Integrative Construction and Analysis of Molecular Association Network in Human Cells by Fusing Node Attribute and Behavior Information.

Detecting whether a pair of biomolecules associate is of great significance in the study of molecular biology. Hence, computational methods are urgently needed as guidance for practice. However, most of the previous prediction models influenced by reductionism focused on isolated research objects, which have their own inherent defects. Inspired by holism, a machine-learning-based framework called MAN-node2vec is proposed to predict multi-type relationships in the molecular associations network (MAN). Specifically, we constructed a large-scale MAN composed of 1,023 miRNAs, 1,649 proteins, 769 long non-coding RNAs (lncRNAs), 1,025 drugs, and 2,062 diseases. Then, each biomolecule in MAN can be represented as a vector by its attribute learned by k-mer, etc. and its behavior learned by node2vec. Finally, the random forest classifier is applied to carry out the relationship prediction task. The proposed model achieved a reliable performance with 0.9677 areas under the curve (AUCs) and 0.9562 areas under the precision curve (AUPRs) under 5-fold cross-validation. Also, additional experiments proved that the proposed global model shows more competitive performance than the traditional local method. All of these provided a systematic insight for understanding the synergistic interactions between various molecules and diseases. It is anticipated that this work can bring beneficial inspiration and advance to related systems biology and biomedical research.

Introduction

Benefiting from the development of increasingly sophisticated high-throughput technologies, numerous biomolecular relationship networks, such as the non-coding RNA (ncRNA) target-regulation network,, protein-protein interaction network,, ncRNA disease-association network,, etc., are continuously being confirmed to play key roles in cell life activities and processes., The technical threshold and cost of practical experiments has become affordable and begun to change people’s grasp of biological processes like cell-cycle differentiation and apoptosis from a microscopic perspective.

Despite the impressive wet experiment methods making remarkable achievements in sequence identification, relationship mapping, etc., the awareness of relationships between biomarkers remains incomplete. Nevertheless, the approach without guidance is aimless and costly. In addition, identifying relationships between biomolecules by manual experiment is uncertain; especially errors such as false positive rate (FPR) and false negative rate (FNR) can lead to perceived deviations. Compared to these practical methods, computational models can learn intrinsic characteristics of biomolecules and infer the potential relationships simultaneously. The accumulation of data and the demand of reality make them become popular. Chen et al. utilized stacking automatic encoders for data preprocessing and support vector machines for classification to discover potential microRNA (miRNA)-disease associations. Guo et al. predict uncovered long non-coding RNA (lncRNA)-disease associations by combining known associations and disease characteristics. Cheng et al. infer new targets for known drugs only through drug-target bipartite network topology similarity.

All of the above methods are supporters of reductionism and are the products of compromise under the condition of missing data. They are typical representatives of building, analyzing, and predicting based on a single relationship. Hence, more and more researchers are paying attention to this issue and are working to improve this situation through different strategies. For instance, Chen predicted that lncRNA-disease associations were only intermediated by indirect miRNAs and still achieved higher areas under the curve (AUCs) in the leave-one-out cross-validation. Lin et al. predicted the associations between nodes by constructing a disease-gene-chemical network while increasing predictive coverage without significantly reducing sensitivity and specificity.

Although reductionism provides a wealth of knowledge over a period of time, it ignores that the cell itself is as a whole based on the genetic central dogma. Existing evidence intensely indicates that the function of cells is rarely directly controlled by a determined gene but rather reflects the result of interaction by multiple factors. However, limited by existing incomplete data, computational models are often directed by reductionism which describes the composition and function of cells into various parts. Although the circumstance of data loss is alleviated through different methods, it cannot theoretically correspond with the genetic central dogma to establish a gene-to-expression description to explain why there is a relationship between the biomolecules.

In fact, cells are living organisms with abundant functions under the relationship of different biology molecules. These different biomolecules and their relationships can be treated as vertexes (nodes) and links (edges) in a network or graph (cell). Graph is an important form of data that appears widely in the real world and is studied in depth. Since the “scale-free” and “small-world” network theories were proposed, graphs have become a research hotspot., Analysis of graphs helps not only to understand the hidden knowledge behind data, but also to expand and migrate to other types of data. Network representation is an effective way to solve this problem. The previous representation algorithm aims at acquiring the main components to obtain dimensional reduction, such as singular value decomposition (SVD) and locally linear embedding (LLE)., The maturity of deep-learning technology has promoted the development of many fields. A large number of new network representation technologies, such as DeepWalk, node2vec, and LINE, can more effectively extract the structure of the network and facilitate downstream tasks such as link prediction, node classification, community discovery, and visualization.23, 24, 25 Inspired by Guo et al., rescanning some fundamental biological problems from a global network viewpoint can aid researchers in treating the problem from a different perspective in order to find a new solution. The differences between diverse methods can be seen in Figure 1.

Figure 1

The Differences between Diverse Methods

(A–C) Comparison between traditional method (A), intermediary-based method (B), and the proposed method (C). The traditional method (A) often focuses on the research itself and ignores the mediation role of other kinds of biomolecules in the cell. The intermediary-based method (B) is often limited without considering second- or higher-order neighbors. The proposed method (C) can reflect the relationships in the cell macroscopically and completely and effectively promote the prediction task.

In this paper, a relatively complete molecular association network (MAN) is constructed, including various sub-networks to reveal the flow of genetic information. The entire network can be described as follows: protein as a direct participant in the expression of genetic information is regarded as the core of the entire network. With the introduction of competing endogenous RNA (ceRNA), the establishment of a link between ncRNA including miRNA, lncRNA, etc., proves that they are not transcribed garbage but more or less regulated gene expression. The increasing evidence about the inextricable associations between ncRNA and disease also confirms the above hypothesis. Relative to the composition inside the cell, factors outside the cell will have a crucial impact on life activities from another perspective; the drug-target-disease subnet has long been experimentally proven to play an irreplaceable role in drug development and reposition. Although intuitively, there are many different types of nodes and complex interlaced edges in the network, the exchange of information between different molecules is very clear even under the overlap of different modules and subnets. The perspective of MAN is shown in Figure 2.

Figure 2

The Structure of the MAN

The relationship prediction problem in the above description network can be formally defined as follows: A graph is , where and . The adjacency matrix is a symmetric matrix where each element is equal to 1 if and only if node and node are experimentally verified to be associated. The aim of the model is to find the uncovered element 1 in . The main steps of the entire model are as follows: first, the relationships collected by various databases are summarized after redundancy removal and identifier uniform to construct the MAN. After the complex network consisting of five kinds of nodes and nine kinds of edges can be defined as a homogeneous undirected graph, adjacency matrix can be constructed to contain all information of nodes and edges. In order to simplify the calculation and facilitate storage, we only take the lower triangular part of matrix . Second, k-mer, node2vec, etc., which are widely used in bioinformatics and network embedding, are applied to map the nodes to a low-dimensional dense feature space. The attribute information and behavior information of each node can be represented as a 64-dimensional vector, respectively. This process can be called biomolecular digitization, or biomolecule2vec. Third, relationships that have been validated by manual experiments are considered positive samples. An equal number of negative samples from unknown pairs are randomly extracted. All of the positive and negative samples are sent to random forest for training and prediction. For fairness, all parameters are set to default values in each step. There is no need to guarantee that the degree of each node is bigger than 0 when the dataset is segmented, so some nodes may be isolated. This is our consideration based on some actual situations such as new sample problems that may be encountered in actual experiments. In addition, an additional experiment based on lncRNA-miRNA interaction prediction is performed to compare the differences of the results between the proposed global method and previous local method. Although this complex biomolecular network is not perfect, we hope that it will not only be treated as an assistance to manual experiments, but also hope that this work will stimulate researchers’ interest in system biology to establish a comprehensive framework from molecules, pathways, and modules. The seamless integration of complex network technology with biological big data will promote the development of all aspects of the life sciences. The flowchart of the proposed framework can be seen in Figure 3.

Figure 3

The Flowchart of MAN-node2vec

Results

5-Fold Cross-Validation

In this section, we assess the performance of the proposed model under 5-fold cross-validation based on receiver operating characteristics (ROCs), AUCs, precision recall (PR), areas under the precision curve (AUPRs), and extensive evaluation criteria. 5-fold cross-validation is a common way to objectively evaluate classifier capability based on existing datasets. Under this strategy, the entire dataset is divided into five mutually exclusive subsets of roughly equal numbers, each of which is evaluated as the test set, and the remaining 4 subsets are used to construct the model.

The ROC is a curve that determines the abscissa True Positive Rate (TPR) and the ordinate False Positive Rate (FPR) by using the predicted probability of the test sample as the classification threshold. The area enclosed by the ROC and the coordinate axis is called the AUC. The drawing process of the PR curve is similar to the ROC and the area enclosed by the abscissa recall and the ordinate AUPR. In order to fairly and comprehensively evaluate the proposed model, extensive evaluation criteria, including accuracy (acc.), sensitivity (sen.), specificity (spec.), precision (prec.), and matthews correlation coefficient (MCC) are applied from different perspectives. Although the dataset is balanced, we still hope to provide a reference for subsequent models through this overall measurement system. The details of results under 5-fold cross-validation are shown in the Table 1 and Figure 4.

Table 1

Performance of the Proposed Model on Various Evaluation Criteria under 5-Fold Cross-Validation

Fold	Acc. (%)	Sen. (%)	Spec. (%)	Prec. (%)	MCC (%)	AUC (%)
0	91.69	90.98	92.40	92.29	83.39	96.83
1	91.85	91.07	92.64	92.52	83.71	96.86
2	91.49	90.58	92.41	92.27	83.00	96.68
3	91.62	90.99	92.25	92.15	83.24	96.74
4	91.52	90.74	92.30	92.17	83.04	96.74
Average	91.63 ± 0.14	90.87 ± 0.20	92.4 ± 0.15	92.28 ± 0.15	83.28 ± 0.29	96.77 ± 0.07

Figure 4

The ROCs, AUCs, PRs, and AUPRs of the Proposed Method under 5-Fold Cross-Validation

Analysis of Figure 4 and Table 1 concludes that the method based on random forest produces satisfactory results on the MAN. The outstanding results of AUC, AUPR, and various evaluation criteria at each fold suggest superior predictive ability of the proposed model, while the lower standard deviation demonstrates the stability and robustness of the prediction method.

Feature Importance Comparison

As mentioned above, each node in the biomolecular network can be represented by two kinds of information. It is obvious that there still exists some predictive ability with the model when either kind of information is lost, so the common situation, such as new sample problem, can be alleviated to some extent. In this chapter, we hope to explore the impact of different information on the prediction effect, that is, the practical application value of the proposed model even under the characterization of a single kind of information. In order to verify only the impact of different features on the prediction results, the random forest classifier is set as the default parameter. The ROC, AUC, PR, AUPR, and extensive evaluation criteria under the 5-fold cross-validation are shown in Table 2 and Figure 5.

Table 2

Performance of Three Methods Based on Different Features

Feature	Acc. (%)	Sen. (%)	Spec. (%)	Prec. (%)	MCC (%)	AUC (%)
Attribute	87.97 ± 0.10	90.63 ± 0.08	85.30 ± 0.20	86.05 ± 0.16	76.04 ± 0.20	93.88 ± 0.12
Behavior	89.16 ± 0.12	86.21 ± 0.23	92.10 ± 0.15	91.61 ± 0.14	78.45 ± 0.23	95.07 ± 0.09
Both	91.63 ± 0.14	90.87 ± 0.20	92.4 ± 0.15	92.28 ± 0.15	83.28 ± 0.29	96.77 ± 0.07

Figure 5

Comparison of the ROCs, AUCs, PRs, and AUPRs Based on Different Features under 5-Fold Cross-Validation

Feature comparison experiments indicate that attribute and behavior complement each other and contribute to detect potential associations. Although the combination of the two kinds of information shows the best results, even in the case of a single kind of feature, the proposed model is an excellent method that can adapt to various real environments as an auxiliary tool for manual experiments.

Comparison with Different Classifers

Although many classic machine-learning algorithms have achieved great success and impressive influence in both industry and academia, the prediction effect of the traditional algorithm on the dataset of this article is quite different. In this chapter, we compare the performance of several common classifiers, including random forest, Xgboost, Adaboost, logistic regression, and naive Bayes, and try to analyze the reasons for this situation. In order to fairly compare the performance of the classifier on this dataset, all parameters are set to default values. The detailed results under 5-fold cross-validation based on different classifiers are as shown in Table 3 and Figure 6.

Table 3

Comparison of Different Classifiers on Various Evaluation Criteria

Classifier	Acc. (%)	Sen. (%)	Spec. (%)	Prec. (%)	MCC (%)	AUC (%)
NaiveBayes	60.59 ± 20.58	73.98 ± 0.68	47.20 ± 0.79	58.36 ± 0.47	21.98 ± 1.19	70.91 ± 0.47
Logistic	76.89 ± 0.30	78.92 ± 0.19	74.86 ± 0.56	75.85 ± 0.41	53.83 ± 0.58	83.75 ± 0.46
AdaBoost	77.78 ± 0.18	80.03 ± 0.30	75.52 ± 0.13	76.58 ± 0.14	55.61 ± 0.37	85.19 ± 0.18
XgBoost	86.17 ± 0.31	87.39 ± 0.49	84.95 ± 0.57	85.31 ± 0.46	72.37 ± 0.61	93.20 ± 0.22
Random forest	91.63 ± 0.14	90.87 ± 0.20	92.4 ± 0.15	92.28 ± 0.15	83.28 ± 0.29	96.77 ± 0.07

Figure 6

Comparison of the ROCs, AUCs, PRs, and AUPRs Based on Different Classifiers under 5-Fold Cross-Validation

The results can be explained as follows: (1) For naive Bayes, there might be strong correlations in each dimension of the representation vectors, making the performance unsatisfactory. (2) For logistic regression, the high complexity of the dataset may not be concomitant with the linear classification surface, making it difficult for the logical return to fit the sample. (3) It is curious that random forest shows better classification results than Xgboost and Adaboost with advanced assemble strategies. The reasons for this are probably attributed to the setting of the default parameters making it hard for the latter to fit the data.

Additional Comparison Experiment Based on lncRNA-miRNA Interaction Prediction

Predicting multi-type relationships between different biomolecules to evaluate the performance of the model is limited in some respects. The proposed model can predict not only multiple relationships, but also single associations. Considering the large accumulation of ceRNA evidence and miRNA and lncRNA as a hotspot in the field, the lncRNA-miRNA interaction was chosen as a special additional experiment to compare the proposed method with the state-of-the-art model. 8374 lncRNA-miRNA interactions containing 467 different lncRNAs and 254 different miRNAs were downloaded from lncRNASNP2 on April 26, 2019 after removing redundancy and unfirming identifiers. Four different kinds of experiments under 5-fold cross-validation were performed separately, and the results are as shown in Figure 7.

Figure 7

Comparison of the ROCs, AUCs, PRs, and AUPRs Based on Different Methods under 5-Fold Cross-Validation

For Figure 7A, each lncRNA or miRNA is represented as a 64-dimensional vector only based on its attribute feature. Thus, each lncRNA-miRNA interaction pair can be viewed as a 128-dimensional vector with a label of 0 or 1. It can be treated as a baseline compared with other methods. For Figure 7B, influenced by the method proposed by Chen, we completely ignore the direct interactions between lncRNA and miRNA and use the remaining eight kinds of relationships in the network to represent lncRNA or miRNA by node2vec. Each lncRNA or miRNA can be represented as a 64-dimensional vector only based on its behavior information. Thus, each lncRNA-miRNA interaction pair can be viewed as a 128-dimensional vector. For Figure 7C, the traditional method of measuring functional similarity through the Gaussian profile kernel function proposed by van Laarhoven et al. is essentially a description of single association and is widely used in ncRNA-disease association prediction. Each lncRNA or miRNA can be represented as a 64-dimensional vector based on both attribute and behavior information. The results indicate that this classic state-of-the-art method has a positive effect on the discovery of potential interactions. For Figure 7D, this is the performance of the proposed method. Each node is represented by both attribute and behavior information. When node2vec is implied, 80% lncRNA-miRNA interactions and the other eight kinds of associations together describe the behavior of the node. The outstanding performance of the proposed method can be attributed to two aspects: first, noe2vec is a more advanced algorithm that can extract structural information from the network more easily than the Gaussian profile kernel function. Second, MAN as a whole contains more abundant biological information than direct lncRNA-miRNA interactions. All above experiments show that the additional relationships in MAN indeed contain an amount of biology information and can be used as a kind of auxiliary information to assist the prediction of a single research object.

Discussion

Networks naturally exist in a wide diversity of real-world scenarios, e.g., social networks, citation networks, knowledge networks, etc. Effective network analytics provides researchers a deeper understanding of what is behind the data and provides insights into how to make good use of this information.

Inspired by holism, we constructed a MAN by integrating different types of biomolecules to analyze and describe the state and function of various modules from different angles. The computational model called MAN-node2vec was proposed based on MAN to predict arbitrary relationships between any nodes from a global perspective and achieved remarkable prediction performance. Additional experiments indicate that even on specific issues, the proposed approach demonstrated a more competitive ability than traditional methods. All the results demonstrate the feasibility and superiority of uncover potential associations from a global perspective. In fact, holism is not a negation of reductionism, but complementary.

Generally, our research will expand the research paradigm of computational biology and establish interesting connections between biological data and complex network techniques. It can be seen as a foundation for advancing both methodology and technology. MAN-node2vec is not only a supplement to manual experiments, but also a new chapter on the study of the laws of life sciences based on collection, integration, and data mining from a comprehensive perspective.

Materials and Methods

Construction of the MAN

Since the existing database does not integrate all the data we need, we have to collect diverse associations from multiple databases as the basis of construction for the MAN.29, 30, 31, 32, 33, 34, 35, 36, 37 Specifically, nine kinds of associations that are the edges or links in MAN can be obtained from the corresponding databases shown in Table 4.

Table 4

The Details of Nine Kinds of Relationships in MAN

Relationship Type	Database	Number of Pairs
miRNA-lncRNA	lncRNASNP2	8,374
miRNA-disease	HMDD	16,427
miRNA-protein	miRTarBase	4,944
lncRNA-disease	lncRNADisease, lncRNASNP2	1,264
lncRNA-protein	lncRNA2Target	690
Protein-disease	DisGeNET	25,087
Drug-protein	DrugBank	11,107
Drug-disease	CTD	18,416
Protein-protein	STRING	19,237
Total	MAN	105,546

The identifiers of miRNA, lncRNA, protein, and drug are based on the nomenclature provided by miRBase, NONCODE, STRING, and DrugBank, respectively. The identifiers of disease are used directly from the original database. After the operation of identifier transformation, redundancy removal, and data filtering from different databases, we get a total of 6,528 biomolecules (nodes) including five different types. The statistics on details of diverse nodes are shown in Table 5.

Table 5

The Details of Five Types of Nodes (Biomolecules) in MAN

Node	Number of Nodes
Disease	2,062
lncRNA	769
miRNA	1,023
Protein	1,649
Drug	1,025
Total	6,528

Obviously, 105,546 experimental valid association pairs can be treated as positive samples. The remaining unlabeled samples are composed of true negative samples and potential positive samples. Considering that the potential positive samples are a small part of all unlabeled samples, a common method widely used in bioinformatics that randomly extracts the same number unlabeled samples as negative samples is applied. Finally, the whole sample set is composed of 211,092 association pairs. Data used for analysis are available on GitHub page: https://github.com/CocoGzh/MAN-1.0.

ncRNA and Protein Sequence

We collected the sequences of miRNA, lncRNA, and protein from miRbase, NONCODE, and String, respectively, and processed them as described in Shen et al. It is well known that the RNA sequence is composed of four kinds of nucleotides: A, adenine; G, guanine; C, cytosine; and U, uracil. The protein sequence is composed of 20 kinds of amino acids, which is quite unfriendly for encoding and storage. Therefore, we divide the 20 kinds of amino acids into four groups, including (1) Ala, Val, Leu, Ile, Met, Phe, Trp, Pro; (2) Gly, Ser, Thr, Cys, Asn,Gln, Tyr; (3) Arg, Lys, His; and (4) Asp, Glu, according to the polarity of the side chain. Thus, each sequence of ncRNA or protein can be represented by a vector in which each dimension of the vector can treated as normalized frequency of the k-mer in the sequence.

In this article, k is set to 3 and each sequence is represented as a 64-dimensional vector (4 × 4 × 4). Each dimension of the vector is the full array of three nucleotide combinations of AAA, AAC, ..., UUU. A window of size 3 can get all the fragments of the current sequence when sliding in steps of 1. Each dimension value of the representation vector can be obtained by counting and normalizing the appearance number of these fragments.

Disease MeSH Descriptors and Directed Acyclic Graph

Medical subject headings (MeSHs) is a rigorous term developed and published by the National Library of Medicine for use in management and inquiries in the fields of biology and medicine. The previous work of calculating similarities through the MeSH descriptors to define the disease is effective and attracts widespread attention. Thus, we adopted this method and filtered out the disease-related keywords of the data downloaded from https://www.nlm.nih.gov/.

In this system, each disease with a descriptor can generate a directed acyclic graph and can be accurately and comprehensively characterized. The details of the calculation are described below: The directed acyclic graph (DAG) of disease D is defined as DAG(D) = (D, N(D), E(D)), N(D) is a set of points containing all diseases in the DAG, and E(D) is a set of edges containing all relationships between diseases in the DAG. The contribution of the ancestral node to the disease D in the directed acyclic graph is calculated by the following formula:t is the element of N(D) and is an attenuation factor. The farther the ancestral disease distance D is, the smaller the contribution to D. D has the greatest contribution to itself and is defined as 1. The total contribution of all elements in the set N(D) to disease D isThe similarity between disease I and disease j can be calculated by the following formula

Drug Morgan Molecular Fingerprint

RDkit is an open-source chemical informatics and machine learning toolkit. SMILES (simplified molecular input line entry specification), which was proposed by David Weininger, is a specification for clearly describing molecular structure using ASCII strings. The SMILES were downloaded from DrugBank and converted to Morgan molecular fingerprint by the python package called RDkit to represent the characteristics of the drug.

Sparse Autoencoder

After obtaining the high-dimensional representation vector from disease semantics and drug Morgan molecular fingerprints, we use the sparse autoencoder to reconstruct new vectors from the original space to improve feature quality and reduce noise. The sparse autoencoder is an unsupervised learning algorithm that uses the backpropagation algorithm to make the output value as equal as possible to the input value. It consists of two parts, including the encoder that performs the compression function and the decoder that performs the reconstruction function. In addition to the input layer, the input to the i-th node of the l-th layer iswhere is the weight of the (l-1)-th layer neuron to the i-th neuron of the l-th layer, is the number of neurons in the (l-1)-layer, and is the output of the (l-1)-th layer of neurons.

The output of the i-th node of the l-th layer iswhere b is the bias and is the activation function. Relu was chosen to perform this operation.The loss function is defined as follows:The first part is like a normal autoencoder, describing the error between input and output, where m is the number of samples in the training set, and is the number of hidden layers. The second part is a sparsity penalty term called Kullback-Leibler (KL) divergence used to constrain the activity of the hidden layer unit, where n is the number of hidden layer units. The third part is weight decay to help prevent overfitting.

Node2vec

The behavior information of a node can also be considered as a measure of the function of this node. A row or column in the adjacency matrix is a one-hot description of such information. Considering the disadvantages of sparseness, discreteness, and occupying a large amount of storage space, we hope to find a kind of simple and efficient low-dimensional representation.

Node2vec is a kind of representation algorithm with the purpose of mapping of nodes to a new low-dimensional feature space and at the same time maximizing the preservation of the network structure in the original space. The main idea of node2vec is to treat the random walk path of the nodes in the network, that is, the node sequence, as a text, and then use word2vec to model the path, maximize the likelihood probability, and learn the parameters through the random gradient. By introducing two parameters p and q, breadth-first search and depth-first search are introduced into the generation process of random-walk sequences. The general flow of the algorithm is as follows: G = (V, E) is a given network and is the mapping function from nodes to feature representation. Here, d is a hyperparameter representing the dimension of the vector and f is a matrix of size |V| × d. For each source node , is defined as a neighborhood of node u generated through a neighborhood sampling strategy S. The problem translates to optimizing the following objective functions:Two standard assumptions are made in order to make the optimization problem tractable: conditional independence:and symmetry in feature space:With the above assumptions, the objective in Equation 8 simplifies toGive the source node u a random walk with length l, let be the i-th node of the walk, and the starting node . The node obeys the following distribution:where is the unnormalized transition probability between nodes v and x, and Z is the normalizing constant. Directly setting the transition probability to the edge weight cannot effectively consider the network structure and search for different neighbor spaces. The walk now needs to decide on the next step, so it evaluates the transition probabilities on edges (v, x) leading from v by setting two parameters p and q. Let , whereand is the shortest path distance between nodes t and x.

The node2vec algorithm is as follows:

Algorithm 1

LearnFeatures (Graph G = (V, E, W), Dimensions d, Walks per node r, Walk length l, Context size k, Return p, In-out q)

= Preprocess Modified Weights (G, p, q)

= (V, E, π)

Initialize walks to Empty

for iter = 1 to r do

for all nodes do

walk = node2vecWalk (, u, l)

Append walk to walks

f = Stochastic Gradient Descent (k, d, walks)

return f

node2vecWalk (Graph  = (V, E, π), Start node u, Length l)

Inititalize walk to [u]

for walk_iter = 1 to l do

curr = walk [−1]

Vcurr = Get Neighbors (curr, )

s = Alias Sample (Vcurr, π)

Append s to walk

return walk

Note that whenever the representation of the node is embedding via node2vec, the tested link is stripped to ensure that the tag information is not leaked into the test set. The behavior information of all nodes in each fold of 5-fold cross-validation can be described by node2vec based on 80% associations, that is, 80% of the edges in the network.

Author Contributions

Z.-H.G., H.-C.Y., and Z.-H.Y. conceived the algorithm and carried out analyses. Z.-H.G. and Z.-H.Y. wrote the manuscript. All authors read and approved the final manuscript.