Network Features Research Articles

Identifiability of Level-1 Species Networks from Gene Tree Quartets

When hybridization or other forms of lateral gene transfer have occurred, evolutionary relationships of species are better represented by phylogenetic networks than by trees. While inference of such networks remains challenging, several recently proposed methods are based on quartet concordance factors—the probabilities that a tree relating a gene sampled from the species displays the possible 4-taxon relationships. Building on earlier results, we investigate what level-1 network features are identifiable from concordance factors under the network multispecies coalescent model. We obtain results on both topological features of the network, and numerical parameters, uncovering a number of failures of identifiability related to 3-cycles in the network. Addressing these identifiability issues is essential for designing statistically consistent inference methods.

4D dynamic spatial brain networks at rest linked to cognition show atypical variability and coupling in schizophrenia.

Despite increasing interest in the dynamics of functional brain networks, most studies focus on the changing relationships over time between spatially static networks or regions. Here we propose an approach to study dynamic spatial brain networks in human resting state functional magnetic resonance imaging (rsfMRI) data and evaluate the temporal changes in the volumes of these 4D networks. Our results show significant volumetric coupling (i.e., synchronized shrinkage and growth) between networks during the scan, that we refer to as dynamic spatial network connectivity (dSNC). We find that several features of such dynamic spatial brain networks are associated with cognition, with higher dynamic variability in these networks and higher volumetric coupling between network pairs positively associated with cognitive performance. We show that these networks are modulated differently in individuals with schizophrenia versus typical controls, resulting in network growth or shrinkage, as well as altered focus of activity within a network. Schizophrenia also shows lower spatial dynamical variability in several networks, and lower volumetric coupling between pairs of networks, thus upholding the role of dynamic spatial brain networks in cognitive impairment seen in schizophrenia. Our data show evidence for the importance of studying the typically overlooked voxel-wise changes within and between brain networks.

Frontoparietal and salience network synchronizations during nonsymbolic magnitude processing predict brain age and mathematical performance in youth.

The development and refinement of functional brain circuits crucial to human cognition is a continuous process that spans from childhood to adulthood. Research increasingly focuses on mapping these evolving configurations, with the aim to identify markers for functional impairments and atypical development. Among human cognitive systems, nonsymbolic magnitude representations serve as a foundational building block for future success in mathematical learning and achievement for individuals. Using task-based frontoparietal (FPN) and salience network (SN) features during nonsymbolic magnitude processing alongside machine learning algorithms, we developed a framework to construct brain age prediction models for participants aged 7-30. Our study revealed differential developmental profiles in the synchronization within and between FPN and SN networks. Specifically, we observed a linear increase in FPN connectivity, concomitant with a decline in SN connectivity across the age span. A nonlinear U-shaped trajectory in the connectivity between the FPN and SN was discerned, revealing reduced FPN-SN synchronization among adolescents compared to both pediatric and adult cohorts. Leveraging the Gradient Boosting machine learning algorithm and nested fivefold stratified cross-validation with independent training datasets, we demonstrated that functional connectivity measures of the FPN and SN nodes predict chronological age, with a correlation coefficient of .727 and a mean absolute error of 2.944 between actual and predicted ages. Notably, connectivity within the FPN emerged as the most contributing feature for age prediction. Critically, a more matured brain age estimate is associated with better arithmetic performance. Our findings shed light on the intricate developmental changes occurring in the neural networks supporting magnitude representations. We emphasize brain age estimation as a potent tool for understanding cognitive development and its relationship to mathematical abilities across the critical developmental period of youth. PRACTITIONER POINTS: This study investigated the prolonged changes in the brain's architecture across childhood, adolescence, and adulthood, with a focus on task-state frontoparietal and salience networks. Distinct developmental pathways were identified: frontoparietal synchronization strengthens consistently throughout development, while salience network connectivity diminishes with age. Furthermore, adolescents show a unique dip in connectivity between these networks. Leveraging advanced machine learning methods, we accurately predicted individuals' ages based on these brain circuits, with a more mature estimated brain age correlating with better math skills.

Conceptualizing the social networks of children of parents with serious mental illness: a thematic analysis.

Social networks, defined as the set of active and significant ties surrounding an individual, influence the wellbeing of vulnerable children. The best evidenced mechanism through which this occurs is where networks act as a vehicle to access social support. Little is known about the content and function of social networks of children of parents with severe and enduring mental illness (COPMI). COPMI are a frequently under-identified vulnerable child population at risk of negative outcomes. This qualitative study investigates the structure, role and function of these children's networks. Researchers conducted 17 semi-structured egocentric social network interviews. Interviews incorporated personal network mapping as a data collection method. COPMI were recruited through third sector organizations and interviewed across three sites in England. Data was analyzed using an inductive thematic analysis. Five network features were identified (i) parents as primary providers of support (i) limited networks and diminished connections over time (iii) substitutable ties (formal and informal) (iv) peer connections as source of both support and strain (v) coping strategies: self-censorship, avoidance and animals. Children of parents with severe and enduring mental illness networks are structurally typical of vulnerable children in that they are limited, rely on parents as primary ties but allow for some substitution of support ties. COPMI-specific features included peer relationships at times as source of strain and network level coping strategies used to manage wellbeing, including pets. This latter reflects previous findings in vulnerable adult populations so far unevidenced in children. Little evidence as to the mechanistic effect at work within networks was collected. However, COPMI were clearly shown to be engaged in active management and strategising in network navigation approaches, indicating the need to engage with children in this capacity, rather than approaching them as passive recipients of support. As such, effective network level interventions for this group are likely to prioritize access to beneficial substitute ties when support is limited. Additionally, interventions that promote network navigation skills and help foster productive coping strategies can capitalize on the child's active management role within their network.

Fault Diagnosis in Induction Motors through Infrared Thermal Images Using Convolutional Neural Network Feature Extraction

The development of diagnostic systems for rotating machines such as induction motors (IMs) is a task of utmost importance for the industrial sector. Reliable diagnostic systems allow for the accurate detection of different faults. Different methods based on the acquisition of thermal images (TIs) have emerged as diagnosis systems for the detection of IM faults to prevent the further generation of faults. However, these methods are based on artisanal feature selection, so obtaining high accuracy rates is usually challenging. For this reason, in this work, a new system for fault detection in IMs based on convolutional neural networks (CNNs) and thermal images (TIs) is presented. The system is based on the training of a CNN using TIs to select and extract the most salient features of each fault present in the IM. Subsequently, a classifier based on a decision tree (DT) algorithm is trained using the features learned by the CNN to infer the motor conditions. The results of this methodology show an improvement in the accuracy, precision, recall, and F1-score metrics for 11 different conditions.

Factors shaping network emergence: A cross-country comparison of quality of care networks in Bangladesh, Ethiopia, Malawi, and Uganda.

The Quality-of-Care Network (QCN) was conceptualized by the World Health Organization (WHO) and other global partners to facilitate learning on and improve quality of care for maternal and newborn health within and across low and middle-income countries. However, there was significant variance in the speed and extent to which QCN formed in the involved countries. This paper investigates the factors that shaped QCN's differential emergence in Bangladesh, Ethiopia, Malawi, and Uganda. Drawing on network scholarship, we conducted a replicated case study of the four country cases and triangulated several sources of data, including a document review, observations of national-level and district level meetings, and key informant interviews in each country and at the global level. Thematic coding was performed in NVivo 12. We find that QCN emerged most quickly and robustly in Bangladesh, followed by Ethiopia, then Uganda, and slowest and with least institutionalization in Malawi. Factors connected to the policy environment and network features explained variance in network emergence. With respect to the policy environment, pre-existing resources and initiatives dedicated to maternal and newborn health and quality improvement, strong data and health system capacity, and national commitment to advancing on synergistic goals were crucial drivers to QCN's emergence. With respect to the features of the network itself, the embedding of QCN leadership in powerful agencies with pre-existing coordination structures and trusting relationships with key stakeholders, inclusive network membership, and effective individual national and local leadership were also crucial in explaining QCN's speed and quality of emergence across countries. Studying QCN emergence provides critical insights as to why well-intentioned top-down global health networks may not materialize in some country contexts and have relatively quick uptake in others, and has implications for a network's perceived legitimacy and ultimate effectiveness in producing stated objectives.

TransUNet: Rethinking the U-Net architecture design for medical image segmentation through the lens of transformers

Medical image segmentation is crucial for healthcare, yet convolution-based methods like U-Net face limitations in modeling long-range dependencies. To address this, Transformers designed for sequence-to-sequence predictions have been integrated into medical image segmentation. However, a comprehensive understanding of Transformers’ self-attention in U-Net components is lacking. TransUNet, first introduced in 2021, is widely recognized as one of the first models to integrate Transformer into medical image analysis. In this study, we present the versatile framework of TransUNet that encapsulates Transformers’ self-attention into two key modules: (1) a Transformer encoder tokenizing image patches from a convolution neural network (CNN) feature map, facilitating global context extraction, and (2) a Transformer decoder refining candidate regions through cross-attention between proposals and U-Net features. These modules can be flexibly inserted into the U-Net backbone, resulting in three configurations: Encoder-only, Decoder-only, and Encoder+Decoder. TransUNet provides a library encompassing both 2D and 3D implementations, enabling users to easily tailor the chosen architecture. Our findings highlight the encoder’s efficacy in modeling interactions among multiple abdominal organs and the decoder’s strength in handling small targets like tumors. It excels in diverse medical applications, such as multi-organ segmentation, pancreatic tumor segmentation, and hepatic vessel segmentation. Notably, our TransUNet achieves a significant average Dice improvement of 1.06% and 4.30% for multi-organ segmentation and pancreatic tumor segmentation, respectively, when compared to the highly competitive nn-UNet, and surpasses the top-1 solution in the BrasTS2021 challenge. 2D/3D Code and models are available at https://github.com/Beckschen/TransUNet and https://github.com/Beckschen/TransUNet-3D, respectively.

Local and Global Context-Enhanced Lightweight CenterNet for PCB Surface Defect Detection.

Printed circuit board (PCB) surface defect detection is an essential part of the PCB manufacturing process. Currently, advanced CCD or CMOS sensors can capture high-resolution PCB images. However, the existing computer vision approaches for PCB surface defect detection require high computing effort, leading to insufficient efficiency. To this end, this article proposes a local and global context-enhanced lightweight CenterNet (LGCL-CenterNet) to detect PCB surface defects in real time. Specifically, we propose a two-branch lightweight vision transformer module with local and global attention, named LGT, as a complement to extract high-dimension features and leverage context-aware local enhancement after the backbone network. In the local branch, we utilize coordinate attention to aggregate more powerful features of PCB defects with different shapes. In the global branch, Bi-Level Routing Attention with pooling is used to capture long-distance pixel interactions with limited computational cost. Furthermore, a Path Aggregation Network (PANet) feature fusion structure is incorporated to mitigate the loss of shallow features caused by the increase in model depth. Then, we design a lightweight prediction head by using depthwise separable convolutions, which further compresses the computational complexity and parameters while maintaining the detection capability of the model. In the experiment, the LGCL-CenterNet increased the mAP@0.5 by 2% and 1.4%, respectively, in comparison to CenterNet-ResNet18 and YOLOv8s. Meanwhile, our approach requires fewer model parameters (0.542M) than existing techniques. The results show that the proposed method improves both detection accuracy and inference speed and indicate that the LGCL-CenterNet has better real-time performance and robustness.

YOLO-ADual: A Lightweight Traffic Sign Detection Model for a Mobile Driving System

Traffic sign detection plays a pivotal role in autonomous driving systems. The intricacy of the detection model necessitates high-performance hardware. Real-world traffic environments exhibit considerable variability and diversity, posing challenges for effective feature extraction by the model. Therefore, it is imperative to develop a detection model that is not only highly accurate but also lightweight. In this paper, we proposed YOLO-ADual, a novel lightweight model. Our method leverages the C3Dual and Adown lightweight modules as replacements for CPS and CBL modules in YOLOv5. The Adown module effectively mitigates feature loss during downsampling while reducing computational costs. Meanwhile, C3Dual optimizes the processing power for kernel feature extraction, enhancing computation efficiency while preserving network depth and feature extraction capability. Furthermore, the inclusion of the CBAM module enables the network to focus on salient information within the image, thus augmenting its feature representation capability. Our proposed algorithm achieves a mAP@0.5 of 70.1% while significantly reducing the number of parameters and computational requirements to 51.83% and 64.73% of the original model, respectively. Compared to various lightweight models, our approach demonstrates competitive performance in terms of both computational efficiency and accuracy.

Integration Policy Networks and the Potential for Local Integration Policy Diffusion in European Small- and Medium-Sized Towns and Rural Areas: A Comparative Analysis

This article aims to open a debate about the diffusion of local integration policies in European small- and medium-sized towns and rural areas (SMsTRAs), shedding light on local policymakers’ relational environment and key features of policy networks that influence policy diffusion. Elaborating on data collected through 343 interviews across 34 SMsTRAs, analysed through social network analysis and qualitative content analysis, it concludes that the relational environment in SMsTRAs is unfavourable for integration policy diffusion due to specific characteristics of integration policy networks and the growing politicisation of local integration policymaking. Nonetheless, relevant variation is identified across different types of SMsTRAs.

An Algorithm for Ship Detection in Complex Observation Scenarios Based on Mooring Buoys

Marine anchor buoys, as fixed-point profile observation platforms, are highly susceptible to the threat of ship collisions. Installing cameras on buoys can effectively monitor and collect evidence from ships. However, when using a camera to capture images, it is often affected by the continuous shaking of buoys and rainy and foggy weather, resulting in problems such as blurred images and rain and fog occlusion. To address these problems, this paper proposes an improved YOLOv8 algorithm. Firstly, the polarized self-attention (PSA) mechanism is introduced to preserve the high-resolution features of the original deep convolutional neural network and solve the problem of image spatial resolution degradation caused by shaking. Secondly, by introducing the multi-head self-attention (MHSA) mechanism in the neck network, the interference of rain and fog background is weakened, and the feature fusion ability of the network is improved. Finally, in the head network, this model combines additional small object detection heads to improve the accuracy of small object detection. Additionally, to enhance the algorithm’s adaptability to camera detection scenarios, this paper simulates scenarios, including shaking blur, rain, and foggy conditions. In the end, numerous comparative experiments on a self-made dataset show that the algorithm proposed in this study achieved 94.2% mAP50 and 73.2% mAP50:95 in various complex environments, which is superior to other advanced object detection algorithms.

GSRF-DTI: a framework for drug-target interaction prediction based on a drug-target pair network and representation learning on a large graph

BackgroundIdentification of potential drug-target interactions (DTIs) with high accuracy is a key step in drug discovery and repositioning, especially concerning specific drug targets. Traditional experimental methods for identifying the DTIs are arduous, time-intensive, and financially burdensome. In addition, robust computational methods have been developed for predicting the DTIs and are widely applied in drug discovery research. However, advancing more precise algorithms for predicting DTIs is essential to meet the stringent standards demanded by drug discovery.ResultsWe proposed a novel method called GSRF-DTI, which integrates networks with a deep learning algorithm to identify DTIs. Firstly, GSRF-DTI learned the embedding representation of drugs and targets by integrating multiple drug association information and target association information, respectively. Then, GSRF-DTI considered the influence of drug-target pair (DTP) association on DTI prediction to construct a drug-target pair network (DTP-NET). Next, we utilized GraphSAGE on DTP-NET to learn the potential features of the network and applied random forest (RF) to predict the DTIs. Furthermore, we conducted ablation experiments to validate the necessity of integrating different types of network features for identifying DTIs. It is worth noting that GSRF-DTI proposed three novel DTIs.ConclusionsGSRF-DTI not only considered the influence of the interaction relationship between drug and target but also considered the impact of DTP association relationship on DTI prediction. We initially use GraphSAGE to aggregate the neighbor information of nodes for better identification. Experimental analysis on Luo’s dataset and the newly constructed dataset revealed that the GSRF-DTI framework outperformed several state-of-the-art methods significantly.

A multi-model attention based CNN-BiLSTM model for personality traits prediction based on user behavior on social media

The prediction of an individual’s personality traits through the analysis of their online social media activities is an area of research that has gained considerable attention in the digital era. The statistical data derived from people’s thoughts that are conveyed through their status updates on social media serves as an essential resource for understanding the various aspects of human behavior and personality. The present study is motivated by the various applications associated with personality prediction, such as targeted advertising, personalized entertainment, and customized recommendations. A multi-model attention-based convolutional neural network-bidirectional long short-term memory (CNN+BiLSTM) is proposed in the present work for personality traits prediction. The proposed model utilizes pre-trained language models, such as Global Vectors for Word Representation (GloVe) and Bidirectional Encoder Representations from Transformers (BERT), to create vector representations of words, which effectively captures word semantics. Additionally, network features such as size, betweenness, transitivity, and density are integrated with text features to enhance personality traits prediction. The results highlight the contextual understanding of the BERT model and emphasize the effectiveness of the proposed model, particularly the fusion of the attention layer with the CNN+BiLSTM architecture, which significantly improves information extraction and prediction capabilities. The integration of social network features strengthens the classifier’s ability to predict personality traits, resulting in improved overall performance.

Quantifying the uncertainty of LLM hallucination spreading in complex adaptive social networks

Large language models (LLMs) are becoming a significant source of content generation in social networks, which is a typical complex adaptive system (CAS). However, due to their hallucinatory nature, LLMs produce false information that can spread through social networks, which will impact the stability of the whole society. The uncertainty of LLMs false information spread within social networks is attributable to the diversity of individual behaviors, intricate interconnectivity, and dynamic network structures. Quantifying the uncertainty of false information spread by LLMs in social networks is beneficial for preemptively devising strategies to defend against threats. To address these challenges, we propose an LLMs hallucination-aware dynamic modeling method via agent-based probability distributions, spread popularity and community affiliation, to quantify the uncertain spreading of LLMs hallucination in social networks. We set up the node attributes and behaviors in the model based on real-world data. For evaluation, we consider the spreaders, informed people, discerning and unwilling non-spreaders as indicators, and quantified the spreading under different LLMs task situations, such as QA, dialogue, and summarization, as well as LLMs versions. Furthermore, we conduct experiments using real-world LLM hallucination data combined with social network features to ensure the validity of the proposed quantifying scheme.

MRAU-net: Multi-scale residual attention U-shaped network for medical image segmentation

Medical image segmentation is a pivotal technology that assists doctors in making correct diagnoses and provides reliable evidence for pathological research. To address the insufficient attention to medical image details and the weak generalization ability of convolutional neural networks, we propose a novel multi-scale residual attention U-shaped network (MRAU-Net) for medical image segmentation. MRAU-Net employs a channel-wise compression strategy to construct the squeezed double convolution in the encoder, significantly reducing the network parameters while maintaining segmentation performance. In the decoder, a multi-scale residual attention block is designed to learn rich context information with multiple receptive fields, which effectively focuses on the target area and compensates for the lost information during the upsampling process through skip connections, enhancing the network's feature extraction capability. Experimental results on four biomedical image datasets show that our MRAU-Net performs better than the existing methods in terms of segmentation accuracy and generalization ability. mDices of MRAU-Net on JSUAHCerebellum, Kvasir-SEG, ISIC 2018 Challenge, and 2018 Data Science Bowl are 92.81 %, 88.64 %, 91.88 %, and 93.14 %, respectively, which are 7.61 %, 7.48 %, 6.34 %, and 2.34 % higher than that of the original U-Net.

A novel facial expression recognition model based on harnessing complementary features in multi-scale network with attention fusion

This paper presents a novel method for facial expression recognition using the proposed feature complementation and multi-scale attention model with attention fusion (FCMSA-AF). The proposed model consists of four main components: the shallow feature extractor module, parallel structured two-branch multi-scale attention module (MSA), feature complementing module (FCM), and attention fusion and classification module. The MSA module contains multi-scale attention modules in a cascaded fashion in two paths to learn diverse features. The upper and lower paths use left and right multi-scale blocks to extract and aggregate the features at different receptive fields. The attention networks in MSA focus on salient local regions to extract features at granular levels. The FCM uses the correlation between the feature maps in two paths to make the multi-scale attention features complementary to each other. Finally, the complementary features are fused through an attention network to form an informative holistic feature which includes subtle, visually varying regions in similar classes. Hence, complementary and informative features are used in classification to minimize information loss and capture the discriminating finer aspects of facial expression recognition. Experimental evaluation of the proposed model carried out on AffectNet and CK+ datasets achieve accuracies of 64.59% and 98.98%, respectively, outperforming some of the state-of-the-art methods.

К ВОПРОСУ ОБЕСПЕЧЕНИЯ СЕТЕВОЙ БЕЗОПАСНОСТИ

The following are considered:  principles and means of ensuring the security of a corporate network, as well as features of virtual private networks that provide reliable protection and secure data transmission;  principles and measures to ensure the security of the corporate network, as well as the types of information protection provided by these security measures;  virtual private networks (VPNs) that provide a secure encrypted user connection to the network. Using a VPN provides reliable data protection, masking the user's geolocation, access to regional content and secure data transfer;  systems for detecting and preventing network hacking threats, among which the main focus is on the Kali Linux software package, as well as features of the Windows subsystem for Linux and Windows network monitoring tools;  Windows network monitoring tools, including utilities that work in console command-line mode and allow you to check the availability of remote personal computers and diagnose the connection. The Kali Linux software package is a distribution package for the Linux operating system that has more than 600 preinstalled network penetration testing programs. Among the features of the package, the article discusses the search and exploitation of network vulnerabilities, checking the correct configuration of the SSL certificate and open ports, tracing the data transfer route, checking the availability of servers and searching for network problems.

The cereal network: a baseline approach to current configurations of trade communities

This paper attempts to provide insights into the current network configurations of the food-trade system and to study the short-term effects of one of the ongoing and lasting global crises, the Ukraine War, on the link intensity. Towards this end, this analysis (1) reveals the pattern of countries’ network positions in two most traded subcategories of the cereal network: wheat and meslin, and maize or corn, and (2) discusses the characteristics of the global cereal networks over the 2021–2022 period. The results highlight several features of the trade networks: (1) the distribution of cereal trade is highly concentrated, with considerable dependency on a small number of exporters and a low import diversification, making the system rigid and prone to shocks; (2) a central role of several key developed countries that leave many developing countries outside the centre of the networks; (3) a high network heterogeneity which confirms the propensity to have hub nodes. Particular indicators show that the highest level of interconnectivity is specific to the cereals’ export network, the densest networks are the maize or corn ones, and the greatest heterogeneity appears for the cereals export network.

DMFVAE: miRNA-disease associations prediction based on deep matrix factorization method with variational autoencoder

MicroRNAs (miRNAs) are closely related to numerous complex human diseases, therefore, exploring miRNA-disease associations (MDAs) can help people gain a better understanding of complex disease mechanism. An increasing number of computational methods have been developed to predict MDAs. However, the sparsity of the MDAs may hinder the performance of many methods. In addition, many methods fail to capture the nonlinear relationships of miRNA-disease network and inadequately leverage the features of network and neighbor nodes. In this study, we propose a deep matrix factorization model with variational autoencoder (DMFVAE) to predict potential MDAs. DMFVAE first decomposes the original association matrix and the enhanced association matrix, in which the enhanced association matrix is enhanced by self-adjusting the nearest neighbor method, to obtain sparse vectors and dense vectors, respectively. Then, the variational encoder is employed to obtain the nonlinear latent vectors of miRNA and disease for the sparse vectors, and meanwhile, node2vec is used to obtain the network structure embedding vectors of miRNA and disease for the dense vectors. Finally, sample features are acquired by combining the latent vectors and network structure embedding vectors, and the final prediction is implemented by convolutional neural network with channel attention. To evaluate the performance of DMFVAE, we conduct five-fold cross validation on the HMDD v2.0 and HMDD v3.2 datasets and the results show that DMFVAE performs well. Furthermore, case studies on lung neoplasms, colon neoplasms, and esophageal neoplasms confirm the ability of DMFVAE in identifying potential miRNAs for human diseases.

Deep network embedding with dimension selection

Network embedding is a general-purpose machine learning technique that converts network data from non-Euclidean space to Euclidean space, facilitating downstream analyses for the networks. However, existing embedding methods are often optimization-based, with the embedding dimension determined in a heuristic or ad hoc way, which can cause potential bias in downstream statistical inference. Additionally, existing deep embedding methods can suffer from a nonidentifiability issue due to the universal approximation power of deep neural networks. We address these issues within a rigorous statistical framework. We treat the embedding vectors as missing data, reconstruct the network features using a sparse decoder, and simultaneously impute the embedding vectors and train the sparse decoder using an adaptive stochastic gradient Markov chain Monte Carlo (MCMC) algorithm. Under mild conditions, we show that the sparse decoder provides a parsimonious mapping from the embedding space to network features, enabling effective selection of the embedding dimension and overcoming the nonidentifiability issue encountered by existing deep embedding methods. Furthermore, we show that the embedding vectors converge weakly to a desired posterior distribution in the 2-Wasserstein distance, addressing the potential bias issue experienced by existing embedding methods. This work lays down the first theoretical foundation for network embedding within the framework of missing data imputation.