According to the actual situation, we first download eight known kinds of associations from multiple databases. Then a set of data pre-processing operators, including identifier unification, de-redundancy, and deletion of the irrelevant items, are implemented. Besides, we gathered known experimentally supported LDAs data from the lncRNASNP2 and the LncRNADisease database, and we thus obtained 345 different lncRNAs and 295 different diseases (i.e., 1264 independent lncRNA-disease association pairs as positive samples). The details of the final LDAGRL objects data are shown in Table 1 and Figure 1.

The prediction performance of LDAGRL was evaluated mainly using the area under the receiver operating characteristic curve (AUC). Relevant evaluation metrics include Accuracy (Acc.), Precision (Prec.), Sensitivity (Sen.) or Recall, Specificity (Spec.) F1-Score and MCC (Matthews correlation coefficient) and their definitions as follows: A c c u r a c y   A c c . = T P + T N T P + T N + F P + F N (1) P r e c i s i o n P r e c . = T P T P + F P (2) S e n s i t i v i t y S e n . = R e c a l l = T P T P + F N (3) S p e c i f i c i t y   S p e c . = 1 − T P F P + T N (4) F 1 − S c o r e = 2 × P r e c i s i o n × R e c a l l P r e c i s i o n + R e c a l l (5) M a t t h e w s   c o r r e l a t i o n   c o e f f i c i e n t   M C C = T P × T N − F P × F N T P + F P T P + F N T N + F P T N + F N (6) where TP, FP, TN, and FN respectively represent the number of true positives, false positives, true negatives, and false negatives.

We adopted eight out of nine kinds of associations to construct BHnet. Then, the bridge feature of the node can be obtained by graph embedding algorithm on the BHnet. Note that LDAs are not included in the BHnet such that we can explore the potential relationship possibility between the lncRNA nodes and the disease nodes in the case of no prior edges (LDAs) in the BHnet for LDAGR. In other words, this article sets out to explore the association possibilities between lncRNAs and diseases only relying on their bridge nodes. Hence, we used LDAs as a training set and test set to conduct 5-CV, while the bridge feature (learned from eight types of associations) was the node/edge feature.

According to available datasets, the proposed BHnet based on biomolecules can be composed of nodes and edges. For nodes, there are five kinds of molecular such as ncRNA (miRNA, lncRNA), protein (target), drug, and disease. For edges, it consists of eight associations except known lncRNA-disease associations. Since the unknown lncRNA disease association would have been predicted, eight associations were embedded in BHnet. As shown in Figure 2, LDAGRL consists of three parts. First, we construct a BHnet by integrating biomolecule data, including five types of molecules. Second, we leveraged SDNE to learn node representations (node embedding) as dense feature vectors for LDA pairs. Third, we used a supervised machine learning-based XGBoost classifier to predict unknown LDAs.

Specifically, in the LDAGRL, by integrating multiple molecules information, we leveraged multiple relationships (associations) to construct a BHnet for lncRNAs and diseases, including eight kinds of associations (i.e., miRNA-lncRNA, miRNA-disease, lncRNA-protein, protein-disease, drug-disease, miRNA-protein, drug-protein, protein-protein). Then, based on the graph embedding framework, we employed SDNE to learn the embedding vector of nodes. Finally, we adopted the embedding vector combined with the positive and negative samples constructed by LDAs to train the XGBoost classifier, aiming to predict potential links.

As shown in Figure 1, we downloaded the sequences information of lncRNA, miRNA, and protein from miRbase (Kozomara et al., 2019), NONCODE (Fang et al., 2018), and STRING (Szklarczyk et al., 2016) database respectively. Similar to the previous methods, we utilize a 64-dimensional vector to encode ncRNA (i.e., lncRNA and miRNA) sequences, where each attribute in nodes represents the normalized frequency of the k-mer for corresponding sequences. Based on the polarity of the side chain, we first divide 20 amino acids into four types and then represent each protein sequence by k-mer to form a 64-dimensional vector following the method proposed by Shen et al. (Shen et al., 2007).

In LDAGRL, the smiles of drugs are downloaded from the DrugBank database (Wishart et al., 2018), which combines detailed drug data with comprehensive drug target information. By RDKit (Open-Source Cheminformatics Software) API, we transform the smiles of drugs into corresponding Morgan fingerprints to get drug molecular fingerprint representation.

The MeSH (Medical Subject Headings) is a comprehensive searchable control vocabulary primarily employed for indexing journal articles and books in the life sciences (Wang et al., 2010). In MeSH, related disease annotation terms can be represented by a Directed Acyclic Graph (DAG) structure that can be expressed as DAG = (D, N(D), E(D)). The D _d (t) of a disease t in a DAG to the semantics of disease D is defined as follows: D d D = 1 D d t = max 0.5 * D d t ′ | t ′ ϵ   c h i l d r e n   o f   t   i f   t ≠ d (7) where for a given disease D, N(D) denotes D itself together with all its ancestor nodes, while E(D) denotes all relationships connecting between nodes in the DAG(D). So, the semantic feature score between two diseases, where the i and j, can then be calculated by: S i , j = ∑ t ∈ T i ∩ T j D i t + D j t ∑ t ∈ T i D i t + ∑ t ∈ T j D j t (8)

Numerical studies substantiate the effectiveness and superior abilities of the proposed Structural Deep Network Embedding (SDNE)(Wang et al., 2016), which is a semi-supervised deep model to perform network embedding. It can preserve the highly-nonlinear local-global network structure well and is robust to sparse networks, with its advantages mainly focusing on the following crucial two points: A deep architecture: To capture the highly nonlinear network structure, it is composed of multiple nonlinear mapping functions to map the input data to a highly nonlinear latent space to capture the network structure; A semi-supervised model: To address the structure-preserving and sparsity problems, it exploits both the second-order and first-order proximity. Meanwhile, it designed the unsupervised component to preserve the first- and second-order proximity to refining the representations in the latent space.

Here, unsupervised components preserve global network structures by second-order proximity. As an unsupervised model, Autoencoder consists of two parts, i.e., the encoder and decoder. The Autoencoder aims to minimize the output and input reconstruction error. For given the input x ⁱ , for each layer, the hidden representations are shown as follows: y i 1 = σ W 1 x i + b 1 , k = 1 (9) y i k = σ W k y i k − 1 + b k , k = 2 , … , K (10)

After obtaining y i k , we can obtain the output x ^ i by reversing the calculation process of the encoder. The objective function is shown as follows: O = ∑ n = 1 ∞ ∥ x ^ i − x i ∥ 2 2 (11)

Considering the penalty or regularization, more penalty to the reconstruction error of the non-zero elements than that of zero elements in the adjacency matrix. The revised objective function is shown as follows: O 2 n d = ∑ n = 1 ∞ ∥ x ^ i − x i ⊙ b i ∥ 2 2 (12) = ∥ X ^ − X ⊙ β ∥ F 2 where⊙means the Hadamard product, b _i = b i . j j = 1 n . i f   s i , j = 0 , b i , j = 1 , e l s e   b i , j = β > 1

It is essential to preserve the local structure. Therefore, the supervised component is designed to exploit the first-order proximity. The objective function for this goal is defined as follows: O 1 s t = ∑ i , j = 1 n s i , j ∥ y i k − y j k ∥ 2 2 (13) = ∑ i , j = 1 n s i , j ∥ y i − y j ∥ 2 2

To preserve the first-order and second-order proximity simultaneously, a semi-supervised model was proposed, which combines Eq. 12 and Eq. 13, and joint minimizes the following objective function: O m i x = O 2 n d + α O 1 s t + ν L r e g (14) = ∥ X ^ − X ⊙ B ∥ F 2 + α ∑ i , j = 1 n s i , j ∥ y i − y j ∥ 2 2 + ν L r e g where L r e g is an L 2-norm regularizer term to prevent overfitting, which is defined as follows: L r e g = 1 2 ∑ k = 1 K ∥ W k ∥ F 2 + ∥ W ^ k ∥ F 2 (15)

In this section, to demonstrate the prediction performance of our novel method, the bridge molecular, including lncRNA, miRNA, drug, and protein, are integrated to obtain lncRNA-disease link embedding. Thus, we utilize SDNE to train the proposed BHnet and to get a dense representation of the lncRNA and the disease vector.

For further investigation, we choose XGBoost as a classifier algorithm to verify the classification performance of LDAGRL. Moreover, the AUC scores are used to evaluate the predictive performance of our method. As seen from Table 2 and Figure 3, as illustrated in the method section, LDAGRL effectively predicts potential lncRNAs related to diseases. Specifically, it can be easily found that LDAGRL achieved a reliable AUC of 0.9258, which is the expected AUC we required. We can see that in most previous methods, the characteristics of the research objects themselves were considered to detect unknown relationships in these methods.

Nevertheless, there are many other indirect associations, such as the other associations in LDAGRL. If these previous methods integrate these different indirect associations, the predictive performance can be improved significantly. Our method is better than previous methods (such as bipartite graph) that only focus on single or isolated objects to some extent. As can be seen, LDAGRL works more effectively in predicting potential LDAs when adopting multiple bridge relationships-based methods.

Then, we compared our model with existing state-of-the-art methods, i.e., GCNLDA (Xuan et al., 2019), GCRFLDA (Fan et al., 2022) and gGATLDA (Wang and Zhong, 2022). They were GCN-based models (Kipf and Welling, 2016) on LDAs prediction. For gGATLDA, according to its experimental setup, we correspondingly collected its three benchmark datasets called Dataset1, Dataset2 and Dataset3 to compare the performance. Specifically, Dataset1 contained 3207 LDAs (443 lncRNAs and 608 diseases); Dataset 2 contained 2697 LDAs (240 lncRNAs and 412 diseases) and Dataset3 contained 621 LDAs (285 lncRNAs and 226 diseases). To objectively compare the performance of LDAGRL with the state-of-the-art methods, similarly, we adopt 5-CV to conduct comparison in a targeted manner for false positive rate in identifying novel LDAs by LDAGRL, combining the precision indicator of prediction. As shown in Table 3, gGATLDA show unstable average precision on three kinds of datasets under 5-CV, while LDAGRL exhibits stable average precision under 5-CV and thus lower false positive rate.

Though the AUCs and precisions of GCNLDA and GCRFLDA are higher than the corresponding indicator of LDAGRL, it can be observed from Table 4 that three types of methods, including LDAGRL, keep AUC at the same level (>0.90) and the results of experiment manifested that LDAGRL has a trait of low false negative and low false positive.

To add an independent baseline approach (i.e., graph embedding algorithm) to compare four types of methods, we adopted the node2vec (Grover and Leskovec, 2016) as the baseline model to obtain node embedding and employed the Random Forest classifier to score the potential LDAs. Since node2vec is a graph embedding algorithm that considers both the Depth First Search (DFS) and the Breadth First Search (BFS) neighborhood. It is consistent with our design idea that exploring the association possibilities between lncRNAs and diseases relies on their bridge nodes or bridge paths.

First, as shown in Table 5, we listed all potential paths and calculated the frequency for lncRNA and disease in BHnet dataset (104,282 edges). Here, the node frequency calculation needs to make sure that each node on the same path appears together (i.e., for L-M-D, we calculate L/D frequency under the condition that L-M-D holds simultaneously, instead of one of L-M, M-D and L-D holds).We can observe that the ‘lncRNA-miRNA-disease’ path can be chosen as a BHnet to conduct baseline (node2vec) due to the highest frequency both for each lncRNA and for each disease.

Then, we implemented the predictive performance comparison experiment for five methods over node2vec (with default parameters) by 5-CV. As shown in Table 6, five methods can obtain satisfactory AUCs over node2vec, GCRFLDA achieved the best performance on both AUC and Precision. LDAGRL using L-M-D path get the next best performance and its precision is consistently and even higher related to LDAGRL. These results also indicate bridge paths play a key role in LDA prediction.

Besides, GCNLDA, GCRFLDA and gGATLDA all adopted the similarity subnetwork to build heterogeneous bipartite graph or tripartite graph and followed the assumption that the lncRNAs in the same sets are similar. Then they think of LDAs prediction as a recommender systems issue in which they usually view lncRNA as the user and disease as the item. Despite its rationality from a pure computational perspective, it may be controversial and have not stood up to the biological significances. Sometimes, a single nucleotide difference can completely change the nature of a lncRNA. Surely, the coarse-grained feasibility brought about by the way enable LDAs prediction to a certain extent for researchers, but the false positive problems at the same time cannot be neglected. In LDAGRL, we remove the disadvantage of the similarity hypothesis and depend on the regulatory or targeting relationships between lncRNAs and corresponding bridge molecules, obtaining the satisfactory prediction effects with the same level prediction performance and lower false positive rate.

Network embedding (Yuan et al., 2018) is a crucial method for learning low-dimensional representations of vertexes in network. As described in the method section, the different classifiers may influence LDAGRL prediction performance. Therefore, we implemented the experiment to evaluate the impact of five classifiers.

To evaluate the performance of LDAGRL based on different classifier, we choose XGBoost, Random Forest, Logistic Regression, SVM, and AdaBoost to execute the 5-CV experiment. By validating different classifiers, different values of AUC are obtained through the 5-CV. As seen in Table 7, XGBoost, SVM, Logistic Regression, AdaBoost, and Random Forest are all effective in classification with high AUC values. Moreover, Tree-based classifiers, such as XGBoost and Random Forest, have been demonstrated to be a practical tool in prediction due to their higher operational efficiency and lower over-fitting rate. By looking into the detail of these results, we can observe that, for LDAGRL, compared with the AdaBoost, the XGBoost and the Random Forest achieve higher AUC value. Besides, we can also find that all classifier parameters are default values, and only the bridge feature for nodes is appended to the training process. In the LDAGRL, the result of 5-CV through the XGBoost classifier (with AUC = 0.9258, default parameters) is better than other classifiers. It further verifies the superiority of the SDNE on LDAs prediction.

In the LDAGRL, each node can be represented by its intrinsic attributes and relationship with other nodes. Thus, each node can be represented as a vector (192-dimension) by two kinds of information, including attribute and bridge structure. For attribute information (64-dimensional vectors), the node’s attributes can be the k-mer about sequences of ncRNA and protein, the disease’s semantics, and the drug’s molecular fingerprint. For bridge structure information (128-dimensional vectors), the relationship of each node with others could be abstracted by the network embedding method SDNE.

Here, in comparison with the predictive performance of LDAGRL for different node feature combinations, we mainly divided it into three groups to validate the different performances with Attribute, Bridge, and Attribute + Bridge combinations. It is known that the attribute information is each node’s intrinsic feature, so we design an experiment that can verify the predictive performance of prediction based on attribute information with the previous isolated embedding method.

Furthermore, in the LDAGRL, bridge structure information, as critical relationships among nodes, is vital for LDAs prediction. The main goal we construct LDAGRL is to obtain the network’s relation features. Therefore, it is indispensable to verify the bridge structure’s influence on predictive performance in LDAGRL. After the above two kinds of the feature are verified, considering the complexity of LDAGRL and the character of lncRNAs and diseases, we used the ‘Attribute + Bridge’ combination to evaluate the entire performance, aiming at obtaining optimized features for classifiers and further improve LDAGRL generalization performance.

Among nodes in LDAGRL, bridge structure information is a critical association relationship for LDAs prediction. In other words, the main goal of our constructing LDAGRL is to obtain the relation features, namely, the bridge structure feature.

As shown below, Figure 4 ~ Figure 6 plot the ROC curves of the three combinations’ results and reports their AUROC values of 5-CV. Figure 4 shows the AUC result of the ‘Attribute’ that 5-CV with pure attribute information as the node’s characteristics. Figure 5 shows the AUC result of ‘Bridge’ that 5-CV with pure bridge structure information as the feature of the node. Figure 6 shows the AUC result of the ‘Attribute + Bridge’ combination based on the feature combined attribute information with the bridge structure.

As seen from Table 8, the ‘Attribute’ combination has the lowest AUC and accuracy rate in LDAGRL. When the feature combination is ‘Attribute + Bridge’, the value of AUC based on SDNE for XGBoost barely change, and the average accuracy rate increase more slowly than the ‘Bridge’ combination. Therefore, the predictive performance of LDAs based on the feature combined attribute information with bridge structure information (i.e., ‘Attribute + Bridge’ combination) is not better than the ‘Bridge’ combination, which dominates the highest TPRs under the same FPRs and has the highest AUC (0.9258). It implies that attribute information has a small impact on predictive performance. Besides, it is worth pointing out that though the augment of features information is relatively large for ‘Attribute + Bridge’, the average accuracy rate of the ‘Bridge’ and ‘Attribute + Bridge’ remain stable. It is because we chose the SDEN to globally represent the bridge structure feature of nodes in the entire network and the flow of information directly or latently with other nodes, thus improving the performance. In addition, the results in Figure 5 show that the ‘Bridge’has superiority in LDAGRL.

Endocrine system diseases including type 2 diabetes mellitus, diabetic nephropathy, obesity and osteoporosis are common diseases (Sun et al., 2022). It is evident that the early detection of endocrine system diseases is vital to precise treatment (Hackney and Lane, 2015; Rachdaoui and Sarkar, 2017). Hence, the case study is implemented to identify the possible lncRNAs associated with endocrine system diseases to thus explore the generalization ability of LDAGRL. Specifically, we take LDAGRL to identify novel LDAs and verify the prediction results based on ENCD database (Hao et al., 2023).After scoring those scores for potentially associated lncRNAs with the endocrine system diseases, all predicted disease-related lncRNAs are ranked. Here, we select the top 10 associated lncRNAs which get the highest predicted ranks for endocrine system diseases. Relevant biology literature and databases support predictive results, and the details shown in Table 9. Here, we listed the top 10 predicted lncRNAs and then confirmed them in relevant biology literature or databases, which also indicated the consistency between LDAGRL and biology wet experiments.