Heterogeneous graph

In recent years, multi-omics technologies and approaches to systems biology have created large heterogenized biological networks that provide significant opportunities for graph neural networks (GNN) to accelerate the progress of drug discovery. The heterogeneous graph-based GNN methods are used to predict various potential interactions related to drugs. Drug-drug interactions (DDIs) and drug-side-effect interactions (DSIs) predictions can help pharmacologists discover the potential combinations of drugs and the possible side-effects. Zhao et al. [21] use a graph attention network (GAT) to integrate three different features for DSIs prediction. Yu et al. [22] propose a hybrid GNN framework composed of graph and node embedding to identify potential drug-side-effects interactions. HAN-DDI [23] is a heterogeneous graph attention model consisting of an attention-based heterogeneous graph node encoder for obtaining drug node representations and a decoder for DDIs prediction. In addition, drug-target interactions (DTIs) and drug-disease interactions (DDiIs) prediction are becoming more and more important for researchers as an integral part of drug repurposing. DTINet [24] learns features of drugs and targets from heterogeneous networks, and then adopts inductive matrix completion to predict novel DTIs and repurpose existing drugs. NeoDTI [25] integrates diverse information from the heterogeneous network and automatically learns representations of drugs and targets for DTIs prediction. Zeng et al. [9] integrate large biomedical network datasets and employ positive-unmarked matrix completion to predict previously unknown DTIs. Prior to that, the researchers constructed a heterogeneous network by integrating 10 networks and learning high-level features of drugs to predict drug-disease interactions [8]. Li et al. [26] propose inductive matrix completion with heterogeneous graph attention network for the prediction of DTIs. Zhao et al. [15] integrate the heterogeneous networks information from the topological and biological perspectives to predict unknown DDiIs. Fu et al. [27] develop a novel link prediction model, multi-view graph convolutional network (MVGCN) for link prediction in biomedical bipartite networks.

These methods, which are based upon heterogeneous networks, have utilized most available network information and learned about the characteristics of the nodes by the associated information on the network topology, in order to identify possible relations between the nodes. However, to the best of our knowledge, most existing methods do not take drug substructure information into account and are only effective for a single task.

Hypergraph

A hypergraph is a generalization of a graph, where an edge can connect any number of vertices and has been widely used in the various fields due to its ability to capture higher-order correlations between nodes in ordinary network data [28–32]. In the field of bioinformatics, hypergraph has also begun to attract more research interest. HypergraphSynergy [33] is a multi-way relation-enhanced hypergraph representation learning method to predict anti-cancer drug synergy. EMPHCN [34] is a drug repositioning method, which is based on enhanced message passing and hypergraph convolutional networks to predict DDiIs. WHGMF [35] uses the generalized matrix factorization based on a weighted hypergraph learning model for microbial-drug association predictions. HHDTI [36] is a heterogeneous hypergraph-based framework and fuses the key embeddings from a generative model and side embeddings from hypergraph neural networks for drug-target interaction (HHDTI) predictions. Saifuddin et al. [37] decompose the SMILES of drugs to construct a hyperedge and propose the HyGNN model. In their method, different decomposition methods of a drug are regarded as hyperedges and drug representations are learned from different hyperedges. It shares the same concept as learning the representation of a drug from different perspectives to predict DDI, which indicates the potential effectiveness of incorporating drug substructure networks. Still, it does not explore the full characteristics of the hypergraph.

Description of DSMN and HGDrug

As shown in Fig 1, we first use the reaction information of BRICS to decompose the drugs’ SMILES into fragments and further decompose the fragments to the smallest indivisible fragment, and retain reaction information between these fragments to construct the drug-fragment interactions (DFIs), and fragment-fragment interactions (FFIs) network. Then, we construct the micro-to-macro drug-centric heterogeneous network DSMN by assembling DFIs, FFIs networks, and four molecular interaction networks, namely, drug-drug interactions (DDIs), drug-target interactions (DTIs), drug-disease interactions (DDiIs), and drug-side-effect interactions (DSIs) networks. As shown in Fig 2, we propose a hypergraph learning framework, termed HGDrug, for drug multi-task interaction predictions. The pipeline of HGDrug includes two key steps:(1) hypergraph construction: to formulate the high-order relation information among drugs, we carefully design the triangular and quadrilateral network motifs with underlying semantics, and these motifs are divided into four specific categories according to the latent semantic relationship to guide the construction of hypergraphs over the heterogeneous network (Fig 2(a)). (2) Multi-branches hypergraph attention and graph convolutional networks inferring drug-related interactions: the hypergraph attention network are used to encode different motifs-guided hypergraphs, and the attention mechanism is used to selectively aggregate information from different branch-specific drug embeddings to form the comprehensive drug embeddings. A graph convolution network on the drug-related interaction graph encodes the drug-related nodes information and complements the drug feature information for task-special drug-related interaction prediction (Fig 2(c)). To thoroughly evaluate the prediction capability of HGDrug, we conduct a variety of experiments, including performance comparison of ours with 8 task specific models and 6 general models, the ablation study to examine the contribution of different category branches, the network visualization, case studies and comprehensive analysis to reveal whether HGDrug can better capture the drug substructure features and predict novel interactions on multiple tasks.

Datasets and experimental setup

In this section, we provide details on molecular interaction datasets, baseline methods, and experimental setup.

Baseline comparison models

We evaluate HGDrug on 4 distinct types of drug-related interactions, including DDIs, DTIs, DDiIs, and DSIs. To explore the generality of the HGDrug model and its excellent performance for each drug-related interactions tasks, we select 14 models of 2 types as baseline comparison models, which are 8 task specific models and 6 general models.

To select 8 task specific models for 4 tasks, we pick up 2 up-to-the-date graph neural network models for each task, as illustrated in following:

Performance of HGDrug on the cross-validation

We firstly select the task-specific model for each task for comparison, including comprehensive network models, path-based models, hypergraph models, and considering drug substructures models. For models that can expand network data, we add the DFIs network data as a variant of the original model to verify whether or not the chemical structure information can effectively improve the performance for drug-related interactions prediction. We discover that HGDrug outperforms each of these competitive baseline models, by consistently achieving the highest prediction accuracy for all 4 tasks. HyGNN model [37] is not able to capture high-level information between drugs since it simply uses the different decomposition schemes of each drug as a hyperedge, and constructs a hypergraph of each drug to learn the feature of the drug. It is worth noting that the performance of the original network-based model will be improved by incorporating the dataset from DFIs network, especially for the path-based model. By treating drug substructures that contain pharmacophore information as node types and integrating them into heterogeneous networks, we can enhance the GNN model’s ability to discern relationships between drugs with potential similar efficacy, thereby improving the prediction performance in drug-related tasks. For example, the IMCHGAN [26] model, which introduces meta-path-based neighbors to learn connections between nodes from different semantic perspectives, yields a performance improvement of increasing AUROC from 0.800 to 0.890, and AUPR from 0.796 to 0.902 on the DTIs dataset respectively when the DFIs network is added. These experiments also show that for drug-related interaction prediction tasks, adding DFIs network can learn information about the same functional group fragments between drugs, which helps to improve the performance of drug-related interaction prediction based on network models. Since the HGDrug makes full use of the higher-order relations between nodes in heterogeneous networks and the information of drug substructures, it outperforms other state-of-the-art methods in drug-related interaction prediction performance, even if these methods add substructure networks.

In addition, we compare HGDrug’s performance with 6 general baseline methods. The experimental results are reported in Table 2. It can be seen that HGDrug is the top-performing method out of 6 general methods across all drug-related interaction networks. In the DDIs and DDiIs tasks, HGDrug has achieved a significant performance improvement than the baseline methods. Compared to the second-ranked baseline method, the AUROC and AUPR of the DDIs task are improved by 11.8% and 14.3%, respectively, and the AUROC and AUPR of the DDiIs task are improved by 11.3% and 9.9%, respectively. Note that mining potential drug-drug associations for the DDIs task might be helpful since drug substructure networks brings extra complexities to the network. Drugs with the same basic structure are more likely to have similar pharmacological effects, which indicates that incorporating drug substructure networks can help identify new drug indications. Compared to classical machine learning and the direct embedding methods, the AUROC of HGDrug has up to 36.3% increase over SVM, 31.1% increase over Katz, and 25.4% increase over DeepWalk on DDIs task. These results also reflect that deep graph neural networks can learn to capture more effective features than general machine learning methods and direct embedding methods. It is interesting to observe that the well-performing benchmark, SkipGNN, has worse performance than GCN on the DTIs and DDiIs tasks, which might be due to the fact that DTIs and DDiI have fewer known interactions, while skipGNN skips similarity thus losing its performance advantage. For more evaluation metrics results, see “More evaluation metrics” in S1 Text.

Performance of HGDrug by ablation analysis

We implement 5 simplified variants of HGDrug to exam the effects of each component in our HGDrug in the 4 distinct types of prediction tasks. We run all the experiments with the 5-fold cross-validation, same model parameters and evaluation protocol (see the Implementation details) for a fair comparison. The result is presented in Fig 4. The 5 simplified variants of HGDrug are denoted as:

• HGDrug_0: removing the 1∼4-th all hypergraph branches.
• HGDrug_2f: removing the 3-th and 4-th molecular interactions hypergraph branches and retaining the 1-th and 2-th drug-substructure hypergraph branches.
• HGDrug_2m: removing the 1-th and 2-th drug-substructure hypergraph branches and retaining the 3-th and 4-th molecular interactions hypergraph branches.
• HGDrug_ac: obtaining the drug representation by hypergraph convolutional network.
• HGDrug_self: removing the self-supervised auxiliary task.

Fig 4 shows only minor difference obtained by using drug-substructure hypergraph branches or molecular interactions hypergraph branches alone, which proves that the drug information captured by the drug-substructure networks can rival the drug feature information obtained from the drug-related interaction network. For DDiI tasks with fewer known interactions, a large difference can be observed whether all hypergraph branches are utilized to obtain features (HGDrug_ac, HGDrug_self, HGDrug) or not (HGDrug_0, HGDrug_2m, HGDrug_2f). It illustrates the importance of obtaining more reliable side information when there are insufficient known interactions for the association prediction of molecular interactions. HGDrug uses the hypergraph attention network architecture to focus on the differences of neighbor features in the hypergraph, and uses a self-supervised auxiliary task to weigh the contribution of different types of high-order information in interaction predictions. Therefore, HGDrug can learn higher-quality drug features information from the hypergraph, which is superior to the HGDrug_ac that obtains drug representation through the hypergraph convolutional network and HGDrug_self that removes the self-supervised auxiliary task. These studies also show that additional feature information can be captured by the proposed HGDrug to enhance drug-related interaction predictions, which may provide new insights into understanding interaction mechanisms among drugs, drug substructure, and molecules. To more thoroughly evaluate the significance of utilizing fragments as a basis for hypergraph construction in drug feature learning, we verify the contribution of the four motifs (M₂, M₃, M₅, M₆), the results see Table C in S1 Text.

HGDrug identifies novel associations

The main goal of the HGDrug model is to discover potential novel interactions based on existing known interactions. To further demonstrate the ability of HGDrug for discovering novel interactions, we select the prediction results of DDiIs and DDI tasks for analysis.

Network visualization of the DDiI predictions.

We remove the known DDiIs used in the prediction model and retain the novel top 100 DDiIs with the highest drug-disease association score predicted by HGDrug (Fig 5(a)). Among the top 100 predicting DDiIs, HGDrug can capture the experimental or clinically reported drug-disease associations. For example, the five results with the highest association score predict that drug DB01413 (Cefepime) can act on indications C0178299 (Infection of skin AND/OR subcutaneous tissue) and C0276026 (Haemophilus influenza pneumonia), DB00535 (Cefdinir) can also act on C0178299, DB00833 (Cefaclor) can act on C0554628 (Streptococcus pyogenes infection), and DB01331 (Cefoxitin) can act on C0149725 (Lower respiratory tract infection). As a widely known fact, Cefepime is a fourth-generation cephalosporin antibiotic, which can treat uncomplicated skin and skin structure infections [53–55] and pneumonia caused by susceptible bacteria [56]; Cefdinir is a third-generation cephalosporin, which can also be used to treat uncomplicated skin and skin structure infections [57]; Cefaclor is a second-generation cephalosporin that can be used to treat streptococcus pyogenic infection [58]; Cefoxitin is a semi-synthetic, broad-spectrum antibiotic that can be used to treat lower respiratory tract infection [59]. The above results prove the effectiveness of our model in finding novel potential associations. If properly utilized, it can assist medicinal chemistry learning to discover new associations of approved drugs.

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Fig 5. Network visualization and analysis of the drug-disease associations predicted by HGDrug.

(a) In the network, the predicted novel top 100 DDiI network is visualized. The pink nodes are diseases and the green nodes are drugs. The label of the node represents the ID of the drugs (Drugbank_ID) or diseases (UMLS_ID). The node size denotes the degree. The weight of edges (drug-disease associations) denotes the predicted score by HGDrug. (b) Analysis of top 5 drug-disease associations predicted by HGDrug. Four drugs are included in the top 5 predicted potential associations. The similarity between drugs comes from the drug features learned by HGDrug in the DDiI task, and the drug most similar to these four drugs are selected respectively. This network was generated by Gephi (https://gephi.org).

https://doi.org/10.1371/journal.pcbi.1011597.g005

HGDrug predicts novel interactions by learning more effective drug features. To verify the hypothesis and interpret the results of our HGDrug model, we analyze the above 5 novel associations from the perspective of drug features learned by HGDrug. We extract the drug features obtained in the DDiIs task and calculate the similarity scores between drugs. The result shows that the most similiar drugs for 4 drugs DB01413 (Cefepime), DB00535 (Cefdinir), DB00833 (Cefaclor), and DB01331 (Cefoxitin) are DB01330 (Cefotetan), DB00833 (Cefaclor), DB01416 (Cefpodoxime), and DB01330 (Cefotetan), respectively. We give the top 20 highest similarity score DDIs of these 4 drugs (see Table D in S1 Text). We discover that these 4 drugs with the most similiar drug all are the approved drugs for the predicted corresponding indications (see Fig 5(b)). These results demonstrate that our model can make full use of features information to capture approximate relations between drugs, and reveal potential drug-disease associations based on the relations and the approved drug-disease interactions.

The chemical structures are responsible for specific properties of drugs, and the same basic chemical structure exist in drugs with the same pharmacological effect. Accordingly, identifying the drug substructure information associated with the target property and adding the information into the model is vital for drug discovery. To illustrate HGDrug’s learning ability of chemical structures, we visualize the above 4 pairs of drug with approximate relations. It’s worth noting that these drug pairs share the same substructures that carry pharmacophore information, see Fig 6 for more details. This experimental result also shows that HGDrug can learn the substructure information and capture the same basic chemical structure information to improve the performance of drug repurposing.

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Fig 6. The 4 drugs and their corresponding top 1 drug structures from Fig 5(b).

The same substructures of drug pairs are marked in orange.

https://doi.org/10.1371/journal.pcbi.1011597.g006

Comprehensive analysis: Computationally identified the most relevant entities of paclitaxel

To further illustrate the practical applications of HGDrug, we comprehensively analyze the prediction potential of HGDrug from the perspective of drug, target, side effect and disease. As a widely used and promising anticancer drug, paclitaxel is a type of microtubule stabilizer and used to treat various diseases, including cancers (e.g. breast cancer, ovarian cancer), coronary artery restenosis, renal and hepatic fibrosis [60]. However, severe side effects limit the effectiveness of paclitaxel in the disease treatment, such as myelosuppression and peripheral neuropathy [61]. Therefore, we select paclitaxel as a case for further comprehensive analysis, and predict its potential drugs, targets, side effects, and diseases using HGDrug. For the results of the DTIs prediction task, we do not consider the CYP series of proteins.

As shown in Fig 7, the most relevant entities predicted by paclitaxel in the four tasks are P00372 (ESR1), multiple myeloma, dysaesthesia, and cobicistat. The ESR1, multiple myeloma, and dysaesthesia have almost no drugs shared with paclitaxel, which show that these results cannot be effectively predicted by GNNs that relying on the pairwise links. Recent studies have shown that ESR1 methylation may have a protective effect on neurotoxicity induced by paclitaxel [62]. Paclitaxel have shown therapeutic effect on advanced breast cancer patients with ESR1 mutations [63], which indicate HGDrug provided insight into the potential mechanism for known drug-disease (side effect) interactions. In addations, we analyse the top 10 potential targets and find that 7 targets indeed associate with paclitaxel validated by literature (see the Table H in S1 Text). Several studies have shown that paclitaxel induces dysaesthesia, including pain, allodynia, and numbness [64, 65]. Furthermore, Table I in S1 Text provides the top 10 predicted side effects, and find most side effects are validated to relate to paclitaxel by the literature. It is generally recognized that the identification of drug-disease interactions is laborious and expensive. Several studies reported that paclitaxel selectively modifies the expression of regulatory proteins in the apoptosis signal pathway and can be used to treat multiple myeloma [66, 67]. Furthermore, Bcl-2 is proved to associate with resistance to paclitaxel in multiple myeloma cells, which may relate to its influence on paclitaxel-induced apoptosis [68, 69]. These results indicate that HGDrug has the potential to discover new drug-disease interactions from the perspective of mechanism. To further prove the role of hypergraph and substructure, we give the substructure of the most relevant cobicistat and paclitaxel, and we can find that they have the same substructure information, and this information can be captured through the hypergraph structure with “DISS” semantics.

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Fig 7. Analysis of the predicted results for the four tasks of paclitaxel.

The network contains the known interactions of paclitaxel and the most relevant entity nodes predicted by HGDrug for paclitaxel in the four tasks. The known related drugs of four nodes are given for visualizing the drugs that these nodes share with paclitaxel.

https://doi.org/10.1371/journal.pcbi.1011597.g007

Motifs-driven hypergraph

We decompose the drugs and construct the interaction network between drugs and substructures in order to mine the feature information of drugs and capture potential associations between drugs through the number of drugs with the same substructure and the inclusion relationship between substructures.

To capture higher-order information among drugs, we first align these heterogeneous networks and molecular interaction network for specific prediction task and constructs hypergraphs based on the network motifs over heterogeneous networks (Fig 2(a)). In the work, the DFIs and FFIs networks obtained by decomposing the drugs are directed, the drug-related heterogeneous networks are directed, and the DDIs network is undirected (bidirectional). We focus on triangle and quadrilateral motifs representing high-order relationships between drugs and carefully designed a set of motifs to guide the hypergraph construction. The M₁-M₆ summarizes the common triangle and quadrilateral relations in the DDIs, DFIs, and FFIs networks, describing the high-order correlation for drugs that have the same substructure. In addition to drug substructure networks, we also build hypergraphs based on molecular interaction networks, focusing only on triangular motifs in these heterogeneous networks. The M₇-M₁₂ summarizes the common triangles in the molecular interaction networks. Last while not least, we also take whether the drugs are directly related into consideration, and subdivide the above 2 groups into following groups: M₁-M₃ (drug-related and have the same substructure, DRSS), M₄-M₆ (drug independent and have the same substructure, DISS), M₇-M₉ (drug-related and have the same molecular interactions, DRSM), M₁₀-M₁₂ (drug independent and have the same molecular interactions, DISM). Fig 2(a) shows all the used motifs, it is worth noting that for better personal data protection, we only use the task specific training dataset to build its associated hypergraph in a specific task.

For a motif M, we use the co-occurrence of two nodes in M to capture the higher-order relations of drugs. Specifically, given a motif M_k where A_k represents the motif-based adjacency matrix, A_k(v_i, v_j) refers to the number of times that v_i and v_j appear in the same motif structure of M_k in the global heterogeneous network. The motif-based adjacency matrix for node type O_i in the heterogeneous is denoted as: (1) where i ≠ j, the Φ(v_i) = Φ(v_j) = O_i is considered as the drug node type, and 1() is the truth-value indicator function, in a way that when the statement inside () is true, 1() = 1, otherwise 0. The Table 4 shows how the matrix A_k is calculated with respect to M_k motif. Since drug independent motifs M₄-M₆ and M₁₀-M₁₂ are believed to contain the corresponding triangular or quadrilateral drug related motifs M₁-M₃ and M₇-M₉, we remove the redundancy and eventually make A₄ = A₄ − A₁, A₅ = A₅ − A₂, A₆ = A₆ − A₃,A₁₀ = A₁₀ − A₇,A₁₁ = A₁₁ − A₈, and A₁₂ = A₁₂ − A₉

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Table 4. Computation of motif-induced adjacency matrices.

https://doi.org/10.1371/journal.pcbi.1011597.t004

With the following 4 groups of motifs, e.g., RSS, ISS, RSM, ISM, we construct four hypergraphs that contain different high-order drug relation patterns. We use the incidence matrices I_j = A₁ + A₂ + A₃, I_p = A₄ + A₅ + A₆, I_i = A₇ + A₈ + A₉, and I_u = A₁₀ + A₁₁ + A₁₂ to represent 4 hypergraphs induced by the above 4 motif groups, respectively. Take I_j (based on the heterogeneous network shown in Fig 1) as an example, the related M₁-M₃ and the final incident matrix I_j obtained are shown in the (Fig 2(a)).

Learning drug representation by multi-branches hypergraph attention

Our representation learning method is developed upon MHCN model [32]. Based on the 4 groups of motif-driven hypergraphs obtained in the previous section, 4 branches are used to extract multi-scale drug features of the given heterogeneous network, with each branch capturing high-order drug relationship patterns in a motif-driven hypergraph. To distinguish higher-order drug-drug relations in different hypergraphs to the final drug-related interaction prediction performance, we apply a filtered self-gating unit for pre-processing when drug initial feature vectors matrix are the input for each branch, as defined in following: (2) where x ∈ {j, p, i, u} represents the branches, ⊙ is the element-wise product, σ is the sigmoid nonlinearity, is the parameters matrix to be learned, c is the dimension of the drugs initial feature, and is the parameters vector to be learned.

After the nonlinear gate modulates the drug’s initial features at a feature-wise granularity through dimension re-weighting, we then obtain the branch-specific drug features . The hypergraph attention on each branch is defined as: (3) where l is the propagating layer, , is the degree matrix of I_x, b is the number of drugs. Note that I_x can be replaced with arbitrary I_j, I_p, I_i and I_u to learn drug representations that encode higher-order information in the corresponding branch using a hypergraph attention network. is the parameters matrix to be learned, is the parameters vector to be learned. After the drug embedding is propagated through the L_th layer, the embedding features obtained by each layer are averaged to avoid over-smoothing, and the final representation of the drug obtained in each branch is .

Moreover, the attention mechanism is applied to aggregate the drug feature information obtained from each branch because the drug features obtained from different branch are not equally important. For each drug d in different branch, a ω^x is learned to measure the different contributions of branch-specific embeddings to the final prediction performance. The ω^x is defined as: (4) where , are trainable parameters, and the four-scale drug feature are aggregated as .

Drug multi-task interaction predictions

For the downstream task of drug multi-task interaction prediction, we use graph convolution to obtain the drugs and drug-related nodes information from the known interactions data of specific downstream tasks. is defined as the drug feature from the graph convolution, and can be computed as: (5) where is the gated drug embedding for graph convolution, R ∈ {S, W, G, V} is drug-related interaction adjacency matrix for different tasks, are degree matrices of R, is the parameters matrix to be learned, and is the parameters vector to be learned. is defined as the drug-related node feature from the graph convolution, and can be computed as: (6) where is the drug embedding, which combines the drug feature information from the above multi-branches hypergraph and the drug feature information from the graph convolution , are degree matrices of R^T, and t is the number of drug-related nodes. The is the parameters matrix to be learned, and is the parameters vector to be learned. Note that the dimension of the nodes initial feature equals to the dimension of the drug initial feature.

We can therefore obtain the final drug and drug-related node feature embeddings and by: (7) where , and , are randomly initialized.

Objective functions optimizaion

The model applies the Bayesian Personalized Ranking (BPR) loss [70], which is computed as: (8) where denotes the pairwise training data, indicates the observed interactions, indicates the unobserved interactions, σ(⋅) is the sigmoid function, , is the predicted score of d on i and j, respectively. θ is the parameters of model, ‖θ‖₂ is the L₂ norm of the parameter vector, and δ is the hyper-parameter that controls the L₂ regularization strength to prevent overfitting. The BPR is a pairwise loss that promotes an observed interaction to be ranked higher than its unobserved counterparts. Let drug d be the input to the mode. Assume there is a random positive sample i related to drug d, and a random negative sample j unrelated to the drug d, the goal of the model optimization is then to yield a higher rank for sample i than sample j in the predicted list of drug d.

The different branches can learn drug features with different distributions on different hypergraphs. To avoid the loss of higher-order information possibly caused by aggregation operations, a self-supervised auxiliary task is employed to enhance the performance of the association prediction task. Inspired by the Deep Graph Infomax (DGI) method [71], our model calculates the mutual information between node representations and full graph representations (in large-scale graph networks, sampled sub-graph representations are used). In the self-supervised auxiliary task, a comprehensive drug representation reflecting the local and global higher-order connectivity patterns of drug nodes in different hypergraphs can be obtained by hierarchically maximizing the mutual information between the representation of the drug, the corresponding drug-centric sub-hypergraph and the hypergraph in each branch. For each motifs-driven hypergraph, an adjacency matrix I is built to capture the higher-order association information of the drug, with each row representing a drug-centered sub-hypergraph by row-index of the corresponding hypergraph. The sub-hypergraph representation can be obtained by a readout function , which is depicted as following: (9) where is the row vector of I^x corresponding to the center drug d, and denotes the number of drug d associated nodes in the sub-hypergraph. The representation of the Sub-hypergraph can represent the importance of each drug in the Sub-hypergraph. The hypergraph representation can be obtained by an average pooling to summarize the sub-hypergraph features into a graph level: (10) where .

The pairwise ranking loss [72] is applied to estimate the mutual information, and the objective function of the self-supervised auxiliary task is defined as: where D is the set of drugs, denotes a discriminator function with two vectors as the input and scores the agreement between them, and is the negative examples by both row-wise and column-wise shuffling to corrupt S^x.

Finally, the overall objective of the model is defined as: (12) where λ is a hyper-parameter used to control the effect of the auxiliary task.