Random Walk Graph Research Articles

Hermitian random walk graph Fourier transform for directed graphs and its applications

Signal processing on directed graphs present additional challenges since a complete set of eigenvectors is unavailable generally. To solve this problem, in this paper, a novel graph Fourier transform is constructed for representing and processing signals on directed graphs. Firstly, we introduce a Hermitian random walk Laplacian operator and derive that it is Hermitian positive semi-definite. Hence, the obtained Laplacian operator is diagonalizable and yields orthogonal eigenvectors as graph Fourier basis. Secondly, we propose the Hermitian random walk graph Fourier transform (HRWGFT) with good properties including unitary and preserving inner products. Furthermore, HRWGFT records the directionality of edges without sacrificing the information about the graph signal. Then, using these favorable properties, we derive spectral convolution to define the graph filter which is the core tool for processing graph signals. Finally, based on the proposed Laplacian matrix and HRWGFT, we present several applications on synthetic and real-world networks, including signal denoising, data classification. The rationality and validity of our work are verified by simulations.

Drug–target interaction prediction through fine-grained selection and bidirectional random walk methodology

The study of drug–target interaction plays an important role in the process of drug development. The subject of DTI forecasting has advanced significantly in the last several years, yielding numerous significant research findings and methodologies. Heterogeneous data sources provide richer information and comprehensive perspectives for drug–target interaction prediction, so many existing methods rely on heterogeneous networks, and graph embedding technology becomes an important technology to extract information from heterogeneous networks. These approaches, however, are less concerned with potential noisy information in heterogeneous networks and more focused on the extent of information extraction in those networks. Based on this, a potential DTI predictive network model called FBRWPC is proposed in this paper. It uses a fine-grained similarity selection program to first integrate similarity on similar networks and then a bidirectional random walk graph embedding learning method with restart to obtain an updated drug target interaction matrix. Through the use of similarity selection and fine-grained selection similarity integration, the framework can effectively filter out the noise present in heterogeneous networks and enhance the model's prediction performance. The experimental findings demonstrate that, even after being split up into four distinct types of data sets, FBRWPC can still retain great prediction performance, a sign of the model's resilience and good generalization.

Optimizing wireless sensor networks using centrality metrics: a strategic approach

This research paper presents a methodology for improving wireless sensor network (WSN) performance by leveraging centrality measures, including degree, betweenness, closeness, eigenvector, and Katz centrality. Employing a random walk graph model, this study constructs networks with 30 and 50 nodes to investigate the impact of these centrality metrics on routing decisions to optimize energy efficiency, minimize latency, and enhance overall network reliability. Additionally, the paper provides a comprehensive analysis of the relationships among these centrality measures through various correlation techniques, such as Pearson correlation, Kendall rank correlation, and Spearman correlation, offering insights into how these metrics can effectively improve WSN operations.

Hub‐aware random walk graph embedding methods for classification

AbstractIn the last two decades, we are witnessing a huge increase of valuable big data structured in the form of graphs or networks. To apply traditional machine learning and data analytic techniques to such data it is necessary to transform graphs into vector‐based representations that preserve the most essential structural properties of graphs. For this purpose, a large number of graph embedding methods have been proposed in the literature. Most of them produce general‐purpose embeddings suitable for a variety of applications such as node clustering, node classification, graph visualization and link prediction. In this article, we propose two novel graph embedding algorithms based on random walks that are specifically designed for the node classification problem. Random walk sampling strategies of the proposed algorithms have been designed to pay special attention to hubs–high‐degree nodes that have the most critical role for the overall connectedness in large‐scale graphs. The proposed methods are experimentally evaluated by analyzing the classification performance of three classification algorithms trained on embeddings of real‐world networks. The obtained results indicate that our methods considerably improve the predictive power of examined classifiers compared with currently the most popular random walk method for generating general‐purpose graph embeddings (node2vec).

FlowWalker: A Memory-Efficient and High-Performance GPU-Based Dynamic Graph Random Walk Framework

Dynamic graph random walk (DGRW) emerges as a practical tool for capturing structural relations within a graph. Effectively executing DGRW on GPU presents certain challenges. First, existing sampling methods demand a pre-processing buffer, causing substantial space complexity. Moreover, the power-law distribution of graph vertex degrees introduces workload imbalance issues, rendering DGRW embarrassed to parallelize. In this paper, we propose FlowWalker, a GPU-based dynamic graph random walk framework. FlowWalker implements an efficient parallel sampling method to fully exploit the GPU parallelism and reduce space complexity. Moreover, it employs a sampler-centric paradigm alongside a dynamic scheduling strategy to handle the huge amounts of walking queries. FlowWalker stands as a memory-efficient framework that requires no auxiliary data structures in GPU global memory. We examine the performance of FlowWalker extensively on ten datasets, and experiment results show that FlowWalker achieves up to 752.2×, 72.1×, and 16.4× speedup compared with existing CPU, GPU, and FPGA random walk frameworks, respectively. Case study shows that FlowWalker diminishes random walk time from 35% to 3% in a pipeline of ByteDance friend recommendation GNN training.

Weighted Jump in Random Walk graph sampling

Graph sampling is a challenging problem in network analysis due to the complex structures of networks. Currently, a series of graph sampling algorithms based on random walks achieve good results in graph sampling tasks. However, the existing methods often reduce the conductance of graphs, causing the sampler to stay in the same node for a long time. This results in undersampling. In this paper, we propose a novel Weighted Jump Random Walk (WJRW) algorithm to generate representative samples. We design a parameter in the WJRW algorithm that can adjust the proportions of random walk and random jump in every step. According to the issue of repeated sample nodes in the Generalized Maximum Degree (GMD) method and the problem of large deviations in the Simple Random Walk (SRW), WJRW addresses the weaknesses of the GMD method and enhances the diffusion of a random walker on graphs, leading to a more representative sample. Then, WJRW addresses the issue of large deviations in SRW and enhances the efficiency of the unbiased estimator. By generating smoother stationary distributions. Numerical experiments with extensive real-world networks verify that our method achieves higher accuracy than classical and state-of-the-art methods in estimating distribution estimation.

A multilayer network diffusion-based model for reviewer recommendation

With the rapid growth of manuscript submissions, finding eligible reviewers for every submission has become a heavy task. Recommender systems are powerful tools developed in computer science and information science to deal with this problem. However, most existing approaches resort to text mining techniques to match manuscripts with potential reviewers, which require high-quality textual information to perform well. In this paper, we propose a reviewer recommendation algorithm based on a network diffusion process on a scholar–paper multilayer network, with no requirement for textual information. The network incorporates the relationship of scholar–paper pairs, the collaboration among scholars, and the bibliographic coupling among papers. Experimental results show that our proposed algorithm outperforms other state-of-the-art recommendation methods that use graph random walk and matrix factorization and methods that use machine learning and natural language processing, with improvements of over 7.62% in recall, 5.66% in hit rate, and 47.53% in ranking score. Our work sheds light on the effectiveness of multilayer network diffusion-based methods in the reviewer recommendation problem, which will help to facilitate the peer-review process and promote information retrieval research in other practical scenes.

NLRRC: A Novel Clustering Method of Jointing Non-Negative LRR and Random Walk Graph Regularized NMF for Single-Cell Type Identification.

The development of single-cell RNA sequencing (scRNA-seq) technology has opened up a new perspective for us to study disease mechanisms at the single cell level. Cell clustering reveals the natural grouping of cells, which is a vital step in scRNA-seq data analysis. However, the high noise and dropout of single-cell data pose numerous challenges to cell clustering. In this study, we propose a novel matrix factorization method named NLRRC for single-cell type identification. NLRRC joins non-negative low-rank representation (LRR) and random walk graph regularized NMF (RWNMFC) to accurately reveal the natural grouping of cells. Specifically, we find the lowest rank representation of single-cell samples by non-negative LRR to reduce the difficulty of analyzing high-dimensional samples and capture the global information of the samples. Meanwhile, by using random walk graph regularization (RWGR) and NMF, RWNMFC captures manifold structure and cluster information before generating a cluster allocation matrix. The cluster assignment matrix contains cluster labels, which can be used directly to get the clustering results. The performance of NLRRC is validated on simulated and real single-cell datasets. The results of the experiments illustrate that NLRRC has a significant advantage in single-cell type identification.

ARGLRR: A Sparse Low-Rank Representation Single-Cell RNA-Sequencing Data Clustering Method Combined with a New Graph Regularization.

The development of single-cell transcriptome sequencing technologies has opened new ways to study biological phenomena at the cellular level. A key application of such technologies involves the employment of single-cell RNA sequencing (scRNA-seq) data to identify distinct cell types through clustering, which in turn provides evidence for revealing heterogeneity. Despite the promise of this approach, the inherent characteristics of scRNA-seq data, such as higher noise levels and lower coverage, pose major challenges to existing clustering methods and compromise their accuracy. In this study, we propose a method called Adjusted Random walk Graph regularization Sparse Low-Rank Representation (ARGLRR), a practical sparse subspace clustering method, to identify cell types. The fundamental low-rank representation (LRR) model is concerned with the global structure of data. To address the limited ability of the LRR method to capture local structure, we introduced adjusted random walk graph regularization in its framework. ARGLRR allows for the capture of both local and global structures in scRNA-seq data. Additionally, the imposition of similarity constraints into the LRR framework further improves the ability of the proposed model to estimate cell-to-cell similarity and capture global structural relationships between cells. ARGLRR surpasses other advanced comparison approaches on nine known scRNA-seq data sets judging by the results. In the normalized mutual information and Adjusted Rand Index metrics on the scRNA-seq data sets clustering experiments, ARGLRR outperforms the best-performing comparative method by 6.99% and 5.85%, respectively. In addition, we visualize the result using Uniform Manifold Approximation and Projection. Visualization results show that the usage of ARGLRR enhances the separation of different cell types within the similarity matrix.

Exposing the Self-Supervised Space-Time Correspondence Learning via Graph Kernels

Self-supervised space-time correspondence learning is emerging as a promising way of leveraging unlabeled video. Currently, most methods adapt contrastive learning with mining negative samples or reconstruction adapted from the image domain, which requires dense affinity across multiple frames or optical flow constraints. Moreover, video correspondence predictive models require mining more inherent properties in videos, such as structural information. In this work, we propose the VideoHiGraph, a space-time correspondence framework based on a learnable graph kernel. Concerning the video as the spatial-temporal graph, the learning objectives of VideoHiGraph are emanated in a self-supervised manner for predicting unobserved hidden graphs via graph kernel manner. We learn a representation of the temporal coherence across frames in which pairwise similarity defines the structured hidden graph, such that a biased random walk graph kernel along the sub-graph can predict long-range correspondence. Then, we learn a refined representation across frames on the node-level via a dense graph kernel. The self-supervision of the model training is formed by the structural and temporal consistency of the graph. VideoHiGraph achieves superior performance and demonstrates its robustness across the benchmark of label propagation tasks involving objects, semantic parts, keypoints, and instances. Our algorithm implementations have been made publicly available at https://github.com/zyqin19/VideoHiGraph.

Representation Learning of Enhanced Graphs Using Random Walk Graph Convolutional Network

Nowadays, graph structure data has played a key role in machine learning because of its simple topological structure, and therefore, the graph representation learning methods have attracted great attention. And it turns out that the low-dimensional embedding representation obtained by graph representation learning is extremely useful in various typical tasks, such as node classification and content recommendation. However, most of the existing methods do not further dig out potential structural information on the original graph structure. Here, we propose wGCN, which utilizes random walk to obtain the node-specific mesoscopic structures (high-order local structure) of the graph and utilizes these mesoscopic structures to enhance the graph and organize the characteristic information of the nodes. Our method can effectively generate node embedding for data of previously unknown categories, which has been proven in a series of experiments conducted on many types of graph networks. And compared to baselines, our method shows the best performance on most datasets and achieves competitive results on others. It is believed that combining the mesoscopic structure to further explore the structural information of the graph will greatly improve the learning efficiency of the graph neural network.

Joint L2,p-norm and random walk graph constrained PCA for single-cell RNA-seq data

The development and widespread utilization of high-throughput sequencing technologies in biology has fueled the rapid growth of single-cell RNA sequencing (scRNA-seq) data over the past decade. The development of scRNA-seq technology has significantly expanded researchers’ understanding of cellular heterogeneity. Accurate cell type identification is the prerequisite for any research on heterogeneous cell populations. However, due to the high noise and high dimensionality of scRNA-seq data, improving the effectiveness of cell type identification remains a challenge. As an effective dimensionality reduction method, Principal Component Analysis (PCA) is an essential tool for visualizing high-dimensional scRNA-seq data and identifying cell subpopulations. However, traditional PCA has some defects when used in mining the nonlinear manifold structure of the data and usually suffers from over-density of principal components (PCs). Therefore, we present a novel method in this paper called joint -norm and random walk graph constrained PCA (RWPPCA). RWPPCA aims to retain the data’s local information in the process of mapping high-dimensional data to low-dimensional space, to more accurately obtain sparse principal components and to then identify cell types more precisely. Specifically, RWPPCA combines the random walk (RW) algorithm with graph regularization to more accurately determine the local geometric relationships between data points. Moreover, to mitigate the adverse effects of dense PCs, the -norm is introduced to make the PCs sparser, thus increasing their interpretability. Then, we evaluate the effectiveness of RWPPCA on simulated data and scRNA-seq data. The results show that RWPPCA performs well in cell type identification and outperforms other comparison methods.

Social Relationship Link Inference Based on Graph Convolutional Networks

In the study of social relationship inference, social relationship link inference aims to infer whether there is a social relationship between users. Most previous works applied the unsupervised graph random walk sampling, which had sampling bias and lost much information. In this paper, a Social Relationship Link Inference Based on Graph Convolutional Networks (SLiGCN) is proposed, which learns the spatiotemporal information of check-ins and the impact of related users’ trajectories. It firstly employs the end-to-end supervised learning and applies a recurrent neural network to extract spatiotemporal sequence features from trajectories. Then the graph convolutional network fuses the features of neighboring nodes and employs the fully connected network to infer social relationship links. Finally, it is evaluated with AUC on three real-world datasets. The experiment results show that, compared with baseline models, it not only avoids hand-crafted feature construction that requires much prior knowledge, but also achieves 10% improvement on average.

A scheduling algorithm for heterogeneous computing systems by edge cover queue

In heterogeneous computing systems, excellent task scheduling algorithms can shorten the task completion time and improve system parallelism. With the large-scale deployment of edge computing, the task scheduling algorithm in heterogeneous edge computing servers has become a critical factor in improving the overall system performance. This paper proposes a new task scheduling algorithm called the edge cover scheduling algorithm (ECSA), which schedules tasks based on the edge cover queue of the directed acyclic graph (DAG) for heterogeneous computing systems. Based on the estimation of distribution algorithm (EDA) and the graph random walk algorithm, the ECSA generates an edge cover queue from DAG. Then, the ECSA uses the heuristics greedy method with low time and computational complexity to allocate the edge cover queue to processors. Theoretical analysis and simulation results on random DAGs and real-world DAGs show that the ECSA can achieve better scheduling results in terms of makespan, the schedule length ratio (SLR), efficiency, and frequency of best results with low time and computational complexity.

Random Walk Graph Auto-Encoders With Ensemble Networks in Graph Embedding

Random Walk Graph Auto-Encoders With Ensemble Networks in Graph Embedding

A Survey of Large Graph Sampling Techniques

As a common method for simplifying network graphs, large graph sampling can reduce the size of large graph data significantly. In this paper, related works are summarized from the following perspectives: random graph sampling techniques, feature-driven large graph sampling techniques, evaluation metrics of large graph sampling and applications of large graph sampling technique. Firstly, random graph sampling is categorized into three types, including random node, random edge, and random walk graph sampling. Secondly, the feature-driven large graph sampling techniques are discussed, including topology-preserving, community structure-preserving, dynamic network association and semantic association feature-driven large graph sampling. Thirdly, the evaluation metrics of large graph sampling techniques are introduced, including topological metrics, visual perception metrics and feature-driven metrics. Finally, the applications of large graph sampling technique in social networks, geographic traffic, biomedical and deep learning are summarized, and the development of large graph sampling method is prospected.

Eigen-convergence of Gaussian kernelized graph Laplacian by manifold heat interpolation

This work studies the spectral convergence of graph Laplacian to the Laplace-Beltrami operator when the graph affinity matrix is constructed from $N$ random samples on a $d$-dimensional manifold embedded in a possibly high dimensional space. By analyzing Dirichlet form convergence and constructing candidate approximate eigenfunctions via convolution with manifold heat kernel, we prove that, with Gaussian kernel, one can set the kernel bandwidth parameter $\epsilon \sim (\log N/ N)^{1/(d/2+2)}$ such that the eigenvalue convergence rate is $N^{-1/(d/2+2)}$ and the eigenvector convergence in 2-norm has rate $N^{-1/(d+4)}$; When $\epsilon \sim (\log N/N)^{1/(d/2+3)}$, both eigenvalue and eigenvector rates are $N^{-1/(d/2+3)}$. These rates are up to a $\log N$ factor and proved for finitely many low-lying eigenvalues. The result holds for un-normalized and random-walk graph Laplacians when data are uniformly sampled on the manifold, as well as the density-corrected graph Laplacian (where the affinity matrix is normalized by the degree matrix from both sides) with non-uniformly sampled data. As an intermediate result, we prove new point-wise and Dirichlet form convergence rates for the density-corrected graph Laplacian. Numerical results are provided to verify the theory.

Recommending Crowdfunding Project: A Graph Kernel-Based Link Prediction Method for Extremely Sparse Implicit Feedback.

It is a critical task to provide recommendation on implicit feedback, and one of the biggest challenges is extreme data sparsity. To tackle the problem, a graph kernel-based link prediction method is proposed in this paper for recommending crowdfunding projects combining graph computing with collaborative filtering. First of all, an investor-project bipartite graph is established based on transaction histories. Then, a random walk graph kernel is constructed and computed, and a one-class SVM classifier is built for link prediction based on implicit feedback. At last, top N recommendations are made according to the ranking of investor-project pairs. Comparative experiments are conducted and the results show that the proposed method achieves the best performance on extremely sparse implicit feedback and outperforms baselines. This paper is of help to improve the success rate of crowdfunding by personalized recommendation and is of significance to enrich the research in recommendation systems.

Classifying the toxicity of pesticides to honey bees via support vector machines with random walk graph kernels.

Pesticides benefit agriculture by increasing crop yield, quality, and security. However, pesticides may inadvertently harm bees, which are valuable as pollinators. Thus, candidate pesticides in development pipelines must be assessed for toxicity to bees. Leveraging a dataset of 382 molecules with toxicity labels from honey bee exposure experiments, we train a support vector machine (SVM) to predict the toxicity of pesticides to honey bees. We compare two representations of the pesticide molecules: (i) a random walk feature vector listing counts of length-L walks on the molecular graph with each vertex- and edge-label sequence and (ii) the Molecular ACCess System (MACCS) structural key fingerprint (FP), a bit vector indicating the presence/absence of a list of pre-defined subgraph patterns in the molecular graph. We explicitly construct the MACCS FPs but rely on the fixed-length-L random walk graph kernel (RWGK) in place of the dot product for the random walk representation. The L-RWGK-SVM achieves an accuracy, precision, recall, and F1 score (mean over 2000 runs) of 0.81, 0.68, 0.71, and 0.69, respectively, on the test data set-with L = 4 being the mode optimal walk length. The MACCS-FP-SVM performs on par/marginally better than the L-RWGK-SVM, lends more interpretability, but varies more in performance. We interpret the MACCS-FP-SVM by illuminating which subgraph patterns in the molecules tend to strongly push them toward the toxic/non-toxic side of the separating hyperplane.

Multi-View Random-Walk Graph Regularization Low-Rank Representation for Cancer Clustering and Differentially Expressed Gene Selection.

Cancer genome data generally consists of multiple views from different sources. These views provide different levels of information about gene activity, as well as more comprehensive cancer information. The low-rank representation (LRR) method, as a powerful subspace clustering method, has been extended and applied in cancer data research. Although the multi-view learning methods based on low rank representation have achieved good results in cancer multi-omics analysis because they fully consider the consistency and complementarity between views, these methods have some shortcomings in mining the potential local geometry of data. In view of this, this paper proposes a new method named Multi-view Random-walk Graph regularization Low-Rank Representation (MRGLRR) to comprehensively analyze multi-view genomics data. This method uses multi-view model to find the common centroid of view. By constructing a joint affinity matrix to learn the low-rank subspace representation of multiple sets of data, the hidden information of each view is fully obtained. In addition, this method introduces random walk graph regularization constraint to obtain more accurate similarity between samples. Different from the traditional graph regularization constraint, after constructing the KNN graph, we use the random walk algorithm to obtain the weight matrix. The random walk algorithm can retain more local geometric information and better learn the topological structure of the data. What's more, a feature gene selection strategy suitable for multi-view model is proposed to find more differentially expressed genes with research value. Experimental results show that our method is better than other representative methods in terms of clustering and feature gene selection for cancer multi-omics data.