In this work, the similarity of drug pairs is calculated based on the Jaccard similarity coefficient, and the similarity of disease pairs is obtained by calculating the semantic similarity using medical subject descriptors.The detailed calculations are provided in Supplementary Material. A drug similarity network R and disease similarity network D can be constructed based on drug similarity and disease similarity, and the edge weight is derived from the similarity value. A r = r 1 , r 2 , … , r M denotes the set of M drugs, and A d = d 1 , d 2 , … , d N denotes the set of N diseases. S r ∈ R M × M denotes the adjacency matrix of the drug similarity network, and S d ∈ R N × N denotes the adjacency matrix of the disease similarity network. A drug–disease association network S r d can be constructed based on the known association information between drugs and diseases. An edge exists between r i and d j if there is a known association between drug r i and disease d j . The binary association matrix Y ∈ 0 , 1 M × N corresponds to S r d , the entry y i j of the matrix Y is 1 if there is an edge between drug r i and disease d j , otherwise y i j = 0 which does not mean that there is no association between the drug r i and disease d j , but that there may be a potential association that has not yet been identified. For each drug r i , this study aims to identify diseases that are potentially associated with r i . The drug–disease heterogeneous network is constructed by integrating three networks: drug–drug similarity network, disease–disease similarity network, and drug–disease association network.

To solve the problem of the sparse verified drug-disease associations in drug repositioning, we can leverage the related information of drugs and diseases to predict potential indications of drugs to complement the drug–disease association data. GCN learns the low-dimensional representations of nodes from the irregular graph structure, and each of its layers aggregates the neighboring node information of the target node and uses the output of the previous layer as the input of the next layer, which is a process of continuously recursively aggregating neighborhood features. In this work, GCN is introduced by applying the similarity and association information to predict new drug–disease associations, which can complete the drug–disease association matrix from the biological network perspective and be used as a pre-training step to predict the likelihood of drug–disease associations.

First, the adjacency matrix G corresponding to the drug–disease heterogeneous network is defined. S r ′ = E r − 1 / 2 S r E r − 1 / 2 and S d ′ = E d − 1 / 2 S d E d − 1 / 2 are the normalized drug similarity matrix and disease similarity matrix, respectively, where E r = d i a g Σ j S r i j and E d = d i a g Σ j S d i j ( S r i j or S d i j is ( i , j )th entry of the similarity matrix) are the degree matrices of the drug and disease similarity matrices, respectively. The introduction of an appropriate degree of similarity contribution can better learn the embedding representation of drugs and diseases. Thus, a similarity penalty factor μ is introduced to control the contribution of similarity information, which can be expressed as S ^ r ′ = μ * S r ′ , S ^ d ′ = μ * S d ′ . Then, the adjacency matrix of the drug-disease heterogeneous network is represented by G = S ^ r ′ Y Y T S ^ d ′ (1)

Given the matrix G , the general process of the convolution operation based on the GCN encoder according to the study of Yu et al. (2020a) can be described as H l + 1 = f G , H , W = σ E − 1 2 G E − 1 2 H l W l (2)

Here, H l + 1 is represented as the embeddings of nodes encoded at layer l + 1 , E E = d i a g Σ j G i j is the degree matrix of the adjacency matrix G , and H l represents the embeddings encoded at layer l , which is used as the input at layer l + 1 . W is a learnable weight matrix, and σ is a nonlinear activation function (e.g., RELU activation function).

Following the rule of Eq. 2, the GCN recursively learns node features. After l layers of iterations l = 1 , 2 , … , L , the GCN captures information about different structures of the heterogeneous network at different layers. To enable the GCN to fully learn the features of the nodes, we use the attention mechanism to connect the embeddings of different layers of GCN learning. Different attention weights are set at different layers. The final embeddings of the obtained drugs and diseases are denoted as H R H D T = ∑ β l H l . Here, β l is initialized to 1 / l + 1 , H R ∈ R M × k and H D ∈ R N × k represent the final embeddings of the drugs and diseases, respectively.

To complement the drug–disease association matrix, we feed the final drugs and diseases embeddings into a bilinear decoder (Li et al., 2020b) for link prediction between drugs and diseases. Thus, the reconstruction of the drug–disease association matrix can be represented by Y ∼ = ρ H R W ′ H D T , where ρ is the sigmoid activation function, and W ′ is the trainable weight matrix. Entry y i j ′ in the matrix Y ∼ represents the predicted score between the drug r i and the disease d j .

Ultimately, we use a binary cross-entropy loss function as the objective function to optimize the drug–disease association continuously. Loss = − 1 N × M η × ∑ i , j ∈ Y + log ⁡ y i j ′ + ∑ i , j ∈ Y − log 1 − y i j ′ (3) where i , j indicates the drug–disease pair, and η = Y − / Y + indicates the ratio of the number of positive drug–disease pairs to the number of negative drug–disease pairs to balance positive and negative sample data.

We complement the drug–disease association information to alleviate the data sparsity problem by adopting GCN to implement pre-training on the drug–disease heterogeneous network. An entry of 1 in the drug-disease association matrix indicates that the disease is an indication for the drug and is a known association confirmed in clinical trials. In contrast, an entry of 0 means that there may be a potential association that has not yet been identified. GCN is utilized to preprocess unknown drug–disease associations to obtain more promising association information for subsequent prediction tasks. A threshold θ is set to screen highly confident drug indications. Specifically, we retain the original value if the drug–disease prediction score is greater than or equal to θ . Otherwise, we set it to 0 because a more considerable value suggests a stronger association between the drug and disease. Then, a preprocessed complemented drug–disease association matrix is obtained.

Previous studies based on metric learning have considered drug-centric metrics (Hsieh et al., 2017; Park et al., 2018), neglecting to model drug–disease relationships from the disease perspective, which may lead to biased learning of latent vector representation of drugs and diseases, and limit the predictive performance of the model. Therefore, we take the drug- and disease-centric metrics into account for our reinforcement symmetric metric learning algorithm, which not only considers the relationships between drugs and diseases, but also implicitly establishes drug–drug and disease–disease relationships, thus enhancing the representation learning of drugs and diseases.

The goal of metric learning is to learn a metric function that pulls similar entities closer together and pushes dissimilar ones farther apart (Park et al., 2018; Wu et al., 2020). For example, when identifying possible favorite items for users in the recommendation system, metric learning assigns smaller distances to users and items with existing interactions and larger distances to users and items with unknown interactions. Similarly, it can be applied to the issue of predicting potential possible indications for drugs. The metric learning algorithms project drugs and diseases into the unified vector space and encode the latent vectors of drugs and diseases based on associations between drugs and diseases. This way, distances between drugs and diseases with known associations are closer than that between drugs and diseases without associations or with unknown associations. The likelihood of drug–disease associations is measured by the position of drugs and diseases in the unified metric vector space. Unvalidated diseases are sorted in descending order by prediction scores for a given drug, and top-k disease recommendations can be obtained.

To verify the effectiveness of our method in predicting drug–disease associations, we compared RSML-GCN with five state-of-the-art drug repositioning methods based on recommendation system and GCN including GRGMF (Zhang et al., 2020), DRWBNCF (Meng et al., 2022), LAGCN (Yu et al., 2020b), DRHGCN (Cai et al., 2021) and CMLDR (Luo et al., 2021). These methods are detailed below.

• GRGMF establishes a generalized matrix factorization model that obtains the latent representation of each node by adaptively learning the neighborhood information of each node, and it introduces external similarity information to facilitate the prediction of potential links.

For a fair comparison, we ran these competing methods with the optimal parameters suggested in the original papers on benchmark datasets. The complete evaluation of all methods was performed under 10-fold cross-validation. The specific experimental settings are described in Supplementary Material. Also, we conducted parameter analysis and selected the best parameters as the recommended settings for RSML-GCN in this work.

Considering that hyperparameters could affect model performance, we further investigate the influence of hyperparameters including that used in GCN, such as the latent vector dimension n , the marginal value strengths γ , and weight variables. The specific hyperparameter settings are given in Supplementary Material. According to the previous study (Yu et al., 2020a), we set the parameters for GCN with the embedding dimension k = 64 , number of layers L = 3 , initial learning rate l r 1 = 0.008 , node discard rate β = 0.6 , regularize discard rate ξ = 0.4 , and penalty factor μ = 6 . Moreover, we have investigated the effect of the latent vector dimension n by varying its value from 30 to 400, and examined the influence of the marginal value strengths γ by varying its value from 0.01 to 100. The optimal parameters were determined by the grid search method, and detailed information is provided in the Supplementary Material. Finally, the latent vector dimension of drugs and diseases in the metric space was fixed at 250, the initial learning rate l r 2 was 0.05, and the batch size was 512. In terms of variables, refer to the settings of Li et al. (2020a), all weight variables followed a uniform distribution [-0.01, 0.01] and were randomly initialized, and all latent vectors (such as α r , β d ) that follow a normal distribution (mean: 0.1, variance: 0.03) were randomly initialized. More detailed parameter settings are described in Supplementary Figures S1–S4.

To evaluate the performance of RSML-GCN, we conducted extensive experiments on two benchmark datasets Cdataset and Fdataset in Supplementary Table S1 and compared RSML-GCN with five state-of-the-art association prediction methods. The performance evaluation results of all methods under 10 times 10-fold cross-validation were reported in Table 1. The experimental results show that RSML-GCN had good performance in relevant metrics and was superior to other methods. In terms of the primary metric, AUPR, RSML-GCN achieved the highest average value of 0.7941, which surpasses GRGMF by 33.7%, and the average AUPR values of DRWBNCF, LAGCN, DRHGCN and CMLDR were 0.4992, 0.1562, 0.5480, and 0.2607, respectively. Additionally, RSML-GCN outperformed other methods in terms of AUC, with an average AUC value of 0.9077. This was 0.20% higher than the second-best method, DRHGCN. DRWBNCF, GRGMF, LAGCN and CMLDR have AUCs of 0.8642, 0.8994, 0.7874 and 0.7999, respectively.

We have performed 10 times 10-fold cross-validation and obtained AUC and AUPR values for all methods. The paired t-test is applied to statistically test the significance between the proposed method and other existing methods in terms of AUPR values, which have been conducted in previous studies. The paired t-test results including the p-values are showed in Table 2. It can be observed that RSML-GCN is statistically significantly better than other methods (p < 0.05).

The drug–disease prediction problem was formulated as a top-k recommendation problem, where potential therapeutic diseases are recommended for a specific drug. Therefore, we used top-k prediction results as evaluation metrics, specifically precision@K (p@K) and recall@K (r@K), which are widely used in recommendation domains. The performance of different models in predicting the top-k drug–disease associations on Cdataset was reported in Supplementary Figure S5. RSML-GCN outperformed other models in terms of r@5, r@10, p@5, and p@10. Additionally, in Supplementary Figure S6, we can find that RSML-GCN also achieves excellent performance in the recall and precision values of the top-k predictions on Fdataset, which is much better than collaborative filtering-based, GCN-based, and metric learning-based methods. Notably, the performance indicators of LAGCN in these results were inferior to those of other methods, potentially due to GCN exhibiting over-smoothing issues stemming from dataset imbalances. The prediction results of the matrix factorization method GRGMF were lower than RSML-GCN, indicating that the metric learning method can effectively compensate for the shortcomings of matrix factorization. In contrast, CMLDR yielded significantly lower results than our proposed method, which suggests the usefulness of increasing the disease-centric auxiliary reuse learning for improving the drug-centric metric. The superior performance of RSML-GCN can be attributed to the following aspects. First, deep learning method is utilized to learn the potential representations of drugs and diseases and generate high confident drug–disease associations. This effectively alleviates the sparsity problem of drug–disease association data and improves the performance of subsequent task predictions. Second, we designed a reinforcement metric learning method to learn the metric between drugs and diseases from both drug and disease aspects, which can improve previous metric learning methods. Finally, by integrating the deep learning method and metric learning method, the proposed method can achieve better performance than other drug–disease prediction methods. Furthermore, we have avoided excessive integration of biological data, as improper handling of such data can introduce noise and adversely affect prediction results. These results comprehensively demonstrate the effectiveness of our proposed method in identifying drug–disease associations.

To evaluate the model performance of RSML-GCN, we set up a variant of RSML-GCN, named as RSML. In RSML, we used only reinforcement symmetric metric learning to predict drug–disease association scores, which removes the pre-training step of complementing the drug–disease association matrix using GCN. In order to check the contribution of the pre-training component, we compared RSML-GCN with RSML based on Cdataset.

Based on the drug–disease association matrix, the RSML projected drugs and diseases to the unified metric vector space and learned their latent vectors based on the push–pull mechanism. The Euclidean distance was adopted to obtain the potential treatment probabilities of drugs for diseases. As can be seen in Supplementary Table S2, incorporating GCN in RSML-GCN as a pre-training step to complement the drug–disease association matrix resulted in improved predictive performance. The average AUPR of RSML-GCN was 6.45% higher than that of RSML, while maintaining a comparable AUC. Additionally, significant enhancements were observed across all top-k prediction evaluation metrics, as depicted in Supplementary Figure S7. This improvement can be attributed to GCN’s ability to integrate similarity information from drug–disease associations, enabling the learning of more comprehensive representations and acquiring more confident drug–disease association information. Consequently, this approach helps address the imbalance between positive and negative samples to serve downstream tasks better and improve the predictive potential of metric learning method. The results generally indicate the reliability of RSML-GCN for predicting drug-related diseases.

To assess the ability of RSML-GCN in predicting potential indications for new drugs, we removed the associated diseases of the test drug and predicted indications for it on Cdataset. To more accurately display the top-k recommendation performance of the model, we selected drugs associated with at least 50 diseases to evaluate the performance of RSML-GCN for new drug prediction. After training, the latent vectors of drugs and diseases in the training samples were learned. For a new drug without any known association, RSML-GCN could obtain latent vectors of the drug by utilizing similarity information from its h-nearest neighbors in the training set to predict the potential drug-related diseases. In the experiment, empirically, h was set to 5 to simplify the model.

The results of predicting unknown diseases for new drugs are presented in Supplementary Table S3, RSML-GCN exhibited the best performance in the primary metric AUPR (average AUPR = 0.5555), which is higher than GRGMF and CMLDR based on recommendation system by 49.0% and 74.4% (AUPR value), respectively. In terms of AUC, RSML-GCN had an average AUC of 0.6985, which is higher than that of these state-of-the-art prediction methods. The recall and precision of top-k recommendations of RSML-GCN for predicting potential indications for new drugs were reported in Figure 4, which shows the performance of RSML-GCN over other methods for different values of K. For the average recall value, our RSML-GCN performed better than other methods under most K values. For example, when K = 10 and K = 50, RSML-GCN achieved the best average recall values, 0.0807 and 0.3191, respectively. In particular, when K = 10, DRWBNCF, LAGCN, DRHGCN, and CMLDR obtained recall values of 0.0245, 0.0356, 0.0428 and 0.0565, respectively, the recall values of GRGMF and RSML-GCN were almost comparable. In addition, when K = 10 and K = 50, RSML-GCN attained average precision values of 0.7451 and 0.6072, respectively, which is higher than most competitive methods. Overall, the comprehensive results demonstrate that RSML-GCN has an excellent ability to predict related diseases for new drugs.

For a new disease without any known associations, RSML-GCN can use the similarity information of diseases to predict potential candidate drugs for new diseases. We also conducted the experiments, in which all relationships for each disease were removed to predict candidate drugs for new diseases. The results compared with state-of-the-art methods were reported in Supplementary Table S4 and Supplementary Figure S8. RSML-GCN was the second-best, significantly better than DRWBNCF, LAGCN, DRHGCN, and CMLDR. The recall and precision of RSML-GCN also achieved the second-best performance. The reason is that the input of GRGMF contains both drug–drug similarity and disease–disease similarity, while the input of RSML-GCN only contains known drug–disease associations.

We also investigated the performance of these prediction methods on the independent test set, another dataset released by Luo et al. (2016) is used to assess the performance of methods. By removing the drugs not included in Fdataset, we obtained an independent test set consisting of 89 drug–disease associations involving 71 drugs and 313 diseases. This test set was used to assess the performances of all prediction methods in predicting the drug–disease associations on the Fdataset. Overall, the performance of all the methods moderately deteriorates relative to the 10-fold cross-validations. RSML-GCN remained the best method, which achieved an AUPR value of 0.3030 and an AUC value of 0.6842. DRWBNCF and LAGCN achieved AUC values of 0.6218 and 0.6215, respectively (Table 3). We also show the ability to correctly predict drug–disease associations concerning given top-k thresholds, as shown in Figure 5. Accordingly, RSML-GCN can predict drug–disease associations more accurately than all other five methods on almost every top-rank threshold.

In this section, we conducted a case study to further evaluate the reliable ability of RSML-GCN to predict novel drug–disease associations. For the analysis, we chose three representative drugs for the treatment of high-incidence diseases, Atorvastatin Calcium, Etoposide, and Riluzole. Atorvastatin Calcium is a commonly used lipid-lowering drug in the clinic, which is mainly used to treat mixed hyperlipidemia and hypercholesterolemia (Egom and Hafeez, 2016). These diseases have a high incidence, are difficult to diagnose and treat, and can potentially induce Cardio-cerebrovascular disease (Yao et al., 2019). Therefore, the analysis of Atorvastatin Calcium is of great significance. Etoposide is a cell cycle specific antitumor drug that is primarily effective against small cell lung cancer (Mascaux et al., 2000), acute leukemia, and malignant lymphoma. Given cancer is complicated and difficult to cure, it is valuable to analyze whether Etoposide can treat other similar diseases in drug reuse. Riluzole is a central nervous system drug that plays a pivotal role in the treatment of Alzheimer’s disease, Parkinson’s disease, and brain injury, which have a serious impact on patients. Therefore, it is necessary to analyze the new therapeutic potential for this drug to treat a variety of neurological degenerative diseases. Specifically, we applied RSML-GCN to predict candidate diseases for three drugs. For each of the three drugs, all predicted candidate disease scores were ranked by priority, and then we excluded all known drug–disease associations from the primary dataset to generate a new top-ranked list of drug–disease associations. Finally, we used highly reliable sources and clinical trials (i.e., DrugBank (DB) (Law et al., 2013), CTD (Davis et al., 2016), PubChem (Kim et al., 2015), DrugCentral (Avram et al., 2020), and ClinicalTrials) as references to examine the predicted drug–disease associations. Table 4 presents the predicted results of the top 10 candidate diseases for three drugs. The results show Atorvastatin Calcium can also be shown to treat lung disease, left ventricular dysfunction, and is also associated with kidney failure, which are supported by CTD, ClinicalTrials, and DrugCentral. The discovery of Etoposide can be verified in all clinical trials, which shows that Etoposide not only has a good therapeutic effect on a variety of tumors but also can be used to treat Exanthema and drug eruption. In addition, Riluzole was also found to be related to heart failure, drug-induced liver injury, and arrhythmia. To sum up, most of our predictions can be verified by reliable sources and clinical trials. The case study results further demonstrate the effectiveness of RSML-GCN in predicting novel drug–disease associations.