At most 1-2% of the global virome has been sampled to date. Recent work has shown that predicting which host-virus interactions are possible but undiscovered or unrealized is, fundamentally, a network science problem. Here, we develop a novel method that combines a coarse recommender system (Linear Filtering; LF) with an imputation algorithm based on low-rank graph embedding (Singular Value Decomposition; SVD) to infer host-virus associations. This combination of techniques results in informed initial guesses based on directly measurable network properties (density, degree distribution) that are refined through SVD (which is able to leverage emerging features). Using this method, we recovered highly plausible undiscovered interactions with a strong signal of viral coevolutionary history, and revealed a global hotspot of unusually unique but unsampled (or unrealized) host-virus interactions in the Amazon rainforest. We develop several tests for quantifying the bias and realism of these predictions, and show that the LF-SVD method is robust in each aspect. We finally show that graph embedding of the imputed network can be used to improve predictions of human infection from viral genome features, showing that the global structure of the mammal-virus network provides additional insights into human disease emergence.
Dynamic Network Embedding (DNE) has recently attracted considerable attention due to the advantage of network embedding in various fields and the dynamic nature of many real-world networks. An input dynamic network to DNE is often assumed to have smooth changes over snapshots, which however would not hold for all real-world scenarios. It is natural to ask if existing DNE methods can perform well for an input dynamic network without smooth changes. To quantify it, an index called Degree of Changes (DoCs) is suggested so that the smaller DoCs indicates the smoother changes. Our comparative study shows several DNE methods are not robust enough to different DoCs even if the corresponding input dynamic networks come from the same dataset, which would make these methods unreliable and hard to use for unknown real-world applications. To propose an effective and more robust DNE method, we follow the notion of ensembles where each base learner adopts an incremental Skip-Gram embedding model. To further boost the performance, a simple yet effective strategy is designed to enhance the diversity among base learners at each timestep by capturing different levels of local-global topology. Extensive experiments demonstrate the superior effectiveness and robustness of the proposed method compared to state-of-the-art DNE methods, as well as the benefits of special designs in the proposed method and its scalability.
This paper explores whether graph embedding methods can be used as a tool for analysing the robustness of power-grids within the framework of network science. The paper focuses on the strain elevation tension spring embedding (SETSe) algorithm and compares it to node2vec and Deep Graph Infomax, and the measures mean edge capacity and line load. These five methods are tested on how well they can predict the collapse point of the giant component of a network under random attack. The analysis uses seven power-grid networks, ranging from 14 to 2000 nodes. In total, 3456 load profiles are created for each network by loading the edges of the network to have a range of tolerances and concentrating network capacity into fewer edges. One hundred random attack sequences are generated for each load profile, and the mean number of attacks required for the giant component to collapse for each profile is recorded. The relationship between the embedding values for each load profile and the mean collapse point is then compared across all five methods. It is found that only SETSe and line load perform well as proxies for robustness with $R^2 = 0.89$ for both measures. When tested on a time series normal operating conditions line load performs exceptionally well ($R=0.99$). However, the SETSe algorithm provides valuable qualitative insight into the state of the power-grid by leveraging its method local smoothing and global weighting of node features to provide an interpretable geographical embedding. This paper shows that graph representation algorithms can be used to analyse network properties such as robustness to cascading failure attacks, even when the network is embedded at node level.
Hyperbolic space and hyperbolic embeddings are becoming a popular research field for recommender systems. However, it is not clear under what circumstances the hyperbolic space should be considered. To fill this gap, This paper provides theoretical analysis and empirical results on when and where to use hyperbolic space and hyperbolic embeddings in recommender systems. Specifically, we answer the questions that which type of models and datasets are more suited for hyperbolic space, as well as which latent size to choose. We evaluate our answers by comparing the performance of Euclidean space and hyperbolic space on different latent space models in both general item recommendation domain and social recommendation domain, with 6 widely used datasets and different latent sizes. Additionally, we propose a new metric learning based recommendation method called SCML and its hyperbolic version HSCML. We evaluate our conclusions regarding hyperbolic space on SCML and show the state-of-the-art performance of hyperbolic space by comparing HSCML with other baseline methods.
Recent years have witnessed the tremendous research interests in network embedding. Extant works have taken the neighborhood formation as the critical information to reveal the inherent dynamics of network structures, and suggested encoding temporal edge formation sequences to capture the historical influences of neighbors. In this paper, however, we argue that the edge formation can be attributed to a variety of driving factors including the temporal influence, which is better referred to as multiple aspects. As a matter of fact, different node aspects can drive the formation of distinctive neighbors, giving birth to the multi-aspect embedding that relates to but goes beyond a temporal scope. Along this vein, we propose a Mixture of Hawkes-based Temporal Network Embeddings (MHNE) model to capture the aspect-driven neighborhood formation of networks. In MHNE, we encode the multi-aspect embeddings into the mixture of Hawkes processes to gain the advantages in modeling the excitation effects and the latent aspects. Specifically, a graph attention mechanism is used to assign different weights to account for the excitation effects of history events, while a Gumbel-Softmax is plugged in to derive the distribution over the aspects. Extensive experiments on 8 different temporal networks have demonstrated the great performance of the multi-aspect embeddings obtained by MHNE in comparison with the state-of-the-art methods.
The prediction for information diffusion on social networks has great practical significance in marketing and public opinion control. It aims to predict the individuals who will potentially repost the message on the social network. One type of method is based on demographics, complex networks and other prior knowledge to establish an interpretable model to simulate and predict the propagation process, while the other type of method is completely data-driven and maps the nodes to a latent space for propagation prediction. Existing latent space design and embedding methods lack consideration for the intervene among users. In this paper, we propose an independent asymmetric embedding method to embed each individual into one latent influence space and multiple latent susceptibility spaces. Based on the similarity between information diffusion and heat diffusion phenomenon, the heat diffusion kernel is exploited in our model and establishes the embedding rules. Furthermore, our method captures the co-occurrence regulation of user combinations in cascades to improve the calculating effectiveness. The results of extensive experiments conducted on real-world datasets verify both the predictive accuracy and cost-effectiveness of our approach.
Network Embedding aims to learn a function mapping the nodes to Euclidean space contribute to multiple learning analysis tasks on networks. However, the noisy information behind the real-world networks and the overfitting problem both negatively impact the quality of embedding vectors. To tackle these problems, researchers utilize Adversarial Training for Network Embedding (AdvTNE) and achieve state-of-the-art performance. Unlike the mainstream methods introducing perturbations on the network structure or the data feature, AdvTNE directly perturbs the model parameters, which provides a new chance to understand the mechanism behind. In this paper, we explain AdvTNE theoretically from an optimization perspective. Considering the Power-law property of networks and the optimization objective, we analyze the reason for its excellent results. According to the above analysis, we propose a new activation to enhance the performance of AdvTNE. We conduct extensive experiments on four real networks to validate the effectiveness of our method in node classification and link prediction. The results demonstrate that our method is superior to the state-of-the-art baseline methods.
Alarm root cause analysis is a significant component in the day-to-day telecommunication network maintenance, and it is critical for efficient and accurate fault localization and failure recovery. In practice, accurate and self-adjustable alarm root cause analysis is a great challenge due to network complexity and vast amounts of alarms. A popular approach for failure root cause identification is to construct a graph with approximate edges, commonly based on either event co-occurrences or conditional independence tests. However, considerable expert knowledge is typically required for edge pruning. We propose a novel data-driven framework for root cause alarm localization, combining both causal inference and network embedding techniques. In this framework, we design a hybrid causal graph learning method (HPCI), which combines Hawkes Process with Conditional Independence tests, as well as propose a novel Causal Propagation-Based Embedding algorithm (CPBE) to infer edge weights. We subsequently discover root cause alarms in a real-time data stream by applying an influence maximization algorithm on the weighted graph. We evaluate our method on artificial data and real-world telecom data, showing a significant improvement over the best baselines.
Over the recent years, Graph Neural Networks have become increasingly popular in network analytic and beyond. With that, their architecture noticeable diverges from the classical multi-layered hierarchical organization of the traditional neural networks. At the same time, many conventional approaches in network science efficiently utilize the hierarchical approaches to account for the hierarchical organization of the networks, and recent works emphasize their critical importance. This paper aims to connect the dots between the traditional Neural Network and the Graph Neural Network architectures as well as the network science approaches, harnessing the power of the hierarchical network organization. A Hierarchical Graph Neural Network architecture is proposed, supplementing the original input network layer with the hierarchy of auxiliary network layers and organizing the computational scheme updating the node features through both - horizontal network connections within each layer as well as the vertical connection between the layers. It enables simultaneous learning of the individual node features along with the aggregated network features at variable resolution and uses them to improve the convergence and stability of the individual node feature learning. The proposed Hierarchical Graph Neural network architecture is successfully evaluated on the network embedding and modeling as well as network classification, node labeling, and community tasks and demonstrates increased efficiency in those.
Signed network embedding is an approach to learn low-dimensional representations of nodes in signed networks with both positive and negative links, which facilitates downstream tasks such as link prediction with general data mining frameworks. Due to the distinct properties and significant added value of negative links, existing signed network embedding methods usually design dedicated methods based on social theories such as balance theory and status theory. However, existing signed network embedding methods ignore the characteristics of multiple facets of each node and mix them up in one single representation, which limits the ability to capture the fine-grained attentions between node pairs. In this paper, we propose MUSE, a MUlti-faceted attention-based Signed network Embedding framework to tackle this problem. Specifically, a joint intra- and inter-facet attention mechanism is introduced to aggregate fine-grained information from neighbor nodes. Moreover, balance theory is also utilized to guide information aggregation from multi-order balanced and unbalanced neighbors. Experimental results on four real-world signed network datasets demonstrate the effectiveness of our proposed framework.
Network-structured data becomes ubiquitous in daily life and is growing at a rapid pace. It presents great challenges to feature engineering due to the high non-linearity and sparsity of the data. The local and global structure of the real-world networks can be reflected by dynamical transfer behaviors among nodes. This paper proposes a network embedding framework to capture the transfer behaviors on structured networks via deep prediction models. We first design a degree-weight biased random walk model to capture the transfer behaviors on the network. Then a deep network embedding method is introduced to preserve the transfer possibilities among the nodes. A network structure embedding layer is added into conventional deep prediction models, including Long Short-Term Memory Network and Recurrent Neural Network, to utilize the sequence prediction ability. To keep the local network neighborhood, we further perform a Laplacian supervised space optimization on the embedding feature representations. Experimental studies are conducted on various datasets including social networks, citation networks, biomedical network, collaboration network and language network. The results show that the learned representations can be effectively used as features in a variety of tasks, such as clustering, visualization, classification, reconstruction and link prediction, and achieve promising performance compared with state-of-the-arts.
We present a collaborative learning method called Mutual Contrastive Learning (MCL) for general visual representation learning. The core idea of MCL is to perform mutual interaction and transfer of contrastive distributions among a cohort of networks. A crucial component of MCL is Interactive Contrastive Learning (ICL). Compared with vanilla contrastive learning, ICL can aggregate cross-network embedding information and maximize the lower bound to the mutual information between two networks. This enables each network to learn extra contrastive knowledge from others, leading to better feature representations for visual recognition tasks. We emphasize that the resulting MCL is conceptually simple yet empirically powerful. It is a generic framework that can be applied to both supervised and self-supervised representation learning. Experimental results on image classification and transfer learning to object detection show that MCL can lead to consistent performance gains, demonstrating that MCL can guide the network to generate better feature representations. Code is available at https://github.com/winycg/MCL.
Answer selection (AS) is an essential subtask in the field of natural language processing with an objective to identify the most likely answer to a given question from a corpus containing candidate answer sentences. A common approach to address the AS problem is to generate an embedding for each candidate sentence and query. Then, select the sentence whose vector representation is closest to the query's. A key drawback is the low quality of the embeddings, hitherto, based on its performance on AS benchmark datasets. In this work, we present ASBERT, a framework built on the BERT architecture that employs Siamese and Triplet neural networks to learn an encoding function that maps a text to a fixed-size vector in an embedded space. The notion of distance between two points in this space connotes similarity in meaning between two texts. Experimental results on the WikiQA and TrecQA datasets demonstrate that our proposed approach outperforms many state-of-the-art baseline methods.
We study the problem of embedding edgeless nodes such as users who newly enter the underlying network, while using graph neural networks (GNNs) widely studied for effective representation learning of graphs. Our study is motivated by the fact that GNNs cannot be straightforwardly adopted for our problem since message passing to such edgeless nodes having no connections is impossible. To tackle this challenge, we propose Edgeless-GNN, a novel inductive framework that enables GNNs to generate node embeddings even for edgeless nodes through unsupervised learning. Specifically, we start by constructing a proxy graph based on the similarity of node attributes as the GNN's computation graph defined by the underlying network. The known network structure is used to train model parameters, whereas a topology-aware loss function is established in such a way that our model judiciously learns the network structure by encoding positive, negative, and second-order relations between nodes. For the edgeless nodes, we inductively infer embeddings by expanding the computation graph. By evaluating the performance of various downstream machine learning tasks, we empirically demonstrate that Edgeless-GNN exhibits (a) superiority over state-of-the-art inductive network embedding methods for edgeless nodes, (b) effectiveness of our topology-aware loss function, (c) robustness to incomplete node attributes, and (d) a linear scaling with the graph size.
Heterogeneous information networks(HINs) become popular in recent years for its strong capability of modelling objects with abundant information using explicit network structure. Network embedding has been proved as an effective method to convert information networks into lower-dimensional space, whereas the core information can be well preserved. However, traditional network embedding algorithms are sub-optimal in capturing rich while potentially incompatible semantics provided by HINs. To address this issue, a novel meta-path-based HIN representation learning framework named mSHINE is designed to simultaneously learn multiple node representations for different meta-paths. More specifically, one representation learning module inspired by the RNN structure is developed and multiple node representations can be learned simultaneously, where each representation is associated with one respective meta-path. By measuring the relevance between nodes with the designed objective function, the learned module can be applied in downstream link prediction tasks. A set of criteria for selecting initial meta-paths is proposed as the other module in mSHINE which is important to reduce the optimal meta-path selection cost when no prior knowledge of suitable meta-paths is available. To corroborate the effectiveness of mSHINE, extensive experimental studies including node classification and link prediction are conducted on five real-world datasets. The results demonstrate that mSHINE outperforms other state-of-the-art HIN embedding methods.
Since many real world networks are evolving over time, such as social networks and user-item networks, there are increasing research efforts on dynamic network embedding in recent years. They learn node representations from a sequence of evolving graphs but not only the latest network, for preserving both structural and temporal information from the dynamic networks. Due to the lack of comprehensive investigation of them, we give a survey of dynamic network embedding in this paper. Our survey inspects the data model, representation learning technique, evaluation and application of current related works and derives common patterns from them. Specifically, we present two basic data models, namely, discrete model and continuous model for dynamic networks. Correspondingly, we summarize two major categories of dynamic network embedding techniques, namely, structural-first and temporal-first that are adopted by most related works. Then we build a taxonomy that refines the category hierarchy by typical learning models. The popular experimental data sets and applications are also summarized. Lastly, we have a discussion of several distinct research topics in dynamic network embedding.
While most network embedding techniques model the relative positions of nodes in a network, recently there has been significant interest in structural embeddings that model node role equivalences, irrespective of their distances to any specific nodes. We present PhUSION, a proximity-based unified framework for computing structural and positional node embeddings, which leverages well-established methods for calculating node proximity scores. Clarifying a point of contention in the literature, we show which step of PhUSION produces the different kinds of embeddings and what steps can be used by both. Moreover, by aggregating the PhUSION node embeddings, we obtain graph-level features that model information lost by previous graph feature learning and kernel methods. In a comprehensive empirical study with over 10 datasets, 4 tasks, and 35 methods, we systematically reveal successful design choices for node and graph-level machine learning with embeddings.
Link prediction is a paradigmatic problem in network science, which aims at estimating the existence likelihoods of nonobserved links, based on known topology. After a brief introduction of the standard problem and metrics of link prediction, this Perspective will summarize representative progresses about local similarity indices, link predictability, network embedding, matrix completion, ensemble learning and others, mainly extracted from thousands of related publications in the last decade. Finally, this Perspective will outline some long-standing challenges for future studies.
As an effective technique to learn low-dimensional node features in complicated network environment, network embedding has become a promising research direction in the field of network analysis. Due to the virtues of better interpretability and flexibility, matrix factorization based methods for network embedding have received increasing attentions. However, most of them are inadequate to learn more complicated hierarchical features hidden in complex networks because of their mechanisms of single-layer factorization structure. Besides, their original feature matrices used for factorization and their robustness against noises also need to be further improved. To solve these problems, we propose a novel network embedding method named DRNMF (deep robust nonnegative matrix factorization), which is formed by multi-layer NMF learning structure. Meanwhile, DRNMF employs the combination of high-order proximity matrices of the network as the original feature matrix for the factorization. To improve the robustness against noises, we use `2,1 norm to devise the objective function for the DRNMF network embedding model. Effective iterative update rules are derived to resolve the model, and the convergence of these rules are strictly proved. Moreover, we introduce a pre-training strategy to improve the efficiency of convergence. Extensive experiments on several benchmarks of complex networks demonstrate that our proposed method DRNMF is effective and has better performance than the state-of-the-art matrix factorization based methods for network embedding.
We consider two popular Graph Representation Learning (GRL) methods: message passing for node classification and network embedding for link prediction. For each, we pick a popular model that we: (i) linearize and (ii) and switch its training objective to Frobenius norm error minimization. These simplifications can cast the training into finding the optimal parameters in closed-form. We program in TensorFlow a functional form of Truncated Singular Value Decomposition (SVD), such that, we could decompose a dense matrix $\mathbf{M}$, without explicitly computing $\mathbf{M}$. We achieve competitive performance on popular GRL tasks while providing orders of magnitude speedup. We open-source our code at http://github.com/samihaija/tf-fsvd