Drug interaction prediction method based on double-view graph neural network

Abstract

The invention discloses a drug interaction prediction method based on a double-view graph neural network, and the method comprises the steps: extracting features in a single drug view in a self-adaptive manner through a directional message passing neural network with a substructure attention mechanism, and extracting interaction features between the drug and the view through a graph attention network; and fusing to generate drug substructure features, so as to more accurately predict the interaction between drugs. And through the common attention mechanism module, drug interaction is converted into pairwise interaction between drug substructures, so that the capability of capturing drug molecular characteristics is greatly enhanced, and the prediction precision is improved. The invention can make full use of the interaction information between drugs and the interaction information of chemical substructures, studies the classification and identification problem of drug interaction prediction, and provides an efficient drug interaction prediction method.

Description

Technical Field

[0001] The invention relates to the fields of applied mathematics and artificial intelligence, and in particular to a drug interaction prediction method based on a dual-view graph neural network. Background Art

[0002] Drug-Drug Interactions (DDI) are widely described as changes in the effects of one drug due to the presence of another drug. This effect may result in enhanced efficacy, reduced efficacy, or adverse reactions. In developed countries, including Europe and the United States, due to their advanced science and technology and medical levels, as well as the emphasis on drug-drug interactions, drug interaction research has developed earlier. For example, Europe and the United States have formulated drug interaction guidelines since the early 1990s, which has promoted progress in their drug interaction field and made them a global leader. In comparison, such research in China started late, and there are no official and clear research guidelines. At present, some medical entities and organizations in China are actively promoting work in this area.

[0003] Due to the complexity of DDI, it is difficult to predict. Traditional prediction methods include experimental and non-experimental methods. Experimental methods focus on studying the interaction between two drugs in the human body, such as clinical trials; while non-experimental methods rely on existing drug data and algorithms to predict possible interactions between different drugs, such as statistical methods. Although these methods provide certain information, they have obvious limitations and shortcomings, such as relying on a large number of biological experiments, time-consuming, high cost, and limited sensitivity and specificity.

[0004] In recent years, many new methods have emerged to predict drug interactions using computer models and artificial intelligence technologies. These methods can comprehensively analyze information such as the molecular structure, pharmacological mechanism, and biological targets of drugs, providing a faster, more accurate, and more cost-effective means of predicting DDI. Currently, the methods for predicting DDI can be roughly divided into three categories: similarity prediction based on molecular feature descriptors, prediction based on network embedding, and prediction based on graph neural networks. Among them, the methods based on graph neural networks can be roughly divided into two categories: one is to regard DDI prediction as a link prediction task, regard drugs as nodes, and regard interaction relationships as edges, and predict whether there are edges between unknown drug nodes based on the known drug interaction network and the embedded representation of drug nodes; the other is to regard DDI prediction as a graph embedding problem, mapping graph data into low-dimensional dense vectors, which can well solve the problem that graph data is difficult to efficiently input into machine learning algorithms.

[0005] Many machine learning-based methods have been proposed for identifying and predicting DDIs. The basic idea is to predict unknown potential drug interactions based on known drug interactions. However, the difficulty of machine learning methods is that drug features need to be manually extracted, which depends on the expert knowledge and level in the medical field. Summary of the invention

[0006] In order to address the shortcomings of the prior art, the present invention proposes a drug interaction prediction method based on a dual-view graph neural network. This method combines the molecular structure information and chemical substructure information of the drugs, can adaptively capture the key substructures of the interaction between the two drugs, and more deeply explore the important functional groups of drug interactions, which is convenient for subsequent research by related researchers; the entire model has high predictive performance and good robustness.

[0007] In order to achieve the above object, the technical solution adopted by the present invention is:

[0008] A method for predicting drug interactions based on a dual-view graph neural network comprises the following steps:

[0009] 1) Atomic feature acquisition: We use a directed message passing neural network with substructure attention mechanism and a graph attention network to learn the relevant features of a single drug and the interactive features between two drugs;

[0010] 2) Substructure feature acquisition: concatenate the learned features of the atomic representations of individual drugs and between drugs, and input them into the self-attention map pooling layer to obtain the global representation of the drug map through weighted summation;

[0011] 3) Drug-drug interaction prediction: After obtaining all substructure information of the two input drugs, the common attention mechanism is used to calculate the interaction score between each pair of substructures between the two drugs, thereby predicting the interaction probability between the two drugs.

[0012] Further, step 1) specifically includes:

[0013] 1.1) Input the drug molecule graph into a directed message passing neural network with a substructure attention mechanism, and then output the updated features of the atomic nodes within a single drug through the readout function of the graph neural network;

[0014] 1.2) Input the drug bipartite graph into the graph attention network to obtain the interaction information between the two drugs, thereby obtaining the updated features of the atomic nodes in the interaction view.

[0015] The calculation process of updating the atomic node features in a single drug in step 1.1) specifically includes:

[0016] 1.1.1) Take the molecular graphs of the two drugs as input and feed them into the feedforward layer, which is a simple multi-layer perceptron. It contains a sequence module of linear layers, which can map the atomic node features of the drugs from the input 55-dimensional to the 128-dimensional representation space. A bias term is added during the mapping process so that the subsequent graph neural network module can process and learn.

[0017] 1.1.2) Directed message passing neural network with substructure attention mechanism extracts substructures of arbitrary size and shape and assigns a unique score to each substructure; specifically:

[0018] For each node v i , the hidden feature at step t is Among them, R is the real number field, R d represents the d-dimensional real number space, Represents node v i The initial feature at t = 0 is x i ;use To represent the edge e i→j Hidden features of , initialize the hidden features of the edge:

[0019]

[0020] Among them, W i ∈R h×d , W j ∈R h×d , W ij ∈R h×d′ are all learnable weight matrices. i ,x j ,x ij Respectively represent the node v i ,v j and edge i→j initial features.

[0021] At step t, for edge-level hidden features First calculate the edge-level adjacency features of each node, and then obtain its edge-level graph representation g (t) ;but

[0022]

[0023] in, Represents node v i The edge-level adjacency feature, N(v i ) indicates v i All neighbor nodes of , m represents the number of atomic nodes in the drug molecule. Substructure-aware global pooling is used to calculate β ij, given a graph with edge feature matrix X and adjacency matrix A, where non-zero elements in A indicate that two edges share a node, SAGPooling calculates the importance vector β ij The formula for calculation is:

[0024] β ij =softmax(GNN(A,X)).

[0025] 1.1.3) For each graph-level representation g (t) , substructure attention score e (t) The calculation is:

[0026] e (t) =w (t) ⊙tanh(Wg (t) +b),

[0027] Among them, w (t) is the weight vector of step t, tanh represents the activation function, and W is the representation of each graph level g (t) The weight vector of , and b is the bias term.

[0028] In order to make the attention scores at different steps easier to compare, a softmax function is used to (t) Normalize:

[0029]

[0030] Among them, α (t) ∈R l Indicates the importance of the substructure with radius t, T is the total number of graph-level representations for each molecule; k is an index variable used to represent every possible input item from 1 to T;

[0031] After updating the hidden features of the edge in the Tth step, the hidden features of the edges of all steps are weighted according to the following formula, and the edge-level features are returned, which are finally expressed as:

[0032]

[0033] Among them, h ij It represents the final edge-level feature after weighting the edge-level features of layer T;

[0034] Finally, the node features are returned by aggregating the edge-level features: f(·) is a multi-layer perceptron.

[0035] Furthermore, the specific calculation process of updating the atomic node features of the interactive view in step 1.2) includes:

[0036] 1.2.1) Use graph attention network to capture the interaction information between two drugs;

[0037] Specifically, each node of a drug is connected to all nodes of another drug to form an interaction edge, and then the node of the drug is updated by aggregating the information of all nodes of another drug;

[0038] 1.2.2) For the representation of atomic nodes learned from a single drug and between two drugs, use the formula Aggregation is performed and the aggregated node representation is propagated to the next iteration to provide multi-view information for each node.

[0039] Further, step 2) specifically includes:

[0040] After updating the node features at each layer, all substructure information of the drug is aggregated, and the global representation of the drug graph is obtained by weighted summation:

[0041]

[0042] in, is the global representation of the drug molecule graph, N represents the number of atomic nodes, and α i Each atomic node in each layer represents the weight vector of the layer, σ is the sigmoid nonlinear function, A is the adjacency matrix of the graph, X (t) is the embedding representation of all nodes in the tth layer, is the trainable matrix of the tth layer, d is the input dimension of the node features, and 1 is the output dimension of the importance score;

[0043] The self-attention graph pooling layer considers both the contextual and topological information of nodes to determine their importance in the entire graph.

[0044] Further, step 3) specifically includes:

[0045] 3.1) After obtaining the input drug D x and D y All substructure information of and Then, the joint attention mechanism is used to calculate D x and D y The interaction score of each pair of substructures is γ ij :

[0046]

[0047] Where L is the number of input drug substructures, b is a learnable parameter vector, and W x , W y is a learnable matrix;

[0048] 3.2) Prediction of drug G xand G y Interaction type I r The probability P(G x ,G y ,r):

[0049]

[0050] 3.3) The model is trained by an end-to-end back-propagation algorithm, using the Adam algorithm as the optimizer, and updating the parameters by minimizing the loss function; the loss function used is the cross entropy Loss:

[0051]

[0052] Among them, p i and p i ′ is based on the formula The calculated prediction probabilities represent the positive sample set and negative sample set of drug pair interactions, respectively.

[0053] The present invention has the following beneficial effects:

[0054] 1. The present invention adaptively extracts the atomic node information of drugs of different sizes and shapes through a directed message passing neural network with a substructure attention mechanism, and then aggregates the atomic node features through a self-attention pooling operation to obtain the substructure information of each drug, which can improve the accuracy of the prediction tasks downstream of the model.

[0055] 2. The present invention adopts a common attention mechanism to obtain the score of the substructure interaction between two drugs, so as to more clearly know which key substructures make the greatest contribution to the drug interaction, and further improve the accuracy of the model in predicting DDI.

[0056] 3. The present invention is simple to operate, easy to implement, and has relatively accurate analysis results, which greatly accelerates the drug development process, provides a reference for the combined use of drugs, and achieves drug safety. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 is a drug molecule diagram in an embodiment of the present invention;

[0058] Figure 2 4 is a diagram of the algorithm structure of an embodiment of the present invention. DETAILED DESCRIPTION

[0059] like Figure 1-2As shown, the present invention provides a drug interaction prediction method based on a substructure-aware dual-view graph neural network, namely SAD-GNN, which adaptively extracts drug atomic node information of different sizes and shapes through a directed message passing neural network with a substructure attention mechanism, and then aggregates the atomic node features through a self-attention pooling operation to obtain the substructure information of each drug. The substructure information can improve the accuracy of the prediction task downstream of the model. Specifically, it includes the following steps:

[0060] 1) Atomic feature acquisition: The SA-DMPNN and GAT are used to learn the relevant features of a single drug and the interactive features between two drugs. Specifically:

[0061] 1.1) Input the drug molecule graph into the directed message passing neural network with substructure attention mechanism, and then output the updated features of the atomic nodes within a single drug through the readout function of the graph neural network. Specifically, it includes:

[0062] 1.1.1) Take the molecular graphs of the two drugs as input and feed them into the feedforward layer, which is a simple multi-layer perceptron. It contains a sequence module of linear layers, which can map the atomic node features of the drugs from the input 55-dimensional to the 128-dimensional representation space. A bias term is added during the mapping process so that the subsequent graph neural network module can process and learn.

[0063] 1.1.2) Directed Message Passing Neural Network with Substructure Attention (SA-DMPNN) can extract substructures with arbitrary size and shape and assign a unique score to each substructure.

[0064] Specifically, for each node v i , the hidden feature at step t is Among them, R is the real number field, R d represents the d-dimensional real number space, Represents node v i The initial feature at t = 0 is x i ;use To represent the edge e i→j Hidden features of , initialize the hidden features of the edge:

[0065]

[0066] Among them, W i ∈R h×d , W j ∈R h×d , W ij ∈R h×d′ represents the learnable weight matrix.i ,x j ,x ij Respectively represent the node v i ,v j and edge i→j initial features.

[0067] At step t, for edge-level hidden features First calculate the edge-level adjacency features of each node, and then obtain its edge-level graph representation g (t) .

[0068]

[0069] in, Represents node v i The edge-level adjacency feature, N(v i ) indicates v i All neighbor nodes of , m represents the number of atomic nodes in the drug molecule. Substructure-aware global pooling is used to calculate β ij , given a graph with edge feature matrix X and adjacency matrix A, where non-zero elements in A indicate that two edges share a node, SAGPooling calculates the importance vector β ij The formula for calculation is:

[0070] β ij =softmax(GNN(A,X)).

[0071] 1.1.3) For each graph-level representation g (t) , calculation of substructure attention score:

[0072] e (t) =w (t) e tanh(Wg (t) +b),

[0073] Among them, w (t) is the weight vector of step t, tanh represents the activation function, and W is the representation of each graph level g (t) The weight vector of , and b is the bias term.

[0074] In order to make the attention scores at different steps easier to compare, a softmax function is used to (t) Normalize:

[0075]

[0076] Among them, α (t) ∈R l Indicates the importance of the substructure with radius t, T is the total number of graph-level representations for each molecule; k is an index variable used to represent every possible input item from 1 to T;

[0077] After updating the hidden features of the edge in the Tth step, the hidden features of the edges of all steps are weighted according to the following formula, and the edge-level features are returned, and finally represented as:

[0078]

[0079] Among them, h ij Represents the final edge-level feature after weighting the edge-level features of T layers.

[0080] Finally, the node features are returned by aggregating the edge-level features: Where f(·) is a multi-layer perceptron.

[0081] 1.2) Input the drug bipartite graph into the graph attention network to obtain the interaction information between the two drugs, thereby obtaining the updated features of the atomic nodes in the interaction view. Specifically:

[0082] 1.2.1) Use graph attention network to capture the interaction information between two drugs. Specifically, each node of one drug is connected to all nodes of the other drug to form an interaction edge, and then the node of the drug is updated by aggregating the information of all nodes in the other drug.

[0083] 1.2.2) For the representation of atomic nodes learned from a single drug and between two drugs, use the formula Aggregation is performed and the aggregated node representation is propagated to the next iteration to provide multi-view information for each node.

[0084] 2) Substructure feature acquisition: concatenate the learned features of the atomic representations of individual drugs and between drugs, and input them into the Self-Attention Graph Pooling (SAGPooling) layer to obtain the global representation of the drug graph through weighted summation. Specifically, it includes:

[0085] After updating the node features at each layer, all substructure information of the drug is aggregated, and the global representation of the drug graph is obtained by weighted summation:

[0086]

[0087] in, is the global representation of the drug molecule graph, N represents the number of atomic nodes, and α i Each atomic node in each layer represents the weight vector of the layer, σ is the sigmoid nonlinear function, A is the adjacency matrix of the graph, X (t) is the embedding representation of all nodes in the tth layer, is a trainable matrix for the tth layer, d is the input dimension of node features, and 1 is the output dimension of importance scores. Self-Attention Graph Pooling (SAGPooling) considers both the contextual information and topological information of nodes to determine their importance in the entire graph.

[0088] 3) Drug-drug interaction prediction: After obtaining all substructure information of the two input drugs, the common attention mechanism is used to calculate the interaction score between each pair of substructures between the two drugs, thereby predicting the interaction probability between the two drugs. Specifically, it includes:

[0089] 3.1) After obtaining the input drug D x and D y All substructure information of and After (chemical substructure extraction part), the joint attention mechanism is used to calculate D x and D y The interaction score of each pair of substructures is γ ij .

[0090]

[0091] Where L is the number of input drug substructures, b is a learnable parameter vector, and W x , W y is a learnable matrix.

[0092] 3.2) Prediction of drug G x and G y Interaction type I r Probability:

[0093]

[0094] 3.3) The model is trained by an end-to-end back-propagation algorithm, using the Adam algorithm as the optimizer, and updating the parameters by minimizing the loss function. The loss function used is the cross entropy Loss:

[0095]

[0096] Among them, p i and p i ′ is based on the formula The calculated prediction probabilities represent the positive sample set and negative sample set of drug pair interactions, respectively.

[0097] The present invention uses a directed message passing neural network with a substructure attention mechanism to adaptively extract features within a single drug view, a graph attention network to extract interaction features between drug pair views, and then uses a graph attention pooling layer to generate drug substructure features, effectively combining the information between a single drug and a drug pair. At the same time, a common attention mechanism is used to obtain the score of the substructure interaction between the two drugs, so as to more clearly know which key substructures make the greatest contribution to the drug interaction, thereby improving the accuracy of DDI prediction and providing an efficient drug interaction prediction method for protecting public health and patient life safety.

[0098] Simulation experiment

[0099] The system of the present invention is further demonstrated by simulation experiments, taking the drug interaction prediction in the DrugBank data set as an example, which is selected as user data and imported into the drug interaction prediction.

[0100] (1) Prediction of drug interactions

[0101] Table 1. Transduction experiments on DrugBank dataset

[0102]

[0103] As shown in Table 1, it can be seen that in terms of key indicators such as accuracy, recall rate and F1 score, the SAD-GNN model performs well and is significantly better than other comparison methods. The practical significance of this result is reflected in the accuracy and credibility of drug interaction predictions. Accurate predictions can directly affect the evaluation and intervention of drug interactions in clinical practice. Through a specific analysis of the model performance, it can be found that SAD-GNN has higher stability and accuracy in predictions for different drug combinations. This performance advantage makes the SAD-GNN model have greater application potential in drug interaction research.

[0104] (2) Prediction of drug interactions in cold start scenarios

[0105] Cold start experiments are more challenging than conduction experiments because there are unseen drugs in the DDI triplets in the test set. This cold start scenario is an extremely difficult experiment for the generalization ability of the model, and there is no prior knowledge of unseen drugs during the training process. In this case, the present invention splits the dataset according to the same scheme as previously used in the literature. Specifically, the present invention randomly selects 20% of the drugs as unknown drugs and regards the remaining drugs as existing drugs. All positive and negative samples on the training set are DDI triplets, and both drugs are existing drugs, while the test set uses a different partitioning scheme:

[0106] S1 Scheme: Both the positive and negative samples of the test set contain two unknown drugs. The task is to predict the interaction between a pair of new drugs that have no known interactions with any combination of other drugs in the training set.

[0107] S2: The positive and negative samples of the test set contain one unknown drug and one known drug. The task is to predict the interaction between a pair of new drugs that have no known interaction with any combination of another existing drug.

[0108] Table 2 Cold start experiment on Drugbank dataset (S1 Scheme: )

[0109]

[0110] Table 3 Cold start experiment on Drugbank dataset (S2 scheme: )

[0111]

[0112] Due to the huge differences in drug structures, the chemical structures of new drugs in the test set are very different from existing drugs in the training set. As shown in Tables 2 and 3, the scores of all evaluation indicators are significantly lower than the performance of the model in the conduction experiment, indicating that it is much more difficult to predict DDI for unknown drugs. In addition, similar to the performance in the conduction experiment, SAD-GNN achieved the best performance in all evaluation indicators compared with the most advanced algorithms in the current state of the art. It is worth noting that the model of the present invention outperforms the second best algorithm GNN-DDI to a large extent. For example, the AUC of the S1 and S2 methods are improved by 8.19% and 7.46%, respectively. These results show that the SAD-GNN model is effective in predicting DDI in cold start scenarios. It not only considers the structure of individual drugs, but also learns interactions from drug pairs, which greatly makes up for the shortcomings of previous experiments.

Claims

1. A method for predicting drug interactions based on a dual-view graph neural network, characterized in that: The steps include: 1) Atomic feature acquisition: We use a directed message passing neural network with substructure attention mechanism and a graph attention network to learn the relevant features of a single drug and the interactive features between two drugs; 2) Substructure feature acquisition: concatenate the learned features of the atomic representations of individual drugs and between drugs, and input them into the self-attention map pooling layer to obtain the global representation of the drug map through weighted summation; 3) Drug-drug interaction prediction: After obtaining all substructure information of the two input drugs, the common attention mechanism is used to calculate the interaction score between each pair of substructures between the two drugs, thereby predicting the interaction probability between the two drugs.

2. The method for predicting drug interactions based on dual-view graph neural network according to claim 1, characterized in that: Step 1) specifically includes: 1.1) Input the drug molecule graph into a directed message passing neural network with a substructure attention mechanism, and then output the updated features of the atomic nodes within a single drug through the readout function of the graph neural network; 1.2) Input the drug bipartite graph into the graph attention network to obtain the interaction information between the two drugs, thereby obtaining the updated features of the atomic nodes in the interaction view.

3. The method for predicting drug interactions based on dual-view graph neural network according to claim 2, characterized in that: The calculation process of updating the atomic node features in a single drug in step 1.1) is as follows: include: 1.1.1) Take the molecular graphs of the two drugs as input and feed them into the feedforward layer, which is a simple multi-layer perceptron. It contains a sequence module of linear layers, which can map the atomic node features of the drugs from the input 55-dimensional to the 128-dimensional representation space. A bias term is added during the mapping process so that the subsequent graph neural network module can process and learn. 1.1.2) Directed message passing neural network with substructure attention mechanism extracts substructures of arbitrary size and shape and assigns a unique score to each substructure; specifically: For each node v i , the hidden feature at step t is Among them, R is the real number field, R d represents the d-dimensional real number space, Represents node v i The initial feature at t = 0 is x i ;use To represent the edge e i→j Hidden features of , initialize the hidden features of the edge: Among them, W i ∈R h×d , W j ∈R h×d , W ij ∈R h×d′ represents the learnable weight matrix; x i ,x j ,x ij Respectively represent the node v i , v j and edge i→j The initial characteristics of At step t, for edge-level hidden features First calculate the edge-level adjacency features of each node, and then obtain its edge-level graph representation g (t) ;but in, Represents node v i The edge-level adjacency feature, N(v i ) indicates v i All neighbor nodes of , m represents the number of atomic nodes in the drug molecule; substructure-aware global pooling is used to calculate β ij , given a graph with edge feature matrix X and adjacency matrix A, where non-zero elements in A indicate that two edges share a node, SAGPooling calculates the importance vector β ij The formula for calculation is: b ij =softmax(GNN(A,X)); 1.1.3) For each graph-level representation g (t) , substructure attention score e (t) The calculation is: e (t) =w (t) ⊙tanh(Wg (t) +b), Among them, w (t) is the weight vector of step t, tanh represents the activation function, and W is the representation of each graph level g (t) The weight vector of , b is the bias term; In order to make the attention scores at different steps easier to compare, a softmax function is used to (t) Normalize: Among them, α (t) ∈R l Indicates the importance of the substructure with radius t, T is the total number of graph-level representations for each molecule; k is an index variable used to represent every possible input item from 1 to T; After updating the hidden features of the edge in the Tth step, the hidden features of the edges of all steps are weighted according to the following formula, and the edge-level features are returned, which are finally expressed as: Among them, h ij It represents the final edge-level feature after weighting the edge-level features of layer T; Finally, the node features are returned by aggregating the edge-level features: Where f(·) is a multi-layer perceptron.

4. The method for predicting drug interactions based on dual-view graph neural network according to claim 2, characterized in that: The specific calculation process of updating the atomic node features of the interactive view in step 1.2) includes: 1.2.1) Use graph attention network to capture the interaction information between two drugs; Specifically, each node of a drug is connected to all nodes of another drug to form an interaction edge, and then the node of the drug is updated by aggregating the information of all nodes of another drug; 1.2.2) For the representation of atomic nodes learned from a single drug and between two drugs, use the formula Aggregation is performed and the aggregated node representation is propagated to the next iteration to provide multi-view information for each node.

5. The method for predicting drug interactions based on dual-view graph neural network according to claim 1, characterized in that: Step 2) specifically includes: After updating the node features at each layer, all substructure information of the drug is aggregated, and the global representation of the drug graph is obtained by weighted summation: in, is the global representation of the drug molecule graph, N represents the number of atomic nodes, and α i Each atomic node in each layer represents the weight vector of the layer, σ is the sigmoid nonlinear function, A is the adjacency matrix of the graph, X (t) is the embedding representation of all nodes in the tth layer, is the trainable matrix of the tth layer, d is the input dimension of the node features, and 1 is the output dimension of the importance score; The self-attention graph pooling layer considers both the contextual and topological information of nodes to determine their importance in the entire graph.

6. The method for predicting drug interactions based on dual-view graph neural network according to claim 1, characterized in that: Step 3) specifically includes: 3.1) After obtaining the input drug D x and D y All substructure information of and Then, the joint attention mechanism is used to calculate D x and D y The interaction score of each pair of substructures is γ ij : Where L is the number of input drug substructures, b is a learnable parameter vector, and W x , W y is a learnable matrix; 3.2) Prediction of drug G x and G y Interaction type I r The probability P(G x ,G y ,r): 3.3) The model is trained by an end-to-end back-propagation algorithm, using the Adam algorithm as the optimizer, and updating the parameters by minimizing the loss function; the loss function used is the cross entropy Loss: Among them, p i and p′ i According to the formula The calculated prediction probabilities represent the positive sample set and negative sample set of drug pair interactions, respectively.

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