Link Prediction Task Research Articles

Construction of Knowledge Graph English Online Homework Evaluation System Based on Multimodal Neural Network Feature Extraction.

This paper defines the data schema of the multimodal knowledge graph, that is, the definition of entity types and relationships between entities. The knowledge point entities are defined as three types of structures, algorithms, and related terms, speech is also defined as one type of entities, and six semantic relationships are defined between entities. This paper adopts a named entity recognition model that combines bidirectional long short-term memory network and convolutional neural network, combines local information and global information of text, uses conditional random field algorithm to label feature sequences, and combines domain dictionary. A knowledge evaluation method based on triplet context information is designed, which combines triplet context information (internal relationship path information in knowledge graph and external text information related to entities in triplet) through knowledge representation learning. The knowledge of triples is evaluated. The knowledge evaluation ability of the English online homework evaluation system was evaluated on the knowledge graph noise detection task, the knowledge graph completion task (entity link prediction task), and the triplet classification task. The experimental results show that the English online homework evaluation system has good noise processing ability and knowledge credibility calculation ability, and has a stronger evaluation ability for low-noise data. Using the online homework platform to implement personalized English homework is conducive to improving students' homework mood, and students' “happy” homework mood has been significantly improved. The implementation of English personalized homework based on the online homework platform is conducive to improving students' homework initiative. With the help of the online homework platform to implement personalized English homework, students' homework time has been reduced, and the homework has been completed well, achieving the purpose of “reducing burden and increasing efficiency.”

Learning structured embeddings of knowledge graphs with generative adversarial framework

Many large knowledge graphs are now available and ready to provide semantically structured information that is regarded as an important resource for question answering and decision support tasks. However, they are built on rigid symbolic frameworks which makes them hard to be used in other intelligent systems. Knowledge graph embedding approaches are gaining increasing attention, which embeds symbolic entities and relations into continuous vector spaces. Such graph embeddings are often learned by training a model to distinguish true triples from negative ones. Unfortunately, the negative triples created by replacing their heads or tails with randomly selected entities are easily identified by the model, which makes them insufficient to train useful models. To this end, we propose a method under a generative adversarial architecture to learn graph embeddings, in which a generative network is trained to provide continually improved “plausible” triples whereas a discriminative network learns to distinguish truth triples from the others by competing with the generator in a two-player minimax game. When arriving at a convergence, the generative network recovers the training data and can be used for knowledge graph completion, while the discriminative network is trained to be a good triple classifier. Extensive experiments demonstrate our method can improve multiple graph embedding models with a significant margin on both link prediction and triple classification tasks.

Impact of Heterogeneity on Network Embedding

In recent years, network embedding has attracted much attention from researchers and achieved excellent performance. But few works investigate the adaptability of network embedding, especially for performance in different network structures. Heterogeneity, as a universal topological characteristic, plays a prominent role in network behaviors. In this study, we investigate the effect of heterogeneity on the effectiveness of existing network embedding approaches. We conduct experiments in scale-free networks with varying power exponents from both macro and micro perspectives to address link prediction and node similarity tasks, respectively. The results indicate that network embedding approaches can be divided into two classes according to their performance in the link prediction task. As the network heterogeneity decreases, the performance of approaches in the first class declines, while the performance of approaches in the second class initially improves and then declines. Moreover, our simulation discovers that, based on the node similarity metric, nodes are partitioned into two clusters by approaches, corresponding to large-degree nodes and small-degree nodes, respectively. Furthermore, approaches in the same class present similar characteristics between large-degree nodes and small-degree nodes, and the embedding is interpreted to some extent. Performance variations in the link prediction task can be explained by the characteristics of approaches, and similar characteristics are confirmed in experiments on real networks. Based on the findings for link prediction, we offer a brief guide for choosing an appropriate method based on the extent of heterogeneity. The investigation provides insight into network embedding and offers some interpretation of embedding.

A Simple Yet Effective Layered Loss for Pre-Training of Network Embedding

Pre-training of network embedding aims to encode unlabeled node proximity into a low-dimensional space, where nodes are close to their neighbors while being far from negative samples. In recent years, Graph Neural Networks have shown groundbreaking performance in semi-supervised learning on the node classification and link prediction tasks. However, because of their inherent information aggregation pattern, almost all these methods can only obtain inferior embedding results in the pre-training of the unlabeled nodes. The margins between a target node and its multi-hop neighbors become hard distinguishable during node message aggregation. To address this problem, we propose a simple yet effective layered loss to combine with a graph attention network, dubbed as LlossNet, for pre-training. We regard the proximity of a target node and its two-hop neighbors as a unit (called a unit graph), where a target node is needed to be more closer to its direct neighbor than its two-hop neighbors. As such, LlossNet would be able to preserve the margins of nodes in the learned embedding space. Experimental results of various downstream tasks including classification and clustering demonstrate the effectiveness of our method on learning discriminative node representations.

Expanded graph embedding for joint network alignment and link prediction

Link prediction in social networks has been an active field of study in recent years fueled by the rapid growth of many social networks. Many link prediction methods are harmed by users’ intention of avoiding being traced across networks. They may provide inaccurate information or overlook a great deal of information in multiple networks. This problem was overcome by developing methods for predicting links in a network based on known links in another network. Node alignment between the two networks significantly improves the efficiency of those methods. This research proposes a new embedding method to improve link prediction and node alignment results. The proposed embedding method is based on the Expanded Graph, which is our new novel network that has edges from both networks in addition to edges across the networks. Matrix factorization on the Finite Step Transition and Laplacian similarity matrices of the Expanded Graph has been used to obtain the embeddings for the nodes. Using the proposed embedding techniques, we jointly run network alignment and link prediction tasks iteratively to let them optimize each other’s results. We performed extensive experiments on many datasets to examine the proposed method. We achieved significant improvements in link prediction precision, which was 50% better than the peer’s method, and in recall, which was 500% better in some datasets. We also scale down the processing time of the solution to be more applicable to big social networks. We conclude that computed embedding in this type of problem is more suitable than learning the embedding since it shortens the processing time and gives better results.

Heterogeneous graph embedding with single-level aggregation and infomax encoding

There has been an increasing interest in developing embedding methods for heterogeneous graph-structured data. The state-of-the-art approaches often adopt a bi-level aggregation scheme, where the first level aggregates information of neighbors belonging to the same type or group, and the second level employs the averaging or attention mechanism to aggregate the outputs of the first level. We find that bi-level aggregation may suffer from a down-weighting issue and overlook individual node information, especially when there is an imbalance in the number of different typed relations. We develop a new simple yet effective single-level aggregation scheme with infomax encoding, named HIME, for unsupervised heterogeneous graph embedding. Our single-level aggregation scheme performs relation-specific transformation to obtain homogeneous embeddings before aggregating information from multiple typed neighbors. Thus, it emphasizes each neighbor’s equal contribution and does not suffer from the down-weighting issue. Extensive experiments demonstrate that HIME consistently outperforms the state-of-the-art approaches in link prediction, node classification, and node clustering tasks.

Learning Context-based Embeddings for Knowledge Graph Completion

Abstract Purpose Due to the incompleteness nature of knowledge graphs (KGs), the task of predicting missing links between entities becomes important. Many previous approaches are static, this posed a notable problem that all meanings of a polysemous entity share one embedding vector. This study aims to propose a polysemous embedding approach, named KG embedding under relational contexts (ContE for short), for missing link prediction. Design/methodology/approach ContE models and infers different relationship patterns by considering the context of the relationship, which is implicit in the local neighborhood of the relationship. The forward and backward impacts of the relationship in ContE are mapped to two different embedding vectors, which represent the contextual information of the relationship. Then, according to the position of the entity, the entity's polysemous representation is obtained by adding its static embedding vector to the corresponding context vector of the relationship. Findings ContE is a fully expressive, that is, given any ground truth over the triples, there are embedding assignments to entities and relations that can precisely separate the true triples from false ones. ContE is capable of modeling four connectivity patterns such as symmetry, antisymmetry, inversion and composition. Research limitations ContE needs to do a grid search to find best parameters to get best performance in practice, which is a time-consuming task. Sometimes, it requires longer entity vectors to get better performance than some other models. Practical implications ContE is a bilinear model, which is a quite simple model that could be applied to large-scale KGs. By considering contexts of relations, ContE can distinguish the exact meaning of an entity in different triples so that when performing compositional reasoning, it is capable to infer the connectivity patterns of relations and achieves good performance on link prediction tasks. Originality/value ContE considers the contexts of entities in terms of their positions in triples and the relationships they link to. It decomposes a relation vector into two vectors, namely, forward impact vector and backward impact vector in order to capture the relational contexts. ContE has the same low computational complexity as TransE. Therefore, it provides a new approach for contextualized knowledge graph embedding.

TGL

Many real world graphs contain time domain information. Temporal Graph Neural Networks capture temporal information as well as structural and contextual information in the generated dynamic node embeddings. Researchers have shown that these embeddings achieve state-of-the-art performance in many different tasks. In this work, we propose TGL, a unified framework for large-scale offline Temporal Graph Neural Network training where users can compose various Temporal Graph Neural Networks with simple configuration files. TGL comprises five main components, a temporal sampler, a mailbox, a node memory module, a memory updater, and a message passing engine. We design a Temporal-CSR data structure and a parallel sampler to efficiently sample temporal neighbors to form training mini-batches. We propose a novel random chunk scheduling technique that mitigates the problem of obsolete node memory when training with a large batch size. To address the limitations of current TGNNs only being evaluated on small-scale datasets, we introduce two large-scale real-world datasets with 0.2 and 1.3 billion temporal edges. We evaluate the performance of TGL on four small-scale datasets with a single GPU and the two large datasets with multiple GPUs for both link prediction and node classification tasks. We compare TGL with the open-sourced code of five methods and show that TGL achieves similar or better accuracy with an average of 13X speedup. Our temporal parallel sampler achieves an average of 173X speedup on a multi-core CPU compared with the baselines. On a 4-GPU machine, TGL can train one epoch of more than one billion temporal edges within 1-10 hours. To the best of our knowledge, this is the first work that proposes a general framework for large-scale Temporal Graph Neural Networks training on multiple GPUs.

OLMNE+FT: Multiplex network embedding based on overlapping links

Network embedding or graph representation learning has recently attracted more researchers’ attention and achieved state-of-the-art performance in many areas and tasks. Nevertheless, most of these methods are targeted for monolayer networks and ignore the multiplexity property of nodes which refers to the multifaceted relationships between two elements. Multiplexity provides multiple types of auxiliary information to refine the characteristics of nodes and can be modeled as a multiplex network. In this study, we propose a multiplex network embedding algorithm to learn a unique embedding for each node in each layer or each relation type. A biased path-dependency random walk strategy is adopted to generate node sequences for integrating different types of relations between nodes, which pays more attention to overlapping links and makes neighbor nodes in the sampling sequence more similar to each other. Then the skip-gram model is used to learn an overall embedding over node sequences. To strengthen the expressive power of the embedding in a specific layer, a fine tuning strategy with low time cost is employed to make the embedding comprise information of nodes at this particular layer and preserve their distinctive properties, and the unique embedding is achieved ultimately. To verify the effectiveness of our algorithms, we validate the performance of our algorithm and other baseline methods in the link prediction task. The results demonstrate that the learned embedding can capture the interlayer relationships and preserve the specific characteristics of nodes, and our algorithms can stably obtain better or comparable performance compared with other methods.

Joint Learning of User Representation With Diffusion Sequence and Network Structure

Information sharing behavior and social link building behavior have shown strong correlation on social media. The aim of this paper is to explore this correlation for simultaneously modeling and predicting sharing behavior in information diffusion sequences and linking behavior in social network, which correspond to information diffusion prediction and social link prediction problems. To achieve this goal, we propose a joint user representation learning model to characterize the two correlated behaviors in a shared latent space. The proposed model learns user representations via two maximum likelihood estimation objectives defined on observed information diffusion sequences and social network structure respectively and incorporates them in a unified framework. A multi-task learning algorithm is designed for efficient model optimization. Based on the learned representations, the model can be directly applied to predicting diffusion processes and inferring unobserved social links at the same time. We evaluate the proposed model on two real social media datasets with extensive experiments. The model consistently achieves significant improvements over the state-of-the-art approaches on diffusion prediction and link prediction tasks. The better robustness of our model in further ablation studies demonstrates that capturing the behavior correlation in the shared representation space is beneficial.

Perturbation of the Normalized Laplacian Matrix for the Prediction of Missing Links in Real Networks

The problem of predicting missing links in real-world networks is an active and challenging research area in both science and engineering. The goal is to model the process of link formation in a complex network based on its observed structure to unveil lost or unseen interactions. In this paper, we use perturbation theory to develop a general link prediction procedure, called Laplacian Perturbation Method (LPM), that relies on relevant structural information encoded in the normalized Laplacian matrix of the network. We implement a general algorithm for our perturbation method valid for different Laplacian-based link prediction schemes that successfully surpass the prediction accuracy of their standard non-perturbed versions in real-world and model networks. The suggested LPM for link prediction also exhibits higher accuracy compared to other extensively used local and global state-of-the-art techniques and, in particular, it outperform the Structural Perturbation Method (SPM), a popular procedure that perturbs the adjacency matrix of a network for inferring missing links, in many real-world and in synthetic networks. Taken together, our results show that perturbation methods can significantly improve Laplacian-based link prediction techniques, and feeds the debate on which representation, Laplacian or adjacency, better represents structural information for link prediction tasks in networks.

Reciprocity, community detection, and link prediction in dynamic networks

Many complex systems change their structure over time, in these cases dynamic networks can provide a richer representation of such phenomena. As a consequence, many inference methods have been generalized to the dynamic case with the aim to model dynamic interactions. Particular interest has been devoted to extend the stochastic block model and its variant, to capture community structure as the network changes in time. While these models assume that edge formation depends only on the community memberships, recent work for static networks show the importance to include additional parameters capturing structural properties, as reciprocity for instance. Remarkably, these models are capable of generating more realistic network representations than those that only consider community membership. To this aim, we present a probabilistic generative model with hidden variables that integrates reciprocity and communities as structural information of networks that evolve in time. The model assumes a fundamental order in observing reciprocal data, that is an edge is observed, conditional on its reciprocated edge in the past. We deploy a Markovian approach to construct the network’s transition matrix between time steps and parameters’ inference is performed with an expectation-maximization algorithm that leads to high computational efficiency because it exploits the sparsity of the dataset. We test the performance of the model on synthetic dynamical networks, as well as on real networks of citations and email datasets. We show that our model captures the reciprocity of real networks better than standard models with only community structure, while performing well at link prediction tasks.

Efficient link prediction in the protein\u2013protein interaction network using topological information in a generative adversarial network machine learning model

BackgroundThe investigation of possible interactions between two proteins in intracellular signaling is an expensive and laborious procedure in the wet-lab, therefore, several in silico approaches have been implemented to narrow down the candidates for future experimental validations. Reformulating the problem in the field of network theory, the set of proteins can be represented as the nodes of a network, while the interactions between them as the edges. The resulting protein–protein interaction (PPI) network enables the use of link prediction techniques in order to discover new probable connections. Therefore, here we aimed to offer a novel approach to the link prediction task in PPI networks, utilizing a generative machine learning model.ResultsWe created a tool that consists of two modules, the data processing framework and the machine learning model. As data processing, we used a modified breadth-first search algorithm to traverse the network and extract induced subgraphs, which served as image-like input data for our model. As machine learning, an image-to-image translation inspired conditional generative adversarial network (cGAN) model utilizing Wasserstein distance-based loss improved with gradient penalty was used, taking the combined representation from the data processing as input, and training the generator to predict the probable unknown edges in the provided induced subgraphs. Our link prediction tool was evaluated on the protein–protein interaction networks of five different species from the STRING database by calculating the area under the receiver operating characteristic, the precision-recall curves and the normalized discounted cumulative gain (AUROC, AUPRC, NDCG, respectively). Test runs yielded the averaged results of AUROC = 0.915, AUPRC = 0.176 and NDCG = 0.763 on all investigated species.ConclusionWe developed a software for the purpose of link prediction in PPI networks utilizing machine learning. The evaluation of our software serves as the first demonstration that a cGAN model, conditioned on raw topological features of the PPI network, is an applicable solution for the PPI prediction problem without requiring often unavailable molecular node attributes. The corresponding scripts are available at https://github.com/semmelweis-pharmacology/ppi_pred.

Pre-training graph neural networks for link prediction in biomedical networks.

Graphs or networks are widely utilized to model the interactions between different entities (e.g. proteins, drugs, etc.) for biomedical applications. Predicting potential interactions/links in biomedical networks is important for understanding the pathological mechanisms of various complex human diseases, as well as screening compound targets for drug discovery. Graph neural networks (GNNs) have been utilized for link prediction in various biomedical networks, which rely on the node features extracted from different data sources, e.g. sequence, structure and network data. However, it is challenging to effectively integrate these data sources and automatically extract features for different link prediction tasks. In this article, we propose a novel Pre-Training Graph Neural Networks-based framework named PT-GNN to integrate different data sources for link prediction in biomedical networks. First, we design expressive deep learning methods [e.g. convolutional neural network and graph convolutional network (GCN)] to learn features for individual nodes from sequence and structure data. Second, we further propose a GCN-based encoder to effectively refine the node features by modelling the dependencies among nodes in the network. Third, the node features are pre-trained based on graph reconstruction tasks. The pre-trained features can be used for model initialization in downstream tasks. Extensive experiments have been conducted on two critical link prediction tasks, i.e. synthetic lethality (SL) prediction and drug-target interaction (DTI) prediction. Experimental results demonstrate PT-GNN outperforms the state-of-the-art methods for SL prediction and DTI prediction. In addition, the pre-trained features benefit improving the performance and reduce the training time of existing models. Python codes and dataset are available at: https://github.com/longyahui/PT-GNN. Supplementary data are available at Bioinformatics online.

MTGNN: Multi-Task Graph Neural Network based few-shot learning for disease similarity measurement.

Similar diseases are usually caused by molecular origins or similar phenotypes. Confirming the relationship between diseases can help researchers gain a deep insight of the pathogenic mechanisms of emerging complex diseases, and improve the corresponding diagnoses and treatment. Therefore, similar diseases are considerably important in biology and pathology. However, the insufficient number of labelled similar disease pairs cannot support the optimal training of the models. In this paper, we propose a Multi-Task Graph Neural Network (MTGNN) framework to measure disease similarity by few-shot learning. To tackle the problem of insufficient number of labelled similar disease pairs, we design the multi-task optimization strategy to train the graph neural network for disease similarity task (lack of labelled training data) by introducing link prediction task (sufficient labelled training data). The similarity between diseases can then be obtained by measuring the distance between disease embeddings in high-dimensional space learning from the double tasks. The experiment results evaluate the performance of MTGNN and illustrate its advantages over previous methods on few labeled training dataset.

Cross-network representation learning for anchor users on multiplex heterogeneous social network

Online users are typically involved in multiple online social networks simultaneously to enjoy a variety of social network services, thus bringing about the interconnection of online social networks via bridge users called anchor users. Anchor users can be beneficial to a wide range of social network analysis applications such as cross-domain system recommendation, cross-network information diffusion, and link prediction, taking anchor user’s intra-network structural information along with its cross-network structural properties into consideration. Several studies have so far tried to learn low-dimensional representations of social users by capturing their network structures inside one social network but they have not fully leveraged their intra-network structures with their cross-network structures to boost the performance of the aforementioned analysis tasks. In this paper, we present a novel deep learning model to learn Overall low-dimensional Vector Representations for Anchor Users (OVRAU), from a multiplex heterogeneous social network by investigating the intra-network as well as the cross-network structural information. Unlike previous works, our proposed model considers the multi-network scenario to encode diverse network structures of anchor users. We propose two types of embeddings to capture the different structural information of an anchor user from multiple social networks: a high-dimensional base embedding and a low-dimensional social edge embedding for each social network. In particular, we learn a function that generates social edge embeddings by sampling and aggregating structural features from an anchor user’s neighborhood inside different social networks through one of three candidate aggregator functions namely mean, max-pooling and LSTM, with a self-attention mechanism. Link prediction is used as a downstream task to evaluate the effectiveness of the learned embeddings. Experiments were conducted on real-world social networks dataset, and the results demonstrate that our proposed model involving all the three variants can significantly outperform the existing network representation learning approaches when applied on the link prediction task and also achieve better performance over all compared baselines.

Cyber threat prediction using dynamic heterogeneous graph learning

Predicting cyber threats is crucial for uncovering underlying security risks and proactively preventing malicious attacks. However, predicting cyber threats and demystifying the evolutionary patterns are challenging due to the heterogeneity and dynamics of cyber threats. In this paper, we propose CTP-DHGL, a novel Cyber Threat Prediction model based on Dynamic Heterogeneous Graph Learning, to predict the potential cyber threats by investigating public security-related data (e.g., CVE details, ExploitDB). Particularly, we first characterize the interactive relationships among different types of cyber threat objects with a heterogeneous graph. We then formalize cyber threat prediction as a dynamic link prediction task on the heterogeneous graph and propose an end-to-end dynamic heterogeneous graph embedding method to learn the dynamic evolutionary patterns of the graph. As a result, CTP-DHGL can infer potential link relationships based on the evolving graph embedding sequences learned from previous snapshots to infer stealthy cyber threats. The experimental results on real-world datasets verify that CTP-DHGL outperforms the baseline models in learning the evolutionary patterns of cyber threats and predicting potential cyber risks.

Geometric Algebra based Embeddings for Static and Temporal Knowledge Graph Completion

Recent years, Knowledge Graph Embeddings (KGEs) have shown promising performance on link prediction tasks by mapping the entities and relations from a Knowledge Graph (KG) into a geometric space and thus have gained increasing attentions. In addition, many recent Knowledge Graphs involve evolving data, e.g., the fact (Obama, PresidentOf, USA) is valid only from 2009 to 2017. This introduces important challenges for knowledge representation learning since such temporal KGs change over time. In this work, we strive to move beyond the complex or hypercomplex space for KGE and propose a novel geometric algebra based embedding approach, GeomE, which uses multivector representations and the geometric product to model entities and relations. GeomE subsumes several state-of-the-art KGE models and is able to model diverse relations patterns. On top of this, we extend GeomE to TGeomE for temporal KGE, which performs 4th-order tensor factorization of a temporal KG and devises a new linear temporal regularization for time representation learning. Moreover, we study the effect of time granularity on the performance of TGeomE models. Experimental results show that our proposed models achieve the state-of-the-art performances on link prediction over four commonly-used static KG datasets and four well-established temporal KG datasets across various metrics.

Link Prediction With Contextualized Self-Supervision

Link prediction aims to infer the link existence between pairs of nodes in networks/graphs. Despite their wide application, the success of traditional link prediction algorithms is hindered by three major challenges&#x2014;<i>link sparsity</i>, <i>node attribute noise</i> and <i>dynamic changes</i>&#x2014;that are faced by many real-world networks. To address these challenges, we propose a <u>C</u>ontextualized <u>S</u>elf-<u>S</u>upervised <u>L</u>earning (CSSL) framework that fully exploits structural context prediction for link prediction. The proposed CSSL framework learns a link encoder to infer the link existence probability from paired node embeddings, which are constructed via a transformation on node attributes. To generate informative node embeddings for link prediction, structural context prediction is leveraged as a self-supervised learning task to boost the link prediction performance. Two types of structural context are investigated, <i>i.e.</i>, context nodes collected from random walks <i>vs.</i> context subgraphs. The CSSL framework can be trained in an end-to-end manner, with the learning of model parameters supervised by both the link prediction and self-supervised learning tasks. The proposed CSSL is a generic and flexible framework in the sense that it can handle both attributed and non-attributed networks, and operate under both transductive and inductive link prediction settings. Extensive experiments and ablation studies on seven real-world benchmark networks demonstrate the superior performance of the proposed self-supervision based link prediction algorithm over state-of-the-art baselines, on different types of networks under both transductive and inductive settings. The proposed CSSL also yields competitive performance in terms of its robustness to node attribute noise and scalability over large-scale networks.

Cold-Start Link Prediction via Weighted Symmetric Nonnegative Matrix Factorization with Graph Regularization

Link prediction has attracted wide attention among interdisciplinary researchers as an important issue in complex network. It aims to predict the missing links in current networks and new links that will appear in future networks. Despite the presence of missing links in the target network of link prediction studies, the network it processes remains macroscopically as a large connected graph. However, the complexity of the real world makes the complex networks abstracted from real systems often contain many isolated nodes. This phenomenon leads to existing link prediction methods not to efficiently implement the prediction of missing edges on isolated nodes. Therefore, the cold-start link prediction is favored as one of the most valuable subproblems of traditional link prediction. However, due to the loss of many links in the observation network, the topological information available for completing the link prediction task is extremely scarce. This presents a severe challenge for the study of cold-start link prediction. Therefore, how to mine and fuse more available non-topological information from observed network becomes the key point to solve the problem of cold-start link prediction. In this paper, we propose a framework for solving the cold-start link prediction problem, a joint-weighted symmetric nonnegative matrix factorization model fusing graph regularization information, based on low-rank approximation algorithms in the field of machine learning. First, the nonlinear features in high-dimensional space of node attributes are captured by the designed graph regularization term. Second, using a weighted matrix, we associate the attribute similarity and first order structure information of nodes and constrain each other. Finally, a unified framework for implementing cold-start link prediction is constructed by using a symmetric nonnegative matrix factorization model to integrate the multiple information extracted together. Extensive experimental validation on five real networks with attributes shows that the proposed model has very good predictive performance when predicting missing edges of isolated nodes.