Multi-graph Embedding Research Articles

MSMGE-CNN: A multi-scale multi-graph embedding convolutional neural network for motor related EEG decoding

Abstract Deep learning (DL) technique has been widely used for decoding motor related electroencephalography (EEG) signals, which has considerably driven the development of motor related brain-computer interfaces (BCIs). However, traditional convolutional neural networks (CNNs) cannot fully represent spatial topology information and dynamic temporal characteristics of multi-channel EEG signals, resulting in limited decoding accuracy. To address such challenges, a novel multi-scale multi-graph embedding convolutional neural network (MSMGE-CNN) is proposed in this study. The proposed MSMGE-CNN contains two crucial components: multi-scale time convolution and multi-graph embedding. Specifically, we design a multi-branch CNN architecture with mixed-scale time convolutions based on EEGNet to sufficiently extract robust time domain features. Afterward, we embed multi-graph information obtained based on physical distance proximity and functional connectivity of multi-channel EEG signals into the time-domain features to capture rich spatial topological dependencies via multi-graph convolution operation. We extensively evaluated the proposed method on three benchmark EEG datasets commonly used for motor imagery/execution (MI/ME) classification and obtained accuracies of 79.59 % (BCICIV-2a Dataset), 69.77 % (OpenBMI Dataset) and 96.34 % (High Gamma Dataset), respectively. These results powerfully demonstrate that MSMGE-CNN outperforms several state-of-the-art algorithms. In addition, we further conducted a series of ablation experiments to validate the rationality of our network architecture. Overall, the proposed MSMGE-CNN method dramatically improves the accuracy and robustness of MI/ME-EEG decoding, which can effectively enhance the performance of motor related BCI system.

Multi‐graph representation spatio‐temporal attention networks for traffic forecasting in the cinematic metaverse

AbstractThe cinematic metaverse aims to create a virtual space with the context of a film. Users can enter this space in the form of avatars, experiencing the cinematic plot firsthand in an immersive manner. This requires us to design a rational computation resource allocation and synchronization algorithm to meet the demands of multi‐objective joint optimization, such as low latency and high throughput, which ensures that users can seamlessly switch between virtual and real worlds and acquire immersive experiences. Unfortunately, the explosive growth in the number of users makes it difficult to jointly optimize multiple objectives. Predicting traffic generated by the users' avatars in the cinematic metaverse is significant for the optimization process. Although graph neural networks‐based traffic prediction models achieve superior prediction accuracy, these methods rely only on physical distances‐based topological graph information, while failing to comprehensively reflect the real relationships between avatars in the cinematic metaverse. To address this issue, we present a novel Multi‐Graph Representation Spatio‐Temporal Attention Networks (MGRSTANet) for traffic prediction in the cinematic metaverse. Specifically, based on multiple topological graph information (e.g., physical distances, centerity, and similarity), we first design Multi‐Graph Embedding (MGE) module to generate multiple graph representations, thus reflecting on the real relationships between avatars more comprehensively. The Spatio‐Temporal Attention (STAtt) module is then proposed to extract spatio‐temporal correlations in each graph representations, thus improving prediction accuracy. We conduct simulation experiments to evaluate the effectiveness of MGRSTANet. The experimental results demonstrate that our proposed model outperforms the state‐of‐the‐art baselines in terms of prediction accuracy, making it appropriate for traffic forecasting in the cinematic metaverse.

Synergistic graph fusion via encoder embedding

In this paper, we introduce a method called graph fusion embedding, designed for multi-graph embedding with shared vertex sets. Under the framework of supervised learning, our method exhibits a remarkable and highly desirable synergistic effect: for sufficiently large vertex size, the accuracy of vertex classification consistently benefits from the incorporation of additional graphs. We establish the mathematical foundation for the method, including the asymptotic convergence of the embedding, a sufficient condition for asymptotic optimal classification, and the proof of the synergistic effect for vertex classification. Our comprehensive simulations and real data experiments provide compelling evidence supporting the effectiveness of our proposed method, showcasing the pronounced synergistic effect for multiple graphs from disparate sources.

Manifold-based multi-graph embedding for semi-supervised classification

Graph semi-supervised learning (GSSL) plays an important role in semi-supervised classification by leveraging the similarity of graph topology and convex optimization with Laplacian-based regularization. Current approaches mainly focus on data representation in the Euclidean space and solely rely on a single graph structure, ignoring the underlined manifold-valued structure of the data. To this end, we propose a novel manifold-based multi-graph embedding (M2GE), which explicitly learns representations on both Riemannian manifold and Euclidean space in the embedding learning process. Incorporating multi-graph structure, the rich and varied features are used by M2GE to more fully capture categorical information, where the heterogeneous spatial representations from manifold are complementary. Extensive experimental results on three popular benchmarks verify demonstrate the superiority of our method over state-of-the art competitors.

Multi-graph embedding for partial label learning

Multi-graph embedding for partial label learning

Applying Joint Graph Embedding to Study Alzheimer's Neurodegeneration Patterns in Volumetric Data.

Neurodegeneration measured through volumetry in MRI is recognized as a potential Alzheimer's Disease (AD) biomarker, but its utility is limited by lack of specificity. Quantifying spatial patterns of neurodegeneration on a whole brain scale rather than locally may help address this. In this work, we turn to network based analyses and extend a graph embedding algorithm to study morphometric connectivity from volume-change correlations measured with structural MRI on the timescale of years. We model our data with the multiple random eigengraphs framework, as well as modify and implement a multigraph embedding algorithm proposed earlier to estimate a low dimensional embedding of the networks. Our version of the algorithm guarantees meaningful finite-sample results and estimates maximum likelihood edge probabilities from population-specific network modes and subject-specific loadings. Furthermore, we propose and implement a novel statistical testing procedure to analyze group differences after accounting for confounders and locate significant structures during AD neurodegeneration. Family-wise error rate is controlled at 5% using permutation testing on the maximum statistic. We show that results from our analysis reveal networks dominated by known structures associated to AD neurodegeneration, indicating the framework has promise for studying AD. Furthermore, we find network-structure tuples that are not found with traditional methods in the field.

Multi-channel graph attention autoencoders for disease-related lncRNAs prediction.

Predicting disease-related long non-coding RNAs (lncRNAs) can be used as the biomarkers for disease diagnosis and treatment. The development of effective computational prediction approaches to predict lncRNA-disease associations (LDAs) can provide insights into the pathogenesis of complex human diseases and reduce experimental costs. However, few of the existing methods use microRNA (miRNA) information and consider the complex relationship between inter-graph and intra-graph in complex-graph for assisting prediction. In this paper, the relationships between the same types of nodes and different types of nodes in complex-graph are introduced. We propose a multi-channel graph attention autoencoder model to predict LDAs, called MGATE. First, an lncRNA-miRNA-disease complex-graph is established based on the similarity and correlation among lncRNA, miRNA and diseases to integrate the complex association among them. Secondly, in order to fully extract the comprehensive information of the nodes, we use graph autoencoder networks to learn multiple representations from complex-graph, inter-graph and intra-graph. Thirdly, a graph-level attention mechanism integration module is adopted to adaptively merge the three representations, and a combined training strategy is performed to optimize the whole model to ensure the complementary and consistency among the multi-graph embedding representations. Finally, multiple classifiers are explored, and Random Forest is used to predict the association score between lncRNA and disease. Experimental results on the public dataset show that the area under receiver operating characteristic curve and area under precision-recall curve of MGATE are 0.964 and 0.413, respectively. MGATE performance significantly outperformed seven state-of-the-art methods. Furthermore, the case studies of three cancers further demonstrate the ability of MGATE to identify potential disease-correlated candidate lncRNAs. The source code and supplementary data are available at https://github.com/sheng-n/MGATE. huanglan@jlu.edu.cn, wy6868@jlu.edu.cn.

Mobile App Cross-Domain Recommendation with Multi-Graph Neural Network

With the rapid development of mobile app ecosystem, mobile apps have grown greatly popular. The explosive growth of apps makes it difficult for users to find apps that meet their interests. Therefore, it is necessary to recommend user with a personalized set of apps. However, one of the challenges is data sparsity, as users’ historical behavior data are usually insufficient. In fact, user’s behaviors from different domains in app store regarding the same apps are usually relevant. Therefore, we can alleviate the sparsity using complementary information from correlated domains. It is intuitive to model users’ behaviors using graph, and graph neural networks have shown the great power for representation learning. In this article, we propose a novel model, Deep Multi-Graph Embedding (DMGE), to learn cross-domain app embedding. Specifically, we first construct a multi-graph based on users’ behaviors from different domains, and then propose a multi-graph neural network to learn cross-domain app embedding. Particularly, we present an adaptive method to balance the weight of each domain and efficiently train the model. Finally, we achieve cross-domain app recommendation based on the learned app embedding. Extensive experiments on real-world datasets show that DMGE outperforms other state-of-art embedding methods.

Private Cell-ID Trajectory Prediction Using Multi-Graph Embedding and Encoder-Decoder Network

Trajectory prediction for mobile phone users is a cornerstone component to support many higher-level applications in LBSs (Location-Based Services). Most existing methods are designed based on the assumption that the explicit location information of the trajectories is available (e.g., GPS trajectories). However, collecting such kind of trajectories lays a heavy burden on the mobile phones and incurs privacy concerns. In this paper, we study the problem of trajectory prediction based on cell-id trajectories without explicit location information and propose a deep learning framework (called DeepCTP) to solve this problem. Specifically, we use a multi-graph embedding method to learn the latent spatial correlations between cell towers by exploiting handoff patterns. Then, we design a novel spatial-aware loss function for the encoder-decoder network to generate cell-id trajectory predictions. We conducted extensive experiments on real datasets. The experiment results show that DeepCTP outperforms the state-of-the-art cell-id trajectory prediction methods in terms of prediction error.

Semi-supervised manifold alignment with multi-graph embedding

In this paper, a novel semi-supervised manifold alignment approach via multiple graph embeddings (MA-MGE) is proposed. Different from the traditional manifold alignment algorithms that use a single graph embedding to learn the latent manifold structure of each data set, our approach utilizes multiple graph embeddings to learn a joint latent manifold structure. Therefore a composite manifold representation with complete and more useful information is obtained from each dataset through a dynamic reconstruction of multiple graphs. Also, an optimization strategy based on eigen-value solutions is provided. Experimental results on Protein, COIL-20 and Face-10 datasets demonstrate superior performance of the proposed method compared with the state-of-the-art methods, such as semi-supervised manifold alignment (SSMA), manifold alignment using Procrustes analysis (PAMA) and manifold alignment without correspondence (UNMA).

Patch Tensor-Based Multigraph Embedding Framework for Dimensionality Reduction of Hyperspectral Images

Graph-based dimensionality reduction (DR) techniques are of great interest in the field of image processing and especially on the analysis of hyperspectral images (HSIs). Considering the characteristics of hyperspectral data, many different types of graphs were designed to describe the structure of HSIs. Generally, the algorithms based on these graphs achieved promising performance. However, most of them only focus on how to improve the measurement of similarity between the data points by a single graph. Specifically, vector-based graph methods fail to capture the spatial information, while tensor-based graph methods assume that the pixels in each patch tensor belong to the same class, which is not exactly correct in practice. To overcome these shortcomings, this article proposes a patch tensor-based multigraph embedding (PTMGE) framework for the DR of HSIs, in which three different types of subgraphs are constructed to comprehensively describe the intrinsic geometrical structures of HSIs. First, a tensor subgraph is constructed to capture the spatial information and local geometrical structure. Second, for each two neighboring patch tensors in the tensor graph, a bipartite graph is designed to characterize the pixel-based relationships between the patch tensors. Then, considering that the diversity of pixels may be existed in each patch tensor, a pixel-based subgraph is built to describe the inner geometrical structures of every patch tensor. Finally, a novel graph fusion strategy is designed to calculate a final similarity matrix for projection learning. Experiments on three real hyperspectral data sets are conducted, and comparison with some state-of-the-art algorithms validated the effectiveness of our proposed PTMGE method.

Human action recognition based on the Grassmann multi-graph embedding

In this paper, a human action recognition method based on the kernelized Grassmann manifold learning is introduced. The goal is to find a map which transfers the high-dimensional data to a discriminative low-dimensional space by considering the geometry of the manifold. To this end, a multi-graph embedding method using three graphs named as center-class, within-class and between-class similarity graphs is proposed. These graphs capture the local and semi-global information of data which is the benefit of the proposed method. Graphs play an important role in subspace learning methods. Most of the graph-based methods ignore the geometry of the manifold-valued data because of using Euclidean distance in graph construction. So, these methods are sensitive to noise and outliers. To handle these problems, the geodesic distance is used to build the neighborhood graphs. We analyze the performance of the proposed method on both noisy (complex) and less noisy (simple) datasets. So, two geodesic distance metrics are used to calculate the geodesic distance of these datasets. Experimental results show the performance of the proposed method.

Multi-View Multi-Graph Embedding for Brain Network Clustering Analysis

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-graph embedding discriminative correlation feature learning for image recognition

Most of existing graph-based correlation analysis algorithms construct one graph for one view. However, only one graph is difficult to well reveal intrinsic geometry structure of the view. In this paper, we construct multiple graphs for each view by means of a dimensionality partitioning method, and then propose a novel multi-graph embedding discriminative correlation feature learning algorithm that focuses on multiple graph learning and label-based discriminating enhancement under the multi-view correlation analysis framework. In the algorithm, an effective combination of multiple graphs in each view can be automatically learned in order to better capture the intrinsic geometry structure of each view. Moreover, the algorithm can learn nonlinear correlation features with well discriminating power by maximizing multi-graph intrinsic correlations of different views and simultaneously minimizing intraclass scatter of each view. Extensive experiments on several real-world image datasets have demonstrated the superiority of the algorithm in image recognition.

SERVE: Soft and Equalized Residual VEctors for image retrieval

In the last decade, a wide variety of image signatures, e.g., Bag-of-Visual-Words (BOVW), Fisher Vector (FV), and Vector of Locally Aggregated Descriptor (VLAD), have been developed for effective image retrieval. These image signatures, however, are either computationally expensive or simplified for the purpose of trading accuracy for efficiency. To simultaneously guarantee efficiency and effectiveness, we propose a novel image signature termed Soft and Equalized Residual VEctors (SERVE) which is more discriminatively formulated and maintains higher accuracy. It improves VLAD by encoding the variability in within-cluster feature points into the summation of Residual Vectors (RV) while manifesting superiority in computational efficiency over FV. To find the latent low-dimensional manifolds underlying in the SERVE feature space, we propose to partition the original feature space into separate subspaces by random projections and employ multi-graph embedding to obtain additional performance gain. In particular, we make use of two fusion strategies for graph ensemble to generate a holistic representation. Extensive empirical studies carried out on the three retrieval-specific public benchmarks reveal that our method outperforms existing state-of-the-art methods and provides a promising paradigm for the image retrieval task.

Matrix Representation of Graph Embedding in a Hypercube

The purpose of this paper is to demonstrate the use of matrices for the representation of graph embedding in a hypercube. We denote the image of an embedding (which is a subgraph of the hypercube) as a matrix. With this representation, we are able to simplify, unify, generalize, or improve existing results regarding multigraph embedding in a hypercube. A class of trees called regular binary-reflected trees is identified, which includes linear paths, binomial trees, and many others. We show that for any regular binary-reflected tree T, n copies of T can be simultaneously embedded in an n-cube with congestion = 2. Embeddings of binary trees and meshes are also discussed.