Multi-layer Graph Research Articles

Self-guided information for few-shot classification

Few-shot classification aims to identify novel categories using only a few labeled samples. Generally, the metric-based few-shot classification methods compare the feature embedding of Query samples (unlabeled samples) with Support samples (labeled samples) in a metric algorithm to predict which category the Query sample belongs to. Obtaining a good feature embedding for each sample in the feature extraction stage can improve the classification accuracy in the metric stage. Based on this, we design the Self-Guided Information Convolution (SGI-Conv), an improved convolution structure, which utilizes the high-level features to guide the network to extract the required discriminative features. To effectively utilize the feature embeddings of samples, we divide the metric network into multiple blocks and build a multi-layer graph convolutional network by sharing adjacent matrices. The multi-layer structure enhances the aggregation ability of graph convolution. Extensive experiments on multiple benchmark datasets demonstrate that our method has achieved competitive results on the few-shot classification tasks.

Spectral clustering of single-cell multi-omics data on multilayer graphs.

Single-cell sequencing technologies that simultaneously generate multimodal cellular profiles present opportunities for improved understanding of cell heterogeneity in tissues. How the multimodal information can be integrated to obtain a common cell type identification, however, poses a computational challenge. Multilayer graphs provide a natural representation of multi-omic single-cell sequencing datasets, and finding cell clusters may be understood as a multilayer graph partition problem. We introduce two spectral algorithms on multilayer graphs, spectral clustering on multilayer graphs and the weighted locally linear (WLL) method, to cluster cells in multi-omic single-cell sequencing datasets. We connect these algorithms through a unifying mathematical framework that represents each layer using a Hamiltonian operator and a mixture of its eigenstates to integrate the multiple graph layers, demonstrating in the process that the WLL method is a rigorous multilayer spectral graph theoretic reformulation of the popular Seurat weighted nearest neighbor (WNN) algorithm. Implementing our algorithms and applying them to a CITE-seq dataset of cord blood mononuclear cells yields results similar to the Seurat WNN analysis. Our work thus extends spectral methods to multimodal single-cell data analysis. The code used in this study can be found at https://github.com/jssong-lab/sc-spectrum. All public data used in the article are accurately cited and described in Materials and Methods and in Supplementary Information. Supplementary data are available at Bioinformatics online.

Deep Learning of Latent Edge Types from Relational Data

Many relational datasets, including relational databases, feature links of different types (e.g., actors act in movies, users rate movies), known as multi-relational, heterogeneous, or multi-layer graphs. Edge types/graph layers are often incompletely labeled. For example, IMDb lists Tom Cruise as a cast member of Mission Impossible, but not as its star. Inferring latent layers is useful for relational prediction tasks (e.g. predict Tom Cruise’s salary or his presence in other movies). This paper describes a Latent Layer Generative Framework - LLGF that extends graph encoder-decoder architectures to include latent layers. The decoder treats the observed edge type signalas a linear combination of latent layers. The encoder infers parallel node representations, one for each latent layer. We evaluate our proposed framework on six benchmark graph learning datasets. Qualitative evidence indicates that LLGF recovers ground truth layers well. For link prediction as a downstream task, we find that extending Variational Graph Auto-Encoders with LLGF increases link prediction accuracy compared to state-of-theart graph Variational Auto-Encoders (up to 6% AUC depending on the dataset).

Enhancing bug localization with bug report decomposition and code hierarchical network

Bug localization, which aims to locate buggy source code files for given bug reports, is a crucial yet challenging software-mining task. Despite remarkable success, the state of the art falls short in handling (1) bug reports with diverse characteristics and (2) programs with wildly different behaviors. In response, this paper proposes a graph-based neural model BLoco for automated bug localization. To be specific, our proposed model decomposes bug reports into several bug clues to capture bug-related information from various perspectives for highly diverse bug reports. To understand the program in depth, we first design a code hierarchical network structure, Code-NoN, based on basic blocks to represent source code files. Correspondingly, a multilayer graph neural network is tailored to capture program behaviors from the Code-NoN structure of each source code file. Finally, BLoco further incorporates a bi-affine classifier to comprehensively predict the relationship between the bug reports and source files. Extensive experiments on five large-scale real-world projects demonstrate that the proposed model significantly outperforms existing techniques.

A multilayered block network model to forecast large dynamic transportation graphs: An application to US air transport

Dynamic transportation networks have been analyzed for years by means of static graph-based indicators in order to study the temporal evolution of relevant network components, and to reveal complex dependencies that would not be easily detected by a direct inspection of the data. This paper presents a state-of-the-art probabilistic latent network model to forecast multilayer dynamic graphs that are increasingly common in transportation and proposes a community-based extension to reduce the computational burden. Flexible time series analysis is obtained by modeling the probability of edges between vertices through latent Gaussian processes. The models and Bayesian inference are illustrated on a sample of 10-year data from four major airlines within the US air transportation system. Results show how the estimated latent parameters from the models are related to the airlines’ connectivity dynamics, and their ability to project the multilayer graph into the future for out-of-sample full network forecasts, while stochastic blockmodeling allows for the identification of relevant communities. Reliable network predictions would allow policy-makers to better understand the dynamics of the transport system, and help in their planning on e.g. route development, or the deployment of new regulations.

Multilayer Spectral-Spatial Graphs for Label Noisy Robust Hyperspectral Image Classification.

In hyperspectral image (HSI) analysis, label information is a scarce resource and it is unavoidably affected by human and nonhuman factors, resulting in a large amount of label noise. Although most of the recent supervised HSI classification methods have achieved good classification results, their performance drastically decreases when the training samples contain label noise. To address this issue, we propose a label noise cleansing method based on spectral-spatial graphs (SSGs). In particular, an affinity graph is constructed based on spectral and spatial similarity, in which pixels in a superpixel segmentation-based homogeneous region are connected, and their similarities are measured by spectral feature vectors. Then, we use the constructed affinity graph to regularize the process of label noise cleansing. In this manner, we transform label noise cleansing to an optimization problem with a graph constraint. To fully utilize spatial information, we further develop multiscale segmentation-based multilayer SSGs (MSSGs). It can efficiently merge the complementary information of multilayer graphs and thus provides richer spatial information compared with any single-layer graph obtained from isolation segmentation. Experimental results show that MSSG reduces the level of label noise. Compared with the state of the art, the proposed MSSG method exhibits significantly enhanced classification accuracy toward the training data with noisy labels. The significant advantages of the proposed method over four major classifiers are also demonstrated. The source code is available at https://github.com/junjun-jiang/MSSG.

DeepMGT-DTI: Transformer network incorporating multilayer graph information for Drug–Target interaction prediction

Drug–target interaction (DTI) prediction reduces the cost and time of drug development, and plays a vital role in drug discovery. However, most of research does not fully explore the molecular structures of drug compounds in DTI prediction. To this end, we propose a deep learning model to capture the molecular structure information of drug compounds for DTI prediction. This model utilizes a transformer network incorporating multilayer graph information, which captures the features of a drug's molecular structure so that the interactions between atoms of drug compounds can be explored more deeply. At the same time, a convolutional neural network is employed to capture the local residue information in the target sequence, and effectively extract the feature information of the target. The experiments on the DrugBank dataset showed that the proposed model outperformed previous models based on the structure of target sequences. The results indicate that the improved transformer network fuses the feature information between layers in the graph convolutional neural network and extracts the interaction data for the molecular structure. The drug repositioning experiment on COVID-19 and Alzheimer's disease demonstrated the proposed model's ability to find therapeutic drugs in drug discovery. The code of our model is available at https://github.com/zhangpl109/DeepMGT-DTI.

Interest-Aware Contrastive-Learning-Based GCN for Recommendation

Graph convolutional networks (GCNs) have shown great potential in recommender systems. GCN models contain multiple layers of graph convolutions to exploit signals from higher-order neighbors. In each graph convolution, the embedding of a user or item is influenced by its directly connected neighbors. Some of the main problems with this approach are as follows. First, too many graph convolutional layers make different users or items have similar embeddings. Second, the obtained interaction data have some unfavorable characteristics, such as the sparsity of the data, the noise inside the data, and the distribution skewness of the data, that may impair the model’s performance. This paper proposes an interest-aware contrastive-learning-based GCN (IC-GCN) model. IC-GCN applies an interest-aware mechanism, divides users into different subgraphs according to their interests, and performs multilayer graph convolution on the subgraphs, where all collaborative signals received from multi-hop neighbors are positive. Furthermore, IC-GCN takes the contrastive learning task as an auxiliary task, where the interest-aware encoder receives two modified graphs generated by applying the node dropout operator on the full interaction graph. These two graphs generate two sets of embeddings as two additional views of the nodes. The contrastive learning loss function compares these two sets of embeddings. Extensive experiments are conducted to demonstrate the effectiveness of our model.

Mixed Loss Graph Attention Network for Few-Shot SAR Target Classification

Restricted by the observation condition, synthetic aperture radar (SAR) automatic target classification based on deep learning usually suffers from insufficient training samples. To tackle this problem, a novel few-shot learning (FSL) framework for SAR target classification, i.e., the mixed loss graph attention network (MGA-Net), is proposed. The classification procedure of the MGA-Net consists of three main stages. In the first stage, the task set is expanded by the data augmentation module to increase diversity. In the second stage, the embedding network is designed to map samples to the embedding space with strong intra-class similarity and inter-class divergence. In the third stage, the multilayer graph attention network (GAT) is constructed and updated according to a novel mixed loss to obtain the classification result. In particular, the data augmentation module alleviates the desire of training samples under large model capacity and enhances the robustness to noise and viewing angle variation; the multilayer GAT accurately captures relations between samples by the attention mechanism; and the mixed loss increases the inter-class separability and accelerates convergence. Experimental results under various few-shot observation settings of the MSTAR and the OpenSARShip benchmark datasets demonstrate that the MGA-Net obtains higher accuracy than typical FSL methods and exhibits robustness to large depression angle variation.

Enhancing interactive graph representation learning for review-based item recommendation

Collaborative filtering has been successful in the recommendation systems of various scenarios, but it is also hampered by issues such as cold start and data sparsity. To alleviate the above problems, recent studies have attempted to integrate review information into models to improve accuracy of rating prediction. While most of the existing models respectively utilize independent module to extract the latent feature representation of user reviews and item reviews, ignoring the correlation between the latent features, which may fail to capture the similarity of user preferences and item attributes hidden in different review text. On the other hand, the graph neural network can realize the information interaction in high dimensional space through deep architecture, which has been extensively studied in many fields. Therefore, in order to explore the high dimensional relevance between users and items hidden in the review information, we propose a new recommendation model enhancing interactive graph representation learning for review-based item recommendation, named IGRec. Specifically, we construct the user-review-item graph with users/items as nodes and reviews as edges. We further add the connection of the user-user and the item-item to the graph by meta-path of user-item-user and item-user-item. Then we utilize the attention mechanism to fuse edges information into nodes and apply the multilayer graph convolutional network to learn the high-order interactive information of nodes. Finally, we obtain the final embedding of user/item and adopt the factorization machine to complete the rating prediction. Experiments on the five real-world datasets demonstrate that the proposed IGRec outperforms the state-of-the-art baselines.

Road intersections vehicle tracking based on multi-layer graphs and multi-angle

Aiming at the problem of tracking uncertain vehicle motion flow at intersections, a method based on multi-level graphs and multi-angle is proposed. Firstly, each motion flow is assigned to different layers with diverse neighborhoods by using the constructed multi-layer graphs. Secondly, all multi-layer graphics under multi-angle views are mapped to the selected main view. Finally, the vehicle tracking is realized by solving the shortest path of the mapping main view motion flow. Through the experiment and analysis of vehicle tracking at intersections, the results show that this method can effectively predict vehicle trajectory for uncertain vehicle flow at intersections, and the misjudgment rate between tracking effect and the real situation on the ground is less than 6%, which can provide a new method for vehicle tracking in intelligent transportation.

Prediction of Nanoparticle Sizes for Arbitrary Methacrylates Using Artificial Neuronal Networks.

Particle sizes represent one of the key factors influencing the usability and specific targeting of nanoparticles in medical applications such as vectors for drug or gene therapy. A multi‐layered graph convolutional network combined with a fully connected neuronal network is presented for the prediction of the size of nanoparticles based only on the polymer structure, the degree of polymerization, and the formulation parameters. The model is capable of predicting particle sizes obtained by nanoprecipitation of different poly(methacrylates). This includes polymers the network has not been trained with, indicating the high potential for generalizability of the model. By utilizing this model, a significant amount of time and resources can be saved in formulation optimization without extensive primary testing of material properties.

MLG: multilayer graph clustering for multi-condition scRNA-seq data.

Single-cell transcriptome sequencing (scRNA-seq) enabled investigations of cellular heterogeneity at exceedingly higher resolutions. Identification of novel cell types or transient developmental stages across multiple experimental conditions is one of its key applications. Linear and non-linear dimensionality reduction for data integration became a foundational tool in inference from scRNA-seq data. We present multilayer graph clustering (MLG) as an integrative approach for combining multiple dimensionality reduction of multi-condition scRNA-seq data. MLG generates a multilayer shared nearest neighbor cell graph with higher signal-to-noise ratio and outperforms current best practices in terms of clustering accuracy across large-scale benchmarking experiments. Application of MLG to a wide variety of datasets from multiple conditions highlights how MLG boosts signal-to-noise ratio for fine-grained sub-population identification. MLG is widely applicable to settings with single cell data integration via dimension reduction.

Dual attentive graph neural network for metro passenger flow prediction

Metro system has been increasingly recognized as a backbone of urban transportation system in many cities around the world. To improve the demand management and operation efficiency, it is crucial to have accurate prediction of real-time metro passenger flow. However, the forecast performance is often subject to the complex spatial and temporal distributions of the metro passenger flow data. To this end, we developed a novel dual attentive graph neural network that can effectively predict the distribution of metro traffic flow considering the spatial and temporal influences. Specifically, two directed complete metro graphs (i.e., inbound and outbound graphs) and the weighted matrix of them are proposed to characterize the inbound (entering the system) and outbound (leaving the system) passenger flow, respectively. The weighted matrix of inbound graph is estimated based on the historical origin-destination demand and that of the outbound graph is estimated based on the similarity metrics between every two stations. Moreover, to capture the dependencies between inbound and outbound flows, multi-layer graph spatial attention networks that incorporate the spatial context are applied to exploit the dynamic inter-station correlations. Then, the acquired dependency features integrated with external factors, such as weather conditions, are filtered by temporal attention and fed into a sequence decoder to produce short-term and long-term passenger flow predictions. Finally, a series experiments are conducted based on a comprehensive empirical dataset. Findings indicated that the proposed model does not only well predict the metro passenger flow, but also effectively detect the emergencies and incidents of metro system.

On the k-Anonymization of Time-Varying and Multi-Layer Social Graphs

The popularity of online social media platforms provides an unprecedented opportunity to study real-world complex networks of interactions. However, releasing this data to researchers and the public comes at the cost of potentially exposing private and sensitive user information. It has been shown that a naive anonymization of a network by removing the identity of the nodes is not sufficient to preserve users' privacy. In order to deal with malicious attacks, k-anonymity solutions have been proposed to partially obfuscate topological information that can be used to infer nodes' identity. In this paper, we study the problem of ensuring k-anonymity in time-varying graphs, i.e., graphs with a structure that changes over time, and multi-layer graphs, i.e., graphs with multiple types of links. More specifically, we examine the case in which the attacker has access to the degree of the nodes. The goal is to generate a new graph where, given the degree of a node in each (temporal) layer of the graph, such a node remains indistinguishable from other k-1 nodes in the graph. In order to achieve this, we find the optimal partitioning of the graph nodes such that the cost of anonymizing the degree information within each group is minimum. We show that this reduces to a special case of a Generalized Assignment Problem, and we propose a simple yet effective algorithm to solve it. Finally, we introduce an iterated linear programming approach to enforce the realizability of the anonymized degree sequences. The efficacy of the method is assessed through an extensive set of experiments on synthetic and real-world graphs.

Simplified multilayer graph convolutional networks with dropout

Simplified multilayer graph convolutional networks with dropout

MuzLink: Connected beeswarm timelines for visual analysis of musical adaptations and artist relationships

The rise of open data in the cultural domain is democratizing access to complex datasets usually presented as large multivariate and multilayered graphs. However, the exploration of such datasets is challenging for laypersons. The objective of this work is to develop and evaluate a new method for exploring and understanding a specific type of multilayered graph that combines a large bipartite graph with a set of tree structures. This paper proposes MuzLink, an interactive visualization tool that allows the user to navigate, search, locate, and compare collaborative and influential relationships between musical artists through the exploration of musical adaptations. The proposed tool is based on a set of connected timelines visualizing how an artist’s collaborations, inspirations, and influences evolved over time. This design study is conducted in close collaboration with BAnQ, the national library and archives agency of the Quebec government. A controlled user study, done with a group of BAnQ users, and two case studies, show how the proposed approach is capable of performing a considerable set of analytical and exploratory tasks.

Leveraging semantic for community mining in multilayer networks

Community detection in multilayer networks aims to identify groups of well-connected nodes across multiple layers. While existing methods have been developed to deal with large graphs with few layers (typically less than 10), many real-world datasets are structured by transitive relationships that give rise to networks with thousands of extremely dense layers (e.g. co-citation networks, IMDb actor graphs, co-reference information network, social net- works). In addition, in these datasets the layers are often associated with textual summaries which provide important and hitherto unexploited information on the nature of the relation encoded by the layer. In this paper, we propose a new method which exploits the text associated with the layers in order to identify communities grouping together nodes connected through several semantically close layers. The method consists in embedding layer textual information in an Euclidean space, and to use it to group together, in the same community, nodes belonging to semantically close layers. To that end, we develop a pattern mining approach that extracts communities from numerical data. This approach, which mixes both symbolic and numeric techniques, is particularly well suited to identify communities in multilayer graphs. Indeed, we show that it obtains more diverse and better quality communities than those obtained by state-of-the-art competitors on datasets where ground truth is known. We also show that taking into account the semantic information improves the quality of the communities.

Multilayer Graph Association Rules for Link Prediction

Multiplex networks allow us to study a variety of complex systems where nodes connect to each other in multiple ways, for example friend, family, and co-worker relations in social networks. Link prediction is the branch of network analysis allowing us to forecast the future status of a network: which new connections are the most likely to appear in the future? In multilayer link prediction we also ask: in which layer? Because this last question is unanswerable with classical link prediction, here we investigate the use of graph association rules to inform multilayer link prediction. We derive such rules by identifying all frequent patterns in a network via multilayer graph mining, and then score each unobserved link's likelihood by finding the occurrences of each rule in the original network. Association rules add new abilities to multilayer link prediction: to predict new node arrivals, to consider higher order structures with four or more nodes, and to be memory efficient. In our experiments, we show that, exploiting graph association rules, we are able to achieve a prediction performance close to an ideal ensemble classifier. Further, we perform a case study on a signed multilayer network, showing how graph association rules can provide valuable insights to extend social balance theory.

Multi-layer and Parallel-connected Graph Convolutional Networks for Detecting Debt Default in P2P Networks

ABSTRACT This paper presents a multilayer and parallel-connected graph convolutional networks (MPGCNs) method to explore whether a debtor–creditor relationship network helps to detect the default risk in peer-to-peer (P2P) lending. Results show that: (1) The debtor–creditor relationship network reflects lenders’ risk preference and borrowers’ successful loan information. (2) The proposed MPGCNs method can detect default risk accurately. Therefore, considering the structure of the debtor–creditor relationship network is helpful for P2P lending regulators and government supervisors to control risk.