Virtual network embedding (VNE) algorithm is always the key problem in network virtualization (NV) technology. At present, the research in this field still has the following problems. The traditional way to solve VNE problem is to use heuristic algorithm. However, this method relies on manual embedding rules, which does not accord with the actual situation of VNE. In addition, as the use of intelligent learning algorithm to solve the problem of VNE has become a trend, this method is gradually outdated. At the same time, there are some security problems in VNE. However, there is no intelligent algorithm to solve the security problem of VNE. For this reason, this paper proposes a security-aware VNE algorithm based on reinforcement learning (RL). In the training phase, we use a policy network as a learning agent and take the extracted attributes of the substrate nodes to form a feature matrix as input. The learning agent is trained in this environment to get the mapping probability of each substrate node. In the test phase, we map nodes according to the mapping probability and use the breadth-first strategy (BFS) to map links. For the security problem, we add security requirements level constraint for each virtual node and security level constraint for each substrate node. Virtual nodes can only be embedded on substrate nodes that are not lower than the level of security requirements. Experimental results show that the proposed algorithm is superior to other typical algorithms in terms of long-term average return, long-term revenue consumption ratio and virtual network request (VNR) acceptance rate.
Network virtualization (NV) is a technology with broad application prospects. Virtual network embedding (VNE) is the core orientation of VN, which aims to provide more flexible underlying physical resource allocation for user function requests. The classical VNE problem is usually solved by heuristic method, but this method often limits the flexibility of the algorithm and ignores the time limit. In addition, the partition autonomy of physical domain and the dynamic characteristics of virtual network request (VNR) also increase the difficulty of VNE. This paper proposed a new type of VNE algorithm, which applied reinforcement learning (RL) and graph neural network (GNN) theory to the algorithm, especially the combination of graph convolutional neural network (GCNN) and RL algorithm. Based on a self-defined fitness matrix and fitness value, we set up the objective function of the algorithm implementation, realized an efficient dynamic VNE algorithm, and effectively reduced the degree of resource fragmentation. Finally, we used comparison algorithms to evaluate the proposed method. Simulation experiments verified that the dynamic VNE algorithm based on RL and GCNN has good basic VNE characteristics. By changing the resource attributes of physical network and virtual network, it can be proved that the algorithm has good flexibility.
The rapid development of virtual network architecture makes it possible for wireless network to be widely used. With the popularity of artificial intelligence (AI) industry in daily life, efficient resource allocation of wireless network has become a problem. Especially when network users request wireless network resources from different management domains, they still face many practical problems. From the perspective of virtual network embedding (VNE), this paper designs and implements a multi-objective optimization VNE algorithm for wireless network resource allocation. Resource allocation in virtual network is essentially a problem of allocating underlying resources for virtual network requests (VNRs). According to the proposed objective formula, we consider the optimization mapping cost, network delay and VNR acceptance rate. VNE is completed by node mapping and link mapping. In the experiment and simulation stage, it is compared with other VNE algorithms, the cross domain VNE algorithm proposed in this paper is optimal in the above three indicators. This shows the effectiveness of the algorithm in wireless network resource allocation.
Virtual network embedding (VNE) is an crucial part of network virtualization (NV), which aims to map the virtual networks (VNs) to a shared substrate network (SN). With the emergence of various delay-sensitive applications, how to improve the delay performance of the system has become a hot topic in academic circles. Based on extensive research, we proposed a multi-domain virtual network embedding algorithm based on delay prediction (DP-VNE). Firstly, the candidate physical nodes are selected by estimating the delay of virtual requests, then particle swarm optimization (PSO) algorithm is used to optimize the mapping process, so as to reduce the delay of the system. The simulation results show that compared with the other three advanced algorithms, the proposed algorithm can significantly reduce the system delay while keeping other indicators unaffected.
Capturing structural similarity has been a hot topic in the field of network embedding recently due to its great help in understanding the node functions and behaviors. However, existing works have paid very much attention to learning structures on homogeneous networks while the related study on heterogeneous networks is still a void. In this paper, we try to take the first step for representation learning on heterostructures, which is very challenging due to their highly diverse combinations of node types and underlying structures. To effectively distinguish diverse heterostructures, we firstly propose a theoretically guaranteed technique called heterogeneous anonymous walk (HAW) and its variant coarse HAW (CHAW). Then, we devise the heterogeneous anonymous walk embedding (HAWE) and its variant coarse HAWE in a data-driven manner to circumvent using an extremely large number of possible walks and train embeddings by predicting occurring walks in the neighborhood of each node. Finally, we design and apply extensive and illustrative experiments on synthetic and real-world networks to build a benchmark on heterostructure learning and evaluate the effectiveness of our methods. The results demonstrate our methods achieve outstanding performance compared with both homogeneous and heterogeneous classic methods, and can be applied on large-scale networks.
Modeling heterogeneity by extraction and exploitation of high-order information from heterogeneous information networks (HINs) has been attracting immense research attention in recent times. Such heterogeneous network embedding (HNE) methods effectively harness the heterogeneity of small-scale HINs. However, in the real world, the size of HINs grow exponentially with the continuous introduction of new nodes and different types of links, making it a billion-scale network. Learning node embeddings on such HINs creates a performance bottleneck for existing HNE methods that are commonly centralized, i.e., complete data and the model are both on a single machine. To address large-scale HNE tasks with strong efficiency and effectiveness guarantee, we present \textit{Decentralized Embedding Framework for Heterogeneous Information Network} (DeHIN) in this paper. In DeHIN, we generate a distributed parallel pipeline that utilizes hypergraphs in order to infuse parallelization into the HNE task. DeHIN presents a context preserving partition mechanism that innovatively formulates a large HIN as a hypergraph, whose hyperedges connect semantically similar nodes. Our framework then adopts a decentralized strategy to efficiently partition HINs by adopting a tree-like pipeline. Then, each resulting subnetwork is assigned to a distributed worker, which employs the deep information maximization theorem to locally learn node embeddings from the partition it receives. We further devise a novel embedding alignment scheme to precisely project independently learned node embeddings from all subnetworks onto a common vector space, thus allowing for downstream tasks like link prediction and node classification.
We study the problem of large-scale network embedding, which aims to learn low-dimensional latent representations for network mining applications. Recent research in the field of network embedding has led to significant progress such as DeepWalk, LINE, NetMF, NetSMF. However, the huge size of many real-world networks makes it computationally expensive to learn network embedding from the entire network. In this work, we present a novel network embedding method called "NES", which learns network embedding from a small representative subgraph. NES leverages theories from graph sampling to efficiently construct representative subgraph with smaller size which can be used to make inferences about the full network, enabling significantly improved efficiency in embedding learning. Then, NES computes the network embedding from this representative subgraph, efficiently. Compared with well-known methods, extensive experiments on networks of various scales and types demonstrate that NES achieves comparable performance and significant efficiency superiority.
Increased attention has been paid over the last four years to dynamic network embedding. Existing dynamic embedding methods, however, consider the problem as limited to the evolution of a topology over a sequence of global, discrete states. We propose a novel embedding algorithm, WalkingTime, based on a fundamentally different handling of time, allowing for the local consideration of continuously occurring phenomena; while others consider global time-steps to be first-order citizens of the dynamic environment, we hold flows comprised of temporally and topologically local interactions as our primitives, without any discretization or alignment of time-related attributes being necessary. Keywords: dynamic networks , representation learning , dynamic graph embedding , time-respecting paths , temporal-topological flows , temporal random walks , temporal networks , real-attributed knowledge graphs , streaming graphs , online networks , asynchronous graphs , asynchronous networks , graph algorithms , deep learning , network analysis , datamining , network science
Graph is a universe data structure that is widely used to organize data in real-world. Various real-word networks like the transportation network, social and academic network can be represented by graphs. Recent years have witnessed the quick development on representing vertices in the network into a low-dimensional vector space, referred to as network representation learning. Representation learning can facilitate the design of new algorithms on the graph data. In this survey, we conduct a comprehensive review of current literature on network representation learning. Existing algorithms can be categorized into three groups: shallow embedding models, heterogeneous network embedding models, graph neural network based models. We review state-of-the-art algorithms for each category and discuss the essential differences between these algorithms. One advantage of the survey is that we systematically study the underlying theoretical foundations underlying the different categories of algorithms, which offers deep insights for better understanding the development of the network representation learning field.
With the increasing relevance of large networks in important areas such as the study of contact networks for spread of disease, or social networks for their impact on geopolitics, it has become necessary to study machine learning tools that are scalable to very large networks, often containing millions of nodes. One major class of such scalable algorithms is known as network representation learning or network embedding. These algorithms try to learn representations of network functionals (e.g.~nodes) by first running multiple random walks and then using the number of co-occurrences of each pair of nodes in observed random walk segments to obtain a low-dimensional representation of nodes on some Euclidean space. The aim of this paper is to rigorously understand the performance of two major algorithms, DeepWalk and node2vec, in recovering communities for canonical network models with ground truth communities. Depending on the sparsity of the graph, we find the length of the random walk segments required such that the corresponding observed co-occurrence window is able to perform almost exact recovery of the underlying community assignments. We prove that, given some fixed co-occurrence window, node2vec using random walks with a low non-backtracking probability can succeed for much sparser networks compared to DeepWalk using simple random walks. Moreover, if the sparsity parameter is low, we provide evidence that these algorithms might not succeed in almost exact recovery. The analysis requires developing general tools for path counting on random networks having an underlying low-rank structure, which are of independent interest.
Link prediction infers potential links from observed networks, and is one of the essential problems in network analyses. In contrast to traditional graph representation modeling which only predicts two-way pairwise relations, we propose a novel tensor-based joint network embedding approach on simultaneously encoding pairwise links and hyperlinks onto a latent space, which captures the dependency between pairwise and multi-way links in inferring potential unobserved hyperlinks. The major advantage of the proposed embedding procedure is that it incorporates both the pairwise relationships and subgroup-wise structure among nodes to capture richer network information. In addition, the proposed method introduces a hierarchical dependency among links to infer potential hyperlinks, and leads to better link prediction. In theory we establish the estimation consistency for the proposed embedding approach, and provide a faster convergence rate compared to link prediction utilizing pairwise links or hyperlinks only. Numerical studies on both simulation settings and Facebook ego-networks indicate that the proposed method improves both hyperlink and pairwise link prediction accuracy compared to existing link prediction algorithms.
Multi-Instance Multi-Label learning (MIML) models complex objects (bags), each of which is associated with a set of interrelated labels and composed with a set of instances. Current MIML solutions still focus on a single-type of objects and assumes an IID distribution of training data. But these objects are linked with objects of other types, %(i.e., pictures in Facebook link with various users), which also encode the semantics of target objects. In addition, they generally need abundant labeled data for training. To effectively mine interdependent MIML objects of different types, we propose a network embedding and meta learning based approach (MetaMIML). MetaMIML introduces the context learner with network embedding to capture semantic information of objects of different types, and the task learner to extract the meta knowledge for fast adapting to new tasks. In this way, MetaMIML can naturally deal with MIML objects at data level improving, but also exploit the power of meta-learning at the model enhancing. Experiments on benchmark datasets demonstrate that MetaMIML achieves a significantly better performance than state-of-the-art algorithms.
Network embedding has emerged as a promising research field for network analysis. Recently, an approach, named Barlow Twins, has been proposed for self-supervised learning in computer vision by applying the redundancy-reduction principle to the embedding vectors corresponding to two distorted versions of the image samples. Motivated by this, we propose Barlow Graph Auto-Encoder, a simple yet effective architecture for learning network embedding. It aims to maximize the similarity between the embedding vectors of immediate and larger neighborhoods of a node, while minimizing the redundancy between the components of these projections. In addition, we also present the variation counterpart named as Barlow Variational Graph Auto-Encoder. Our approach yields promising results for inductive link prediction and is also on par with state of the art for clustering and downstream node classification, as demonstrated by extensive comparisons with several well-known techniques on three benchmark citation datasets.
We demonstrate the applicability of network embedding to vaccine skepticism, a controversial topic of long-past history. With the Covid-19 pandemic outbreak at the end of 2019, the topic is more important than ever. Only a year after the first international cases were registered, multiple vaccines were developed and passed clinical testing. Besides the challenges of development, testing, and logistics, another factor that might play a significant role in the fight against the pandemic are people who are hesitant to get vaccinated, or even state that they will refuse any vaccine offered to them. Two groups of people commonly referred to as a) pro-vaxxer, those who support vaccinating people b) vax-skeptic, those who question vaccine efficacy or the need for general vaccination against Covid-19. It is very difficult to tell exactly how many people share each of these views. It is even more difficult to understand all the reasoning why vax-skeptic opinions are getting more popular. In this work, our intention was to develop techniques that are able to efficiently differentiate between pro-vaxxer and vax-skeptic content. After multiple data preprocessing steps, we analyzed the tweet text as well as the structure of user interactions on Twitter. We deployed several node embedding and community detection models that scale well for graphs with millions of edges.
Evolving temporal networks serve as the abstractions of many real-life dynamic systems, e.g., social network and e-commerce. The purpose of temporal network embedding is to map each node to a time-evolving low-dimension vector for downstream tasks, e.g., link prediction and node classification. The difficulty of temporal network embedding lies in how to utilize the topology and time information jointly to capture the evolution of a temporal network. In response to this challenge, we propose a temporal motif-preserving network embedding method with bicomponent neighbor aggregation, named TME-BNA. Considering that temporal motifs are essential to the understanding of topology laws and functional properties of a temporal network, TME-BNA constructs additional edge features based on temporal motifs to explicitly utilize complex topology with time information. In order to capture the topology dynamics of nodes, TME-BNA utilizes Graph Neural Networks (GNNs) to aggregate the historical and current neighbors respectively according to the timestamps of connected edges. Experiments are conducted on three public temporal network datasets, and the results show the effectiveness of TME-BNA.
Heterogeneous information network (HIN) embedding aims to find the representations of nodes that preserve the proximity between entities of different nature. A family of approaches that are wildly adopted applies random walk to generate a sequence of heterogeneous context, from which the embedding is learned. However, due to the multipartite graph structure of HIN, hub nodes tend to be over-represented in the sampled sequence, giving rise to imbalanced samples of the network. Here we propose a new embedding method CoarSAS2hvec. The self-avoid short sequence sampling with the HIN coarsening procedure (CoarSAS) is utilized to better collect the rich information in HIN. An optimized loss function is used to improve the performance of the HIN structure embedding. CoarSAS2hvec outperforms nine other methods in two different tasks on four real-world data sets. The ablation study confirms that the samples collected by CoarSAS contain richer information of the network compared with those by other methods, which is characterized by a higher information entropy. Hence, the traditional loss function applied to samples by CoarSAS can also yield improved results. Our work addresses a limitation of the random-walk-based HIN embedding that has not been emphasized before, which can shed light on a range of problems in HIN analyses.
Temporal interaction networks are formed in many fields, e.g., e-commerce, online education, and social network service. Temporal interaction network embedding can effectively mine the information in temporal interaction networks, which is of great significance to the above fields. Usually, the occurrence of an interaction affects not only the nodes directly involved in the interaction (interacting nodes), but also the neighbor nodes of interacting nodes. However, existing temporal interaction network embedding methods only use historical interaction relations to mine neighbor nodes, ignoring other relation types. In this paper, we propose a multi-relation aware temporal interaction network embedding method (MRATE). Based on historical interactions, MRATE mines historical interaction relations, common interaction relations, and interaction sequence similarity relations to obtain the neighbor based embeddings of interacting nodes. The hierarchical multi-relation aware aggregation method in MRATE first employs graph attention networks (GATs) to aggregate the interaction impacts propagated through a same relation type and then combines the aggregated interaction impacts from multiple relation types through the self-attention mechanism. Experiments are conducted on three public temporal interaction network datasets, and the experimental results show the effectiveness of MRATE.
Using Service Function Chaining (SFC) in wireless networks became popular in many domains like networking and multimedia. It relies on allocating network resources to incoming SFCs requests, via a Virtual Network Embedding (VNE) algorithm, so that it optimizes the performance of the SFC. When the load of incoming requests -- competing for the limited network resources - increases, it becomes challenging to decide which requests should be admitted and which one should be rejected. In this work, we propose a deep Reinforcement learning (RL) solution that can learn the admission policy for different dependencies, such as the service lifetime and the priority of incoming requests. We compare the deep RL solution to a first-come-first-serve baseline that admits a request whenever there are available resources. We show that deep RL outperforms the baseline and provides higher acceptance rate with low rejections even when there are enough resources.
Graph auto-encoders have proved to be useful in network embedding task. However, current models only consider explicit structures and fail to explore the informative latent structures cohered in networks. To address this issue, we propose a latent network embedding model based on adversarial graph auto-encoders. Under this framework, the problem of discovering latent structures is formulated as inferring the latent ties from partial observations. A latent transmission matrix that describes the strengths of existing edges and latent ties is derived based on influence cascades sampled by simulating diffusion processes over networks. Besides, since the inference process may bring extra noises, we introduce an adversarial training that works as regularization to dislodge noises and improve the model robustness. Extensive experiments on link prediction and node classification tasks show that the proposed model achieves superior results compared with baseline models.
Real-world information networks are increasingly occurring across various disciplines including online social networks and citation networks. These network data are generally characterized by sparseness, nonlinearity and heterogeneity bringing different challenges to the network analytics task to capture inherent properties from network data. Artificial intelligence and machine learning have been recently leveraged as powerful systems to learn insights from network data and deal with presented challenges. As part of machine learning techniques, graph embedding approaches are originally conceived for graphs constructed from feature represented datasets, like image dataset, in which links between nodes are explicitly defined. These traditional approaches cannot cope with network data challenges. As a new learning paradigm, network representation learning has been proposed to map a real-world information network into a low-dimensional space while preserving inherent properties of the network. In this paper, we present a systematic comprehensive survey of network representation learning, known also as network embedding, from birth to the current development state. Through the undertaken survey, we provide a comprehensive view of reasons behind the emergence of network embedding and, types of settings and models used in the network embedding pipeline. Thus, we introduce a brief history of representation learning and word representation learning ancestor of network embedding. We provide also formal definitions of basic concepts required to understand network representation learning followed by a description of network embedding pipeline. Most commonly used downstream tasks to evaluate embeddings, their evaluation metrics and popular datasets are highlighted. Finally, we present the open-source libraries for network embedding.