As an essential resource management problem in network virtualization, virtual network embedding (VNE) aims to allocate the finite resources of physical network to sequentially arriving virtual network requests (VNRs) with different resource demands. Since this is an NP-hard combinatorial optimization problem, many efforts have been made to provide viable solutions. However, most existing approaches have either ignored the admission control of VNRs, which has a potential impact on long-term performances, or not fully exploited the temporal and topological features of the physical network and VNRs. In this paper, we propose a deep Hierarchical Reinforcement Learning approach to learn a joint Admission Control and Resource Allocation policy for VNE, named HRL-ACRA. Specifically, the whole VNE process is decomposed into an upper-level policy for deciding whether to admit the arriving VNR or not and a lower-level policy for allocating resources of the physical network to meet the requirement of VNR through the HRL approach. Considering the proximal policy optimization as the basic training algorithm, we also adopt the average reward method to address the infinite horizon problem of the upper-level agent and design a customized multi-objective intrinsic reward to alleviate the sparse reward issue of the lower-level agent. Moreover, we develop a deep feature-aware graph neural network to capture the features of VNR and physical network and exploit a sequence-to-sequence model to generate embedding actions iteratively. Finally, extensive experiments are conducted in various settings, and show that HRL-ACRA outperforms state-of-the-art baselines in terms of both the acceptance ratio and long-term average revenue. Our code is available at \url{https://github.com/GeminiLight/hrl-acra}.
The recent past has witnessed a notable surge in on-demand food delivery (OFD) services, offering delivery fulfillment within dozens of minutes after an order is placed. In OFD, pooling multiple orders for simultaneous delivery in real-time order assignment is a pivotal efficiency source, which may in turn extend delivery time. Constructing high-quality order pooling to harmonize platform efficiency with the experiences of consumers and couriers, is crucial to OFD platforms. However, the complexity and real-time nature of order assignment, making extensive calculations impractical, significantly limit the potential for order consolidation. Moreover, offline environment is frequently riddled with unknown factors, posing challenges for the platform's perceptibility and pooling decisions. Nevertheless, delivery behaviors of skilled couriers (SCs) who know the environment well, can improve system awareness and effectively inform decisions. Hence a SC delivery network (SCDN) is constructed, based on an enhanced attributed heterogeneous network embedding approach tailored for OFD. It aims to extract features from rich temporal and spatial information, and uncover the latent potential for order combinations embedded within SC trajectories. Accordingly, the vast search space of order assignment can be effectively pruned through scalable similarity calculations of low-dimensional vectors, making comprehensive and high-quality pooling outcomes more easily identified in real time. SCDN has now been deployed in Meituan dispatch system. Online tests reveal that with SCDN, the pooling quality and extent have been greatly improved. And our system can boost couriers'efficiency by 45-55% during noon peak hours, while upholding the timely delivery commitment.
Deriving meaningful representations from complex, high-dimensional data in unsupervised settings is crucial across diverse machine learning applications. This paper introduces a framework for multi-scale graph network embedding based on spectral graph wavelets that employs a contrastive learning approach. We theoretically show that in Paley-Wiener spaces on combinatorial graphs, the spectral graph wavelets operator provides greater flexibility and control over smoothness compared to the Laplacian operator, motivating our approach. An additional key advantage of the proposed embedding is its ability to establish a correspondence between the embedding and input feature spaces, enabling the derivation of feature importance. We validate the effectiveness of our graph embedding framework on multiple public datasets across various downstream tasks, including clustering and unsupervised feature importance.
Heterogeneous, interconnected, systems-level, molecular data have become increasingly available and key in precision medicine. We need to utilize them to better stratify patients into risk groups, discover new biomarkers and targets, repurpose known and discover new drugs to personalize medical treatment. Existing methodologies are limited and a paradigm shift is needed to achieve quantitative and qualitative breakthroughs. In this perspective paper, we survey the literature and argue for the development of a comprehensive, general framework for embedding of multi-scale molecular network data that would enable their explainable exploitation in precision medicine in linear time. Network embedding methods map nodes to points in low-dimensional space, so that proximity in the learned space reflects the network's topology-function relationships. They have recently achieved unprecedented performance on hard problems of utilizing few omic data in various biomedical applications. However, research thus far has been limited to special variants of the problems and data, with the performance depending on the underlying topology-function network biology hypotheses, the biomedical applications and evaluation metrics. The availability of multi-omic data, modern graph embedding paradigms and compute power call for a creation and training of efficient, explainable and controllable models, having no potentially dangerous, unexpected behaviour, that make a qualitative breakthrough. We propose to develop a general, comprehensive embedding framework for multi-omic network data, from models to efficient and scalable software implementation, and to apply it to biomedical informatics. It will lead to a paradigm shift in computational and biomedical understanding of data and diseases that will open up ways to solving some of the major bottlenecks in precision medicine and other domains.
Virtual network embedding (VNE) is an essential resource allocation task in network virtualization, aiming to map virtual network requests (VNRs) onto physical infrastructure. Reinforcement learning (RL) has recently emerged as a promising solution to this problem. However, existing RL-based VNE methods are limited by the unidirectional action design and one-size-fits-all training strategy, resulting in restricted searchability and generalizability. In this paper, we propose a FLexible And Generalizable RL framework for VNE, named FlagVNE. Specifically, we design a bidirectional action-based Markov decision process model that enables the joint selection of virtual and physical nodes, thus improving the exploration flexibility of solution space. To tackle the expansive and dynamic action space, we design a hierarchical decoder to generate adaptive action probability distributions and ensure high training efficiency. Furthermore, to overcome the generalization issue for varying VNR sizes, we propose a meta-RL-based training method with a curriculum scheduling strategy, facilitating specialized policy training for each VNR size. Finally, extensive experimental results show the effectiveness of FlagVNE across multiple key metrics. Our code is available at GitHub (https://github.com/GeminiLight/flag-vne).
Latent fingerprints are one of the most widely used forensic evidence by law enforcement agencies. However, latent recognition performance is far from the exemplary performance of sensor fingerprint recognition due to deformations and artifacts within these images. In this study, we propose a fusion based local matching approach towards latent fingerprint recognition. Recent latent recognition studies typically relied on local descriptor generation methods, in which either handcrafted minutiae features or deep neural network features are extracted around a minutia of interest, in the latent recognition process. Proposed approach would integrate these handcrafted features with a recently proposed deep neural network embedding features in a multi-stage fusion approach to significantly improve latent recognition results. Effectiveness of the proposed approach has been shown on several public and private data sets. As demonstrated in our experimental results, proposed method improves rank-1 identification accuracy by considerably for real-world datasets when compared to either the single usage of these features or existing state-of-the-art methods in the literature.
Understanding the structure and dynamics of scientific research, i.e., the science of science (SciSci), has become an important area of research in order to address imminent questions including how scholars interact to advance science, how disciplines are related and evolve, and how research impact can be quantified and predicted. Central to the study of SciSci has been the analysis of citation networks. Here, two prominent modeling methodologies have been employed: one is to assess the citation impact dynamics of papers using parametric distributions, and the other is to embed the citation networks in a latent space optimal for characterizing the static relations between papers in terms of their citations. Interestingly, citation networks are a prominent example of single-event dynamic networks, i.e., networks for which each dyad only has a single event (i.e., the point in time of citation). We presently propose a novel likelihood function for the characterization of such single-event networks. Using this likelihood, we propose the Dynamic Impact Single-Event Embedding model (DISEE). The \textsc{\modelabbrev} model characterizes the scientific interactions in terms of a latent distance model in which random effects account for citation heterogeneity while the time-varying impact is characterized using existing parametric representations for assessment of dynamic impact. We highlight the proposed approach on several real citation networks finding that the DISEE well reconciles static latent distance network embedding approaches with classical dynamic impact assessments.
Embedding entities and relations into continuous vector spaces has attracted a surge of interest in recent years. Most embedding methods assume that all test entities are available during training, which makes it time-consuming to retrain embeddings for newly emerging entities. To address this issue, recent works apply the graph neural network on the existing neighbors of the unseen entities. In this paper, we propose a novel framework, namely Virtual Neighbor (VN) network, to address three key challenges. Firstly, to reduce the neighbor sparsity problem, we introduce the concept of the virtual neighbors inferred by rules. And we assign soft labels to these neighbors by solving a rule-constrained problem, rather than simply regarding them as unquestionably true. Secondly, many existing methods only use one-hop or two-hop neighbors for aggregation and ignore the distant information that may be helpful. Instead, we identify both logic and symmetric path rules to capture complex patterns. Finally, instead of one-time injection of rules, we employ an iterative learning scheme between the embedding method and virtual neighbor prediction to capture the interactions within. Experimental results on two knowledge graph completion tasks demonstrate that our VN network significantly outperforms state-of-the-art baselines. Furthermore, results on Subject/Object-R show that our proposed VN network is highly robust to the neighbor sparsity problem.
In this paper, we investigate the loss landscape of one-hidden-layer neural networks with ReLU-like activation functions trained with the empirical squared loss. As the activation function is non-differentiable, it is so far unclear how to completely characterize the stationary points. We propose the conditions for stationarity that apply to both non-differentiable and differentiable cases. Additionally, we show that, if a stationary point does not contain "escape neurons", which are defined with first-order conditions, then it must be a local minimum. Moreover, for the scalar-output case, the presence of an escape neuron guarantees that the stationary point is not a local minimum. Our results refine the description of the saddle-to-saddle training process starting from infinitesimally small (vanishing) initialization for shallow ReLU-like networks, linking saddle escaping directly with the parameter changes of escape neurons. Moreover, we are also able to fully discuss how network embedding, which is to instantiate a narrower network within a wider network, reshapes the stationary points.
For analysing real-world networks, graph representation learning is a popular tool. These methods, such as a graph autoencoder (GAE), typically rely on low-dimensional representations, also called embeddings, which are obtained through minimising a loss function; these embeddings are used with a decoder for downstream tasks such as node classification and edge prediction. While GAEs tend to be fairly accurate, they suffer from scalability issues. For improved speed, a Local2Global approach, which combines graph patch embeddings based on eigenvector synchronisation, was shown to be fast and achieve good accuracy. Here we propose L2G2G, a Local2Global method which improves GAE accuracy without sacrificing scalability. This improvement is achieved by dynamically synchronising the latent node representations, while training the GAEs. It also benefits from the decoder computing an only local patch loss. Hence, aligning the local embeddings in each epoch utilises more information from the graph than a single post-training alignment does, while maintaining scalability. We illustrate on synthetic benchmarks, as well as real-world examples, that L2G2G achieves higher accuracy than the standard Local2Global approach and scales efficiently on the larger data sets. We find that for large and dense networks, it even outperforms the slow, but assumed more accurate, GAEs.
Graph theoretical approaches have been proven to be effective in the characterization of connected systems, as well as in quantifying their dysfunction due to perturbation. In this paper, we show the advantage of a non-Euclidean (hyperbolic) representation of networks to identify local connectivity perturbations and to characterize the induced effects on a large scale. We propose two perturbation scores based on representations of the networks in a latent geometric space, obtained through an embedding onto the hyperbolic Poincar\'e disk. We numerically demonstrate that these methods are able to localize perturbations in networks with homogeneous or heterogeneous degree connectivity. We apply this framework to identify the most perturbed brain areas in epileptic patients following surgery. This study is conceived in the effort of developing more powerful tools to represent and analyze brain networks, and it is the first to apply geometric network embedding techniques to the case of epilepsy.
In order to efficiently explore the chemical space of all possible small molecules, a common approach is to compress the dimension of the system to facilitate downstream machine learning tasks. Towards this end, we present a data driven approach for clustering potential energy landscapes of molecular structures by applying recently developed Network Embedding techniques, to obtain latent variables defined through the embedding function. To scale up the method, we also incorporate an entropy sensitive adaptive scheme for hierarchical sampling of the energy landscape, based on Metadynamics and Transition Path Theory. By taking into account the kinetic information implied by a system's energy landscape, we are able to interpret dynamical node-node relationships in reduced dimensions. We demonstrate the framework through Lennard-Jones (LJ) clusters and a human DNA sequence.
Networks are one of the most valuable data structures for modeling problems in the real world. However, the most recent node embedding strategies have focused on undirected graphs, with limited attention to directed graphs, especially directed heterogeneous graphs. In this study, we first investigated the network properties of directed heterogeneous graphs. Based on network analysis, we proposed an embedding method, a bidirectional heterogeneous graph neural network with random teleport (BHGNN-RT), for directed heterogeneous graphs, that leverages bidirectional message-passing process and network heterogeneity. With the optimization of teleport proportion, BHGNN-RT is beneficial to overcome the over-smoothing problem. Extensive experiments on various datasets were conducted to verify the efficacy and efficiency of BHGNN-RT. Furthermore, we investigated the effects of message components, model layer, and teleport proportion on model performance. The performance comparison with all other baselines illustrates that BHGNN-RT achieves state-of-the-art performance, outperforming the benchmark methods in both node classification and unsupervised clustering tasks.
Sustainable investing refers to the integration of environmental and social aspects in investors' decisions. We propose a novel methodology based on the Triangulated Maximally Filtered Graph and node2vec algorithms to construct an hedging portfolio for climate risk, represented by various risk factors, among which the CO2 and the ESG ones. The CO2 factor is strongly correlated consistently over time with the Utility sector, which is the most carbon intensive in the S&P 500 index. Conversely, identifying a group of sectors linked to the ESG factor proves challenging. As a consequence, while it is possible to obtain an efficient hedging portfolio strategy with our methodology for the carbon factor, the same cannot be achieved for the ESG one. The ESG scores appears to be an indicator too broadly defined for market applications. These results support the idea that bank capital requirements should take into account carbon risk.
In this paper, we address the problem of dynamic network embedding, that is, representing the nodes of a dynamic network as evolving vectors within a low-dimensional space. While the field of static network embedding is wide and established, the field of dynamic network embedding is comparatively in its infancy. We propose that a wide class of established static network embedding methods can be used to produce interpretable and powerful dynamic network embeddings when they are applied to the dilated unfolded adjacency matrix. We provide a theoretical guarantee that, regardless of embedding dimension, these unfolded methods will produce stable embeddings, meaning that nodes with identical latent behaviour will be exchangeable, regardless of their position in time or space. We additionally define a hypothesis testing framework which can be used to evaluate the quality of a dynamic network embedding by testing for planted structure in simulated networks. Using this, we demonstrate that, even in trivial cases, unstable methods are often either conservative or encode incorrect structure. In contrast, we demonstrate that our suite of stable unfolded methods are not only more interpretable but also more powerful in comparison to their unstable counterparts.
The problem of representing nodes in a signed network as low-dimensional vectors, known as signed network embedding (SNE), has garnered considerable attention in recent years. While several SNE methods based on graph convolutional networks (GCN) have been proposed for this problem, we point out that they significantly rely on the assumption that the decades-old balance theory always holds in the real-world. To address this limitation, we propose a novel GCN-based SNE approach, named as TrustSGCN, which corrects for incorrect embedding propagation in GCN by utilizing the trustworthiness on edge signs for high-order relationships inferred by the balance theory. The proposed approach consists of three modules: (M1) generation of each node's extended ego-network; (M2) measurement of trustworthiness on edge signs; and (M3) trustworthiness-aware propagation of embeddings. Furthermore, TrustSGCN learns the node embeddings by leveraging two well-known societal theories, i.e., balance and status. The experiments on four real-world signed network datasets demonstrate that TrustSGCN consistently outperforms five state-of-the-art GCN-based SNE methods. The code is available at https://github.com/kmj0792/TrustSGCN.
Graph representation learning (GRL) has become a prominent tool for furthering the understanding of complex networks providing tools for network embedding, link prediction, and node classification. In this paper, we propose the Hybrid Membership-Latent Distance Model (HM-LDM) by exploring how a Latent Distance Model (LDM) can be constrained to a latent simplex. By controlling the edge lengths of the corners of the simplex, the volume of the latent space can be systematically controlled. Thereby communities are revealed as the space becomes more constrained, with hard memberships being recovered as the simplex volume goes to zero. We further explore a recent likelihood formulation for signed networks utilizing the Skellam distribution to account for signed weighted networks and extend the HM-LDM to the signed Hybrid Membership-Latent Distance Model (sHM-LDM). Importantly, the induced likelihood function explicitly attracts nodes with positive links and deters nodes from having negative interactions. We demonstrate the utility of HM-LDM and sHM-LDM on several real networks. We find that the procedures successfully identify prominent distinct structures, as well as how nodes relate to the extracted aspects providing favorable performances in terms of link prediction when compared to prominent baselines. Furthermore, the learned soft memberships enable easily interpretable network visualizations highlighting distinct patterns.
In this paper, we propose an efficient numerical implementation of Network Embedding based on commute times, using sparse approximation of a diffusion process on the network obtained by a modified version of the diffusion wavelet algorithm. The node embeddings are computed by optimizing the cross entropy loss via the stochastic gradient descent method with sampling of low-dimensional representations of green functions. We demonstrate the efficacy of this method for data clustering and multi-label classification through several examples, and compare its performance over existing methods in terms of efficiency and accuracy. Theoretical issues justifying the scheme are also discussed.
The presence of tertiary lymphoid structures (TLSs) on pancreatic pathological images is an important prognostic indicator of pancreatic tumors. Therefore, TLSs detection on pancreatic pathological images plays a crucial role in diagnosis and treatment for patients with pancreatic tumors. However, fully supervised detection algorithms based on deep learning usually require a large number of manual annotations, which is time-consuming and labor-intensive. In this paper, we aim to detect the TLSs in a manner of few-shot learning by proposing a weakly supervised segmentation network. We firstly obtain the lymphocyte density maps by combining a pretrained model for nuclei segmentation and a domain adversarial network for lymphocyte nuclei recognition. Then, we establish a cross-scale attention guidance mechanism by jointly learning the coarse-scale features from the original histopathology images and fine-scale features from our designed lymphocyte density attention. A noise-sensitive constraint is introduced by an embedding signed distance function loss in the training procedure to reduce tiny prediction errors. Experimental results on two collected datasets demonstrate that our proposed method significantly outperforms the state-of-the-art segmentation-based algorithms in terms of TLSs detection accuracy. Additionally, we apply our method to study the congruent relationship between the density of TLSs and peripancreatic vascular invasion and obtain some clinically statistical results.
The Random Dot Product Graph (RDPG) is a generative model for relational data, where nodes are represented via latent vectors in low-dimensional Euclidean space. RDPGs crucially postulate that edge formation probabilities are given by the dot product of the corresponding latent positions. Accordingly, the embedding task of estimating these vectors from an observed graph is typically posed as a low-rank matrix factorization problem. The workhorse Adjacency Spectral Embedding (ASE) enjoys solid statistical properties, but it is formally solving a surrogate problem and can be computationally intensive. In this paper, we bring to bear recent advances in non-convex optimization and demonstrate their impact to RDPG inference. We advocate first-order gradient descent methods to better solve the embedding problem, and to organically accommodate broader network embedding applications of practical relevance. Notably, we argue that RDPG embeddings of directed graphs loose interpretability unless the factor matrices are constrained to have orthogonal columns. We thus develop a novel feasible optimization method in the resulting manifold. The effectiveness of the graph representation learning framework is demonstrated on reproducible experiments with both synthetic and real network data. Our open-source algorithm implementations are scalable, and unlike the ASE they are robust to missing edge data and can track slowly-varying latent positions from streaming graphs.