminative subgraph features for graph classification.