Microbial-drug association prediction method based on regularized variational graph neural network

Abstract

The application provides a microorganism-drug association prediction method based on a regularized variational graph neural network, and relates to the technical field of bioinformatics. The method comprises the following steps: S1, constructing a microorganism-drug association network by using a microorganism-drug association database; S2, constructing a multi-modal attribute graph of microorganism-drug; S3, establishing a variational graph neural network model with regularization; S4, constructing a training set and a test set by using the microorganism-drug association database, training the graph neural network model with regularization by using the training set; inputting the test set into the trained graph neural network model to predict the microorganism-drug association in the test set. The variational graph neural network model can capture edge information and node information, has good prediction ability, and can prevent overfitting by introducing regularization, thereby solving the problem of isolated nodes, effectively utilizing the information of isolated nodes, and improving the accuracy of microorganism-drug association prediction.

Description

Technical Field

[0001] This invention relates to the field of bioinformatics technology, and more specifically, to a method for predicting microbial-drug associations based on regularized variational graph neural networks. Background Technology

[0002] In recent years, medical research has focused on exploring the relationship between microbial community imbalance and drug efficacy and toxicity. However, a comprehensive understanding of the complex mechanisms of interaction between microbial communities and drugs in the human body remains lacking. Currently, new drug development faces two major challenges. On the one hand, the number of discovered antibiotics is limited, with most work concentrating on optimizing or combining known compounds. It is difficult to culture target bacterial strains under laboratory conditions, and most drugs fail during experiments. On the other hand, the number of drug-resistant bacteria is also increasing at an alarming rate. Increasing research indicates a close interaction between microorganisms and drugs, and some connections between microorganisms and drugs have been confirmed by culture experiments, but these are still insufficient to elucidate the complex interaction mechanisms between microorganisms and drugs. Therefore, there is an urgent need to develop an effective method to systematically explore the possible links between microorganisms and drugs.

[0003] Currently, there are two main types of computational methods used to predict the relationship between microorganisms and drugs.

[0004] The first type of method mainly focuses on similarity measurement. For example, in [1] L. Zhu, G. Duan, C. Yan and J. Wang, "Prediction of Microbe-Drug Associations Based on KATZ Measure," 2019IEEE International Conference on Bioinformatics and Biomedicine (BIBM), 2019, pp. 183-187, doi: 10.1109 / BIBM47256.2019.8983209, Zhu et al. proposed the HMDAKATZ method using KATZ measurement. However, this type of measurement is too simple and cannot fully reflect similarity, which will lead to inaccurate association identification.

[0005] The second type of method uses graph-based learning, which leverages rich semantic information in graph data representations and exhibits better predictive capabilities compared to previous similarity-based methods. Currently, there are two common graph representation learning methods: meta-paths and graph convolutional networks (GCNs).

[0006] Metapath algorithms primarily utilize edge information for microbial-drug association prediction. For example, in [2] Y. Longand J. Luo, "Association Mining to Identify Microbe Drug Interactions Based on Heterogeneous Network Embedding Representation," in IEEE Journal of Biomedical and Health Informatics, vol. 25, no. 1, pp. 266-275, Jan. 2021, doi: 10.1109 / JBHI.2020.2998906, Long et al. proposed a novel heterogeneous network embedding representation framework, HNERMDA, for microbial-drug association prediction. This framework combines metapath2vec with neural network proposals to learn low-dimensional embedding representations of microorganisms and drugs. Metapath algorithms do help improve the predictive ability of models, but they rely too heavily on edge information. When introducing new drugs or microorganisms, the lack of existing edge information naturally leads to prediction failure.

[0007] Compared with metapaths, GCN methods can capture not only edge information but also node information. Therefore, among current methods, the use of GCN methods to predict microbe-drug associations has attracted widespread interest. In [3] Yahui Long, MinWu, Yong Liu, Chee Keong Kwoh, Jiawei Luo, Xiaoli Li, Ensembling graphattention networks for human microbe–drug association prediction, BioinformaticsVolume 36, Issue Supplement_2, December 2020, Pages i779–i786. Long et al. first applied the GCN encoder to the microbial-drug association method GCNMDA and introduced Conditional Random Fields (CRFs) into the GCN hidden layer. Subsequently, Long et al. proposed a node-level attention GCN method, EGATMDA, to learn the embeddings of nodes (i.e., microorganisms and drugs), which can effectively preserve the target neighbors of the graph and retain only relevant information. However, Long et al.'s work failed to construct node features that contain biological information (e.g., drug structural similarity and microbial sequence similarity). Therefore, [4] Deng L, Huang Y, Liu X, Liu H. Graph2MDA: a multi-modalvariational graph embedding model for predicting microbe-drug associations. Bioinformatics. 2021 Nov 23:btab792. doi: 10.1093 / bioinformatics / btab792.Epub ahead of print. PMID: 34864873. LEI et al. constructed a multimodal node attribute graph and used VGAE to extract node representations, which were then used in Graph2MDA for the DNN classifier. However, this method requires complete extraction of the connected graph, so it cannot be used for isolated nodes. Similarly, GAE based on GCN encoders has not been directly used for predicting microbe-drug associations, and graph embedding models based on GCN encoders have difficulty effectively utilizing the information of isolated nodes without connectivity information observed in experiments. Summary of the Invention

[0008] To overcome the above-mentioned technical problems, this invention provides a microbial-drug association prediction method based on a regularized variational graph neural network that can be used for isolated nodes.

[0009] The technical solution of this invention is as follows: A method for predicting microbe-drug associations based on regularized variational graph neural networks includes the following steps: S1. Obtain a microbial-drug association database and construct a microbial-drug association network using the association relationships between microorganisms and drugs in the microbial-drug association database; S2. Construct a multimodal attribute map of microorganisms and drugs based on microbial functional similarity, drug molecular structure similarity, microbial attributes, and drug attributes; S3. Establish a variational graph neural network model with regularization, and train the variational neural network using the microbial-drug association network and the multimodal attribute graph of microbial-drug. S4. Input the microorganisms and drugs whose associations to be predicted into the trained variational neural network to obtain a reconstructed graph. Based on the reconstructed graph, obtain the association probabilities of microorganisms and drugs to complete the association prediction.

[0010] This technical solution proposes a microbial-drug association prediction method based on regularized variational graph neural networks. Based on the microbial-drug association network and the multimodal attribute graph of microbial-drug relationships, a regularized variational graph neural network model is established. This model can capture both edge and node information, achieving good predictive ability for potential connections between microorganisms and drugs. Furthermore, by introducing regularization into the variational graph neural network model, overfitting is prevented, thus solving the isolated node problem and effectively utilizing the information of isolated nodes lacking connection information, thereby improving the accuracy of microbial-drug association prediction.

[0011] Furthermore, the microbial-drug association data in the microbial-drug association database described in step S1 originates from clinical reports or experimental verifications; the microbial-drug association network described in step S1 includes several nodes composed of microorganisms and drugs known to be associated in the microbial-drug association database.

[0012] Furthermore, step S2 specifically includes the following steps: A1. Construct drug similarity feature matrix, drug attribute feature matrix, microbial similarity feature matrix, and microbial attribute feature matrix; A2. Construct a microbial-drug similarity feature network based on the drug similarity feature matrix and the microbial similarity feature matrix; construct a microbial-drug attribute feature network based on the drug attribute feature matrix and the microbial attribute feature matrix; merge the microbial-drug similarity feature network and the microbial-drug attribute feature network to obtain a multimodal attribute map of microorganisms and drugs.

[0013] Further, the expression for the drug similarity feature matrix in step A1 is:

[0014] in, Drug similarity feature matrix; DS struct This is the molecular structure similarity matrix of the drugs, obtained by calculating the molecular structure similarity of the drugs using the SIMCOMP2 tool. DS struct (di,dj) represents drug d i and drug d jMolecular structural similarity between them; The Gaussian kernel similarity matrix is... Indicates drug d i and drug d j Gaussian kernel similarity between them The matrix DIP represents the drug-drug interaction spectrum matrix, DIP(d i ) indicates drug d i Interactions with other drugs; Indicates the standardized kernel bandwidth. , The original bandwidth is set to 1, and nd represents the number of drugs in the microbial-drug association network described in step S1. The method for constructing the drug attribute feature matrix in step A1 is as follows: A topological property network of the drug is constructed using a random walk method with restart. Random drift and restart are performed on this network, and the restart expression is defined as:

[0015] in, ∈ R n×1 θ represents the probability of the i-th node in the drug's topological attribute network moving to another node at time t+1, where θ is the restart probability, T is the transition probability matrix, and p i (0) ∈ R n×1 Let p represent the initial probability vector of the i-th node. i (t) ∈ R n×1 This represents the probability that the i-th node will move to another node at time t; the movement probability refers to the probability of choosing to move or not move given the current topological attribute network node of the drug; the transition probability is the probability of choosing which drug's topological attribute network node as the next node when moving. After the restart expression converges, the movement probability of each drug is obtained, thus yielding the movement probability distribution vector. Based on this vector, a drug attribute feature matrix F is constructed. d ∈ R nd×nd .

[0016] Furthermore, the specific method for constructing the microbial similarity feature matrix in step A1 is as follows: Microbial functional similarity was calculated using the Kamneva tool to obtain the microbial similarity feature matrix. S m ∈ R nm×nm ;in, nm This indicates the number of microorganisms in the microbial-drug association network. Sm ( m i , m j ) represents microorganisms m i and microorganisms m j Similarity between them; The specific method for constructing the microbial attribute feature matrix in step A1 is as follows: The original gene sequences of microorganisms were obtained and encoded using hot coding. Zero-padding was then applied to the encoded gene sequences to ensure all sequences were of equal length. Finally, principal component analysis was used to reduce the dimensionality of the gene sequences, resulting in a k-dimensional microbial sequence attribute matrix. The value of k was set to the number of microorganisms, thus defining the microbial genome sequence attributes as Fi. m ∈R nm×k ;in, nm This indicates the number of microorganisms in the microbial-drug association network.

[0017] Furthermore, the specific method for obtaining the multimodal attribute map of microorganism-drug in step A2 is as follows: Based on the drug similarity feature matrix and the microbial similarity feature matrix, a microbial-drug similarity feature network is constructed. The result is obtained through the following formula: ; A microbial-drug attribute feature network was constructed based on the drug network topology attribute matrix and the microbial sequence genus. The result is obtained through the following formula: ; By combining the microbial-drug similarity feature network and the microbial-drug attribute feature network, a multimodal attribute map of microorganisms and drugs is obtained. The result is obtained through the following formula: .

[0018] Further, step S3, constructing the variational graph neural network model, includes an encoder and a decoder, wherein the encoder is an encoder with L2 regularization introduced; the processing flow of the completed variational graph neural network model is as follows: B1. Obtain the multimodal attribute graph of microorganisms and drugs and the association network of microorganisms and drugs, transform the multimodal attribute graph of microorganisms and drugs into a feature matrix of microorganisms and drugs, and transform the association network of microorganisms and drugs into an adjacency matrix of microorganisms and drugs. B2. Input the microbial-drug feature matrix and the microbial-drug adjacency matrix into the encoder to obtain the latent variable Z as the encoder output; B3. Input the latent variable Z into the decoder. The decoder uses inner product decoding to decode the encoded multimodal attribute map and generate a reconstructed map for calculating the association probability.

[0019] Further, the formula for calculating the microbial-drug feature matrix in step B1 is:

[0020] Where X is the microbial-drug characteristic matrix, It is the content feature vector of node vi in ​​the multimodal attribute graph of microorganism-drug; Step B1, which transforms the microbial-drug association network into a microbial-drug adjacency matrix, involves obtaining the adjacency matrix A ∈ R of the microbial-drug association network. nd×nm If there is a known association between nodes i and j in the microbial-drug association network, then the element A in the adjacency matrix A is... ij Set to 1, if there is no known association between nodes i and j in the microbial-drug association network, then element A in the adjacency matrix A is set to 1. i j Set it to 0; thus obtaining the microbial-drug adjacency matrix A.

[0021] Furthermore, the encoder includes a two-layer graph convolutional neural network and a two-layer regularized graph convolutional network; the expression for the graph convolutional neural network is:

[0022] Where GCN represents Graph Convolutional Neural Network, X is the microbial-drug feature matrix, A is the microbial-drug adjacency matrix, and W... 0 W represents the parameters of the first graph convolutional neural network layer used for training. 1 W represents the parameters of the second graph convolutional neural network layer used for training. 0 ∈R m×f W 1 ∈R m×f The learnable matrix is ​​initialized with random numbers and continuously updated during training; ReLU = max(0, •) is a linear activation function. It is a symmetric normalized adjacency matrix. The expression for a symmetric normalized adjacency matrix is: Where D is the degree matrix of the microbial-drug adjacency matrix A; The expression for a regularized graph convolutional network is:

[0023] Wherein, GNCN represents Regularized Graph Convolutional Network. , It is an N-order identity matrix. for The degree matrix, where s is the scaling factor. The formula used to introduce L2 regularization is:

[0024] in, Set the weight matrix as W∈R m×f The elements of the weight matrix are initialized using random numbers, f is the dimension of the node embedding representation (set by hyperparameters), and n = nd + nm is used as the number of nodes, m = 2 × (nd + nm) is used as the matrix dimension of the nodes, nd is the number of drugs, and nm is the number of microorganisms. And W generate a vector after feature transformation. ; The mean of the normal distribution is calculated using the constructed regularized graph convolutional network, and the variance of the normal distribution is calculated using the graph convolutional neural network. The corresponding normal distribution is constructed using the specific mean and variance of each real sample. Then, the latent variable Z is obtained by sampling the normal distribution using the reparameterization method. The formula for calculating the mean of the normal distribution is:

[0025] Where μ is the mean of the normal distribution; The variance of the normal distribution is obtained by squared standard deviation, and the formula for calculating standard deviation is:

[0026] Where σ is the standard deviation of the normal distribution; The latent variable Z is sampled from the normal distribution Q(Z|X,A) using a reparameterization method. i and Z j Calculate the latent variable Z i The equation is: ; Calculate the latent variable Z j The equation is: ; Where ε i N(0,1), ε j N(0,1), latent variable Z i Let Z be the latent variable of node i in all microbial and drug nodes. j is a hidden variable for node j in all microbial and drug nodes.

[0027] Furthermore, the decoding process described in step B3 is as follows: Decoder retrieves hidden variable Z i and Zj The inner product between the two is used to reconstruct the original adjacency matrix A, thus obtaining the reconstructed graph. Based on the reconstructed graph, a given latent variable p(A) is represented. i j | Z i Z j The probability P of association between microorganisms and drugs is used to predict the association. The correlation probability P is calculated as follows: with

[0028] Here, φ is a sigmoid function.

[0029] This technical solution proposes a microbial-drug association prediction method based on regularized variational graph neural networks. Compared with existing technologies, the beneficial effects of this invention are as follows: Based on the microbial-drug association network and the multimodal attribute graph of microbial-drug, a variational graph neural network model with regularization is established. The variational graph neural network model can capture both edge information and node information, thus obtaining a better predictive ability for potential connections between microorganisms and drugs. Furthermore, by introducing regularization into the variational graph neural network model, overfitting is prevented, thereby solving the isolated node problem and effectively utilizing the information of isolated nodes without connection information, thereby improving the accuracy of microbial-drug association prediction. Attached Figure Description

[0030] Figure 1 This is a schematic diagram of the method steps; Figure 2 A schematic diagram illustrating the process of constructing a multimodal attribute graph of microorganisms and drugs; Figure 3 This is a schematic diagram of the graph neural network processing procedure; Figure 4 This is a schematic diagram of a graph neural network structure. Detailed Implementation

[0031] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0032] Example 1 Microbe-drug association prediction methods based on regularized variational graph neural networks, such as... Figure 1 As shown, the steps include: S1. Obtain a microbial-drug association database and construct a microbial-drug association network using the association relationships between microorganisms and drugs in the microbial-drug association database; S2. Construct a multimodal attribute map of microorganisms and drugs based on microbial functional similarity, drug molecular structure similarity, microbial attributes, and drug attributes; S3. Establish a variational graph neural network model with regularization, and train the variational neural network using the microbial-drug association network and the multimodal attribute graph of microbial-drug. S4. Input the microorganisms and drugs whose associations to be predicted into the trained variational neural network to obtain a reconstructed graph. Based on the reconstructed graph, obtain the association probabilities of microorganisms and drugs to complete the association prediction.

[0033] This embodiment establishes a variational graph neural network model with regularization based on the microbial-drug association network and the multimodal attribute graph of microbial-drug. The variational graph neural network model can capture both edge information and node information, thus obtaining a better predictive ability of potential connections between microorganisms and drugs. Furthermore, by introducing regularization into the variational graph neural network model, overfitting is prevented, thereby solving the isolated node problem and effectively utilizing the information of isolated nodes without connection information, thereby improving the accuracy of microbial-drug association prediction.

[0034] Example 2 This embodiment provides a microbe-drug association prediction method based on regularized variational graph neural network. Based on embodiment 1, in this embodiment, the microbe-drug association data in the microbe-drug association database mentioned in step S1 comes from clinical reports or experimental verifications; the microbe-drug association network mentioned in step S1 includes several nodes composed of microbes and drugs known to be associated in the microbe-drug association database.

[0035] Step S2 specifically includes the following steps: A1. Construct drug similarity feature matrix, drug attribute feature matrix, microbial similarity feature matrix, and microbial attribute feature matrix; A2. Construct a microbial-drug similarity feature network based on the drug similarity feature matrix and the microbial similarity feature matrix; construct a microbial-drug attribute feature network based on the drug attribute feature matrix and the microbial attribute feature matrix; merge the microbial-drug similarity feature network and the microbial-drug attribute feature network to obtain a multimodal attribute map of microorganisms and drugs.

[0036] The expression for the drug similarity feature matrix in step A1 is:

[0037] in, Drug similarity feature matrix; DS structThis is the molecular structure similarity matrix of the drugs, obtained by calculating the molecular structure similarity of the drugs using the SIMCOMP2 tool. DS struct (di,dj) represents drug d i and drug d j Molecular structural similarity between them; The Gaussian kernel similarity matrix is... Indicates drug d i and drug d j Gaussian kernel similarity between them The matrix DIP represents the drug-drug interaction spectrum matrix, DIP(d i ) indicates drug d i Interactions with other drugs; Indicates the standardized kernel bandwidth. , The original bandwidth is set to 1, and nd represents the number of drugs in the microbial-drug association network described in step S1. The method for constructing the drug attribute feature matrix in step A1 is as follows: A topological property network of the drug is constructed using a random walk method with restart. Random drift and restart are performed on this network, and the restart expression is defined as:

[0038] in, ∈ R n×1 θ represents the probability of the i-th node in the drug's topological attribute network moving to another node at time t+1, where θ is the restart probability, T is the transition probability matrix, and p i (0) ∈ R n×1 Let p represent the initial probability vector of the i-th node. i (t) ∈ R n×1 This represents the probability that the i-th node will move to another node at time t; the movement probability refers to the probability of choosing to move or not move given the current topological attribute network node of the drug; the transition probability is the probability of choosing which drug's topological attribute network node as the next node when moving. After the restart expression converges, the movement probability of each drug is obtained, thus yielding the movement probability distribution vector. Based on this vector, a drug attribute feature matrix F is constructed. d ∈ R nd×nd .

[0039] The specific method for constructing the microbial similarity feature matrix in step A1 is as follows: Microbial functional similarity was calculated using the Kamneva tool to obtain the microbial similarity feature matrix.S m ∈ R nm×nm ;in, nm This indicates the number of microorganisms in the microbial-drug association network. S m ( m i , m j ) represents microorganisms m i and microorganisms m j Similarity between them; The specific method for constructing the microbial attribute feature matrix in step A1 is as follows: The original gene sequences of microorganisms were obtained and encoded using hot coding. Zero-padding was then applied to the encoded gene sequences to ensure all sequences were of equal length. Finally, principal component analysis was used to reduce the dimensionality of the gene sequences, resulting in a k-dimensional microbial sequence attribute matrix. The value of k was set to the number of microorganisms, thus defining the microbial genome sequence attributes as Fi. m ∈R nm×k ;in, nm This indicates the number of microorganisms in the microbial-drug association network.

[0040] The specific method for obtaining the multimodal attribute map of microorganism-drug in step A2 is as follows: Based on the drug similarity feature matrix and the microbial similarity feature matrix, a microbial-drug similarity feature network is constructed. The result is obtained through the following formula: ; A microbial-drug attribute feature network was constructed based on the drug network topology attribute matrix and the microbial sequence genus. The result is obtained through the following formula: ; By combining the microbial-drug similarity feature network and the microbial-drug attribute feature network, a multimodal attribute map of microorganisms and drugs is obtained. The result is obtained through the following formula:

[0041] Step S3 constructs the variational graph neural network model, which includes an encoder and a decoder. The encoder is an encoder with L2 regularization. The processing flow of the completed variational graph neural network model is as follows: B1. Obtain the multimodal attribute graph of microorganisms and drugs and the association network of microorganisms and drugs, transform the multimodal attribute graph of microorganisms and drugs into a feature matrix of microorganisms and drugs, and transform the association network of microorganisms and drugs into an adjacency matrix of microorganisms and drugs. The formula for calculating the microbial-drug characteristic matrix in step B1 is as follows:

[0042] Where X is the microbial-drug characteristic matrix, It is the content feature vector of node vi in ​​the multimodal attribute graph of microorganism-drug; Step B1, which transforms the microbial-drug association network into a microbial-drug adjacency matrix, involves obtaining the adjacency matrix A ∈ R of the microbial-drug association network. nd×nm If there is a known association between nodes i and j in the microbial-drug association network, then the element A in the adjacency matrix A is... ij Set to 1, if there is no known association between nodes i and j in the microbial-drug association network, then element A in the adjacency matrix A is set to 1. i j Set it to 0; thus obtaining the microbial-drug adjacency matrix A.

[0043] B2. Input the microbial-drug feature matrix and the microbial-drug adjacency matrix into the encoder to obtain the latent variable Z as the encoder output; The encoder comprises a two-layer graph convolutional neural network and a two-layer regularized graph convolutional network; the expression for the graph convolutional neural network is:

[0044] Where GCN represents Graph Convolutional Neural Network, X is the microbial-drug feature matrix, A is the microbial-drug adjacency matrix, and W... 0 W represents the parameters of the first graph convolutional neural network layer used for training. 1 W represents the parameters of the second graph convolutional neural network layer used for training. 0 ∈R m×f W 1 ∈R m×f The learnable matrix is ​​initialized with random numbers and continuously updated during training; ReLU = max(0, •) is a linear activation function. It is a symmetric normalized adjacency matrix. The expression for a symmetric normalized adjacency matrix is: Where D is the degree matrix of the microbial-drug adjacency matrix A; The expression for a regularized graph convolutional network is:

[0045] Wherein, GNCN represents Regularized Graph Convolutional Network. , It is an N-order identity matrix. for The degree matrix, where s is the scaling factor. The formula used to introduce L2 regularization is:

[0046] in, Set the weight matrix as W∈R m×f The elements of the weight matrix are initialized using random numbers, f is the dimension of the node embedding representation (set by hyperparameters), and n = nd + nm is used as the number of nodes, m = 2 × (nd + nm) is used as the matrix dimension of the nodes, nd is the number of drugs, and nm is the number of microorganisms. And W generate a vector after feature transformation. ; The mean of the normal distribution is calculated using the constructed regularized graph convolutional network, and the variance of the normal distribution is calculated using the graph convolutional neural network. The corresponding normal distribution is constructed using the specific mean and variance of each real sample. Then, the latent variable Z is obtained by sampling the normal distribution using the reparameterization method. The formula for calculating the mean of the normal distribution is:

[0047] Where μ is the mean of the normal distribution; The variance of the normal distribution is obtained by squared standard deviation, and the formula for calculating standard deviation is:

[0048] Where σ is the standard deviation of the normal distribution; The latent variable Z is sampled from the normal distribution Q(Z|X,A) using a reparameterization method. i and Z j Calculate the latent variable Z i The equation is: ; Calculate the latent variable Z j The equation is: ; Where ε i N(0,1), ε j N(0,1), latent variable Z i Let Z be the latent variable of node i in all microbial and drug nodes. j is a hidden variable for node j in all microbial and drug nodes.

[0049] B3. Input the latent variable Z into the decoder. The decoder uses inner product decoding to decode the encoded multimodal attribute map and generate a reconstructed map for calculating the association probability.

[0050] The decoding process described in step B3 is as follows: Decoder retrieves hidden variable Z i and Z j The inner product between the two is used to reconstruct the original adjacency matrix A, thus obtaining the reconstructed graph. Based on the reconstructed graph, a given latent variable p(A) is represented. i j | Z i Z j The probability P of association between microorganisms and drugs is used to predict the association. The correlation probability P is calculated as follows: with

[0051] Here, φ is a sigmoid function.

[0052] Example 3 Based on Examples 1 and 2, this example provides a training method for the variational graph neural network model as follows: Within the framework of k-fold cross-validation, all known microbial-drug association data in the existing microbial-drug association database are randomly divided into k clusters. A subset of each batch of randomly sampled unknown association pairs with the same batch size is selected as the test set, and the remaining known association pairs are selected as the training set. A regularized graph neural network model is trained using the training set. The number of early stops is preset. During the training process, when the loss function converges, the AUC value of the trained graph neural network model is judged in the subsequent training within the number of early stops. If the AUC value of each time is not greater than the AUC value of the previous time, the training is stopped; otherwise, the training continues. The loss function, during learning, aims to optimize the variational lower bound (denoted as L) to minimize the relative entropy between the approximate distribution and the true posterior distribution. A common metric, the Kulbak-Leybauer divergence (denoted as KL), is used. The similarity between two distributions is measured. Then, L is obtained by taking the difference between the expected log-likelihood of A and the Kullback-Leibler divergence, where the equation is:

[0053] Where p(Z) is the Gaussian prior, and in order to optimize the variational lower bound, thus minimizing KL( In VGNAEMDA, stochastic gradient descent is performed for training.

[0054] The AUC value is calculated using the following method: Input the training set into the model to obtain the reconstruction graph of the training set by the current model. Take the score of the edge between each node in the reconstruction graph of the training set by the current model, and record it as the association probability. The association probability takes a value between 0 and 1. Based on the association between microorganisms and drugs in the training set, the true values ​​of the edge labels in the training set are obtained. The true values ​​of the labels are 0 or 1, where 0 indicates that there is no edge and no association, which means that the sample is actually negative, and 1 indicates that there is an edge and an association, which means that the sample is actually positive. Each association probability is used as a classification threshold. When other association probabilities are greater than the classification threshold, they are considered as positive samples, and when other association probabilities are less than the classification threshold, they are considered as negative samples. The true positive rate and false positive rate at each category threshold are calculated using the following formulas:

[0055] in, The true positive rate, The false positive rate, 1 is the true positive rate, which represents the number of samples that are actually negative but are predicted as positive; 2 is the false negative rate, which represents the number of samples that are actually positive but are predicted as negative; 3 is the false positive rate, which represents the number of samples that are actually negative but are predicted as positive; 4 is the true negative rate, which represents the number of samples that are actually negative but are predicted as negative. by The horizontal axis is... Plot the ROC curve on the vertical axis and use the method of infinitesimal elements to calculate the area under the ROC curve, i.e., the AUC value; After training is stopped, the test set is input into the trained graph neural network model. Based on the generated reconstructed graph, the model predicts the association between isolated nodes in the microorganism-drug pair within the test set. This invention improves the predictive performance of the isolated node model by introducing L2 regularization, thus avoiding the zero tendency of the isolated node paradigm.

[0056] To verify that the microbial-drug association prediction method based on variational normalized variational graph neural network provided in this invention is more accurate than existing methods, this embodiment uses default parameter settings to run this method and four existing methods on the MDAD dataset, and uses the AUC value as the performance evaluation index. The larger the AUC value, the higher the accuracy of the method.

[0057] The specific process is as follows: Five-fold cross-validation was performed on all methods. This means that the experimentally validated drug combinations were randomly divided into five equal subsets, each used sequentially as the test set, with the remainder used to train the model. To eliminate random sampling bias, this process was repeated 10 times, and the final AUC score was calculated based on the average AUC values ​​from the 10 repeated validations. The final AUC score was used as the performance metric to evaluate the accuracy of each method; a higher final AUC score indicates higher accuracy.

[0058] An experiment was designed for isolated nodes, with the following settings: when the overall AUC value was at its maximum, the AUC values ​​of isolated nodes in the test set were taken. The highest AUC value (0.958) was achieved by the normalized variational graph neural network method provided in this invention. Therefore, the microbial-drug association prediction method based on normalized variational graph neural networks provided in this invention outperforms existing methods on isolated nodes.

[0059]

[0060] Table 1 Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art can make other variations or modifications based on the above description. It is neither necessary nor possible to exhaustively describe all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A method for predicting microbial-drug associations based on regularized variational graph neural networks, characterized in that, Including the following steps: S1. Obtain a microbial-drug association database and construct a microbial-drug association network using the association relationships between microorganisms and drugs in the microbial-drug association database; S2. Construct a multimodal attribute map of microorganisms and drugs based on microbial functional similarity, drug molecular structure similarity, microbial attributes, and drug attributes; S3. Establish a variational graph neural network model with regularization, and train the variational neural network using the microbial-drug association network and the multimodal attribute graph of microbial-drug. The construction of the variational graph neural network model includes an encoder and a decoder, wherein the encoder is an encoder with L2 regularization. The processing flow of the completed variational graph neural network model is as follows: B1. Obtain the multimodal attribute graph of microorganisms and drugs and the association network of microorganisms and drugs, transform the multimodal attribute graph of microorganisms and drugs into a microorganism-drug feature matrix, and transform the association network of microorganisms and drugs into a microorganism-drug adjacency matrix; the calculation formula of the microorganism-drug feature matrix is ​​as follows: Where X is the microbial-drug characteristic matrix, It is the content feature vector of node vi in ​​the multimodal attribute graph of microorganism-drug; Step B1, which transforms the microbial-drug association network into a microbial-drug adjacency matrix, involves obtaining the adjacency matrix A ∈ R of the microbial-drug association network. nd×nm If there is a known association between nodes i and j in the microbial-drug association network, then the element A in the adjacency matrix A is... ij Set to 1, if there is no known association between nodes i and j in the microbial-drug association network, then element A in the adjacency matrix A is set to 1. i j Set it to 0; thus obtaining the microbial-drug adjacency matrix A; The encoder comprises a two-layer graph convolutional neural network and a two-layer regularized graph convolutional network; the expression for the graph convolutional neural network is: Where GCN represents Graph Convolutional Neural Network, X is the microbial-drug feature matrix, A is the microbial-drug adjacency matrix, and W... 0 W represents the parameters of the first graph convolutional neural network layer used for training. 1 W represents the parameters of the second graph convolutional neural network layer used for training. 0 ∈R m×f W 1 ∈R m×f The learnable matrix is ​​initialized with random numbers and continuously updated during training; ReLU = max(0, •) is a linear activation function. It is a symmetric normalized adjacency matrix. The expression for a symmetric normalized adjacency matrix is: Where D is the degree matrix of the microbial-drug adjacency matrix A; The expression for a regularized graph convolutional network is: Wherein, GNCN represents Regularized Graph Convolutional Network. , It is an N-order identity matrix. for The degree matrix, where s is the scaling factor. The formula used to introduce L2 regularization is: in, Set the weight matrix as W∈R m×f The elements of the weight matrix are initialized using random numbers, f is the dimension of the node embedding representation (set by hyperparameters), and n = nd + nm is used as the number of nodes, m = 2 × (nd + nm) is used as the matrix dimension of the nodes, nd is the number of drugs, and nm is the number of microorganisms. And W generate a vector after feature transformation. ; The mean of the normal distribution is calculated using the constructed regularized graph convolutional network, and the variance of the normal distribution is calculated using the graph convolutional neural network. The corresponding normal distribution is constructed using the specific mean and variance of each real sample. Then, the latent variable Z is obtained by sampling the normal distribution using the reparameterization method. The formula for calculating the mean of the normal distribution is: Where μ is the mean of the normal distribution; The variance of the normal distribution is obtained by squared standard deviation, and the formula for calculating standard deviation is: Where σ is the standard deviation of the normal distribution; The latent variable Z is sampled from the normal distribution Q(Z|X,A) using a reparameterization method. i and Z j Calculate the latent variable Z i The equation is: ; Calculate the latent variable Z j The equation is: ; Where ε i N(0,1), ε j N(0,1), latent variable Z i Let Z be the latent variable of node i in all microbial and drug nodes. j For all microbial nodes and drug nodes, there is a hidden variable for node j; B2. Input the microbial-drug feature matrix and the microbial-drug adjacency matrix into the encoder to obtain the latent variable Z as the encoder output; B3. Input the latent variable Z into the decoder. The decoder uses inner product decoding to decode the encoded multimodal attribute map and generate a reconstructed map for calculating the association probability. S4. Input the microorganisms and drugs whose associations to be predicted into the trained variational neural network to obtain a reconstructed graph. Based on the reconstructed graph, obtain the association probabilities of microorganisms and drugs to complete the association prediction.

2. The microbial-drug association prediction method based on regularized variational graph neural network according to claim 1, characterized in that, The microbial-drug association data in the microbial-drug association database mentioned in step S1 comes from clinical reports or experimental verifications; the microbial-drug association network mentioned in step S1 includes several nodes composed of microorganisms and drugs known to be associated in the microbial-drug association database.

3. The microbial-drug association prediction method based on regularized variational graph neural network according to claim 1, characterized in that, Step S2 specifically includes the following steps: A1. Construct drug similarity feature matrix, drug attribute feature matrix, microbial similarity feature matrix, and microbial attribute feature matrix; A2. Construct a microbial-drug similarity feature network based on the drug similarity feature matrix and the microbial similarity feature matrix; construct a microbial-drug attribute feature network based on the drug attribute feature matrix and the microbial attribute feature matrix; merge the microbial-drug similarity feature network and the microbial-drug attribute feature network to obtain a multimodal attribute map of microorganisms and drugs.

4. The microbial-drug association prediction method based on regularized variational graph neural network according to claim 3, characterized in that, The expression for the drug similarity feature matrix in step A1 is: in, Drug similarity feature matrix; DS struct This is the molecular structure similarity matrix of the drugs, obtained by calculating the molecular structure similarity of the drugs using the SIMCOMP2 tool. DS struct (di,dj) represents drug d i and drug d j Molecular structural similarity between them; The Gaussian kernel similarity matrix is... Indicates drug d i and drug d j Gaussian kernel similarity between them The matrix DIP represents the drug-drug interaction spectrum matrix, DIP(d i ) indicates drug d i Interactions with other drugs; Indicates the standardized kernel bandwidth. , The original bandwidth is set to 1, and nd represents the number of drugs in the microbial-drug association network described in step S1. The method for constructing the drug attribute feature matrix in step A1 is as follows: A topological property network of the drug is constructed using a random walk method with restart. Random drift and restart are performed on this network, and the restart expression is defined as: in, ∈ R n×1 θ represents the probability of the i-th node in the drug's topological attribute network moving to another node at time t+1, where θ is the restart probability, T is the transition probability matrix, and p i (0) ∈ R n×1 Let p represent the initial probability vector of the i-th node. i (t) ∈ R n×1 This represents the probability that the i-th node will move to another node at time t; the movement probability refers to the probability of choosing to move or not move given the current topological attribute network node of the drug; the transition probability is the probability of choosing which drug's topological attribute network node as the next node when moving. After the restart expression converges, the movement probability of each drug is obtained, thus yielding the movement probability distribution vector. Based on this vector, a drug attribute feature matrix F is constructed. d ∈ R nd×nd .

5. The microbial-drug association prediction method based on regularized variational graph neural network according to claim 4, characterized in that, The specific method for constructing the microbial similarity feature matrix in step A1 is as follows: Microbial functional similarity was calculated using the Kamneva tool to obtain the microbial similarity feature matrix. S m ∈ R nm×nm ;in, nm This indicates the number of microorganisms in the microbial-drug association network. S m ( m i , m j ) represents microorganisms m i and microorganisms m j Similarity between them; The specific method for constructing the microbial attribute feature matrix in step A1 is as follows: The original gene sequences of microorganisms were obtained and encoded using hot coding. Zero-padding was then applied to the encoded gene sequences to ensure all sequences were of equal length. Finally, principal component analysis was used to reduce the dimensionality of the gene sequences, resulting in a k-dimensional microbial sequence attribute matrix. The value of k was set to the number of microorganisms, thus defining the microbial genome sequence attributes as Fi. m ∈R nm×k ;in, nm This indicates the number of microorganisms in the microbial-drug association network.

6. The method for predicting microbial-drug associations based on regularized variational graph neural networks according to claim 5, characterized in that, The specific method for obtaining the multimodal attribute map of microorganism-drug in step A2 is as follows: Based on the drug similarity feature matrix and the microbial similarity feature matrix, a microbial-drug similarity feature network is constructed. The result is obtained through the following formula: ； A microbial-drug attribute feature network was constructed based on the drug network topology attribute matrix and the microbial sequence genus. The result is obtained through the following formula: ； By combining the microbial-drug similarity feature network and the microbial-drug attribute feature network, a multimodal attribute map of microorganisms and drugs is obtained. The result is obtained through the following formula: 。 7. The method for predicting microbial-drug associations based on regularized variational graph neural networks according to claim 1, characterized in that, The decoding process described in step B3 is as follows: Decoder retrieves hidden variable Z i and Z j The inner product between the two is used to reconstruct the original adjacency matrix A, thus obtaining the reconstructed graph. Based on the reconstructed graph, a given latent variable p(A) is represented. i j | Z i Z j The probability P of association between microorganisms and drugs is used to predict the association. The correlation probability P is calculated as follows: with Here, φ is a sigmoid function.

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