A high-order interaction prediction method and device with hybrid graph deep learning

Abstract

The application provides a high-order interaction prediction method and device with mixed graph deep learning, which first constructs a drug molecule graph, a microorganism weighted graph, a disease weighted graph and a supergraph connecting the three based on multi-source heterogeneous data such as drug molecular structure, microorganism classification information and disease semantic network, forming a mixed graph structure. Subsequently, through a mixed graph deep learning module fusing a graph convolution network and a supergraph neural network, nonlinear structure features and high-order interaction features of each entity are extracted, and the adaptive fusion of the features is realized by using an attention mechanism. Then, the fused deep features are mapped to the prior expectation of the latent factor matrix in the Bayesian logic tensor decomposition model, a probabilistic graph model is constructed, and the joint adaptive inference of the model parameters, latent variables and deep learning mapping is carried out through a variational expectation maximization algorithm, so that the high-order correlation probability prediction of the whole tensor space is realized without negative sampling.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of bioinformatics and computational biology, and particularly relates to a high-order interaction prediction method and device with hybrid graph deep learning. BACKGROUND

[0002] In biomedical research, human microbiome is confirmed to be closely related to a variety of human diseases (such as obesity, diabetes, inflammatory bowel disease, etc.). At the same time, microorganisms play a key role in regulating drug efficacy and toxicity, and drug intervention will in turn change the composition and function of the microbiome. Therefore, systematically exploring the potential correlation between drug-microbe-disease (DMD) has important clinical significance for understanding the pathogenesis of diseases, promoting drug development, achieving early diagnosis of diseases and precision medicine.

[0003] At present, the methods for identifying the correlation between drugs, microorganisms and diseases mainly include biological experimental methods and computational prediction methods. Although traditional biological experimental methods (such as wet-lab experiments) are considered as the "gold standard" for establishing correlations, they rely on expensive experimental equipment and are limited by the difficulty of completely simulating the complex human body environment in vitro, and require a large amount of time and extensive case samples for clinical observation. In the face of a large number of candidate drugs and microorganism species, it is unrealistic, inefficient and costly to rely solely on traditional experiments for large-scale screening. In order to make up for the shortcomings of experimental methods, computational prediction methods are widely used to integrate multi-source information to predict potential correlations. Existing computational prediction methods mainly include two categories: tensor decomposition-based methods and deep learning-based methods.

[0004] In the tensor decomposition-based method, researchers attempt to model the ternary relationship of drug-microbe-disease as a tensor, and use tensor decomposition techniques such as CANDECOMP / PARAFAC decomposition, non-negative tensor decomposition, etc. to complete the missing relationships. However, most existing tensor decomposition methods use linear models to integrate auxiliary information, which is difficult to mine the complex nonlinear relationships that exist universally in biological data. In addition, such methods usually contain a large number of hyperparameters (such as the rank of the tensor), and the model performance is extremely sensitive to the parameters, making it difficult to adapt to complex and variable data structures. Although some studies have proposed logical tensor decomposition to introduce nonlinearity, there are still limitations in integrating heterogeneous networks.

[0005] In a deep learning-based method, with the development of graph neural networks, methods based on graph convolutional networks (GCN) or hypergraph neural networks (HGNN / HGCN) are used to extract features of biological entities. Such methods learn node embeddings by constructing networks or hypergraphs. However, existing deep learning methods usually need to perform negative sampling to construct a training set. Since unknown associations do not mean that they do not exist (i.e. there may be false negatives), the noise introduced by random negative sampling can reduce the accuracy of prediction. In addition, the supervised learning paradigm is difficult to cover the entire sample space, and a single view of the deep learning model can easily lead to information bias.

[0006] In summary, the prior art is difficult to simultaneously consider deep mining of nonlinear characteristics, avoid bias caused by negative sampling, and adaptive inference of model parameters when dealing with high-order association prediction of drugs-microorganisms-diseases.

[0007] Therefore, the present application is proposed. SUMMARY

[0008] The present application provides a high-order interaction prediction method and device with hybrid graph deep learning, equipment and medium, which can at least partially improve the above problems.

[0009] To achieve the above object, the present application adopts the following technical solutions:

[0010] A high-order interaction prediction method with hybrid graph deep learning comprises:

[0011] Drug data, microorganism data, disease data and auxiliary information are extracted from a plurality of preset databases, and a hybrid graph structure and an association tensor are constructed based on the extracted data;

[0012] A graph convolutional network and a hypergraph convolutional network are used to extract features of the hybrid graph structure, corresponding attention factors and deep learning mappings are introduced, prior expectations and multivariate Gaussian distributions are calculated, joint likelihood probabilities are calculated based on the association tensor, and a joint probability model is obtained by combining the joint likelihood probabilities and the multivariate Gaussian distributions;

[0013] An E-step is performed, and in the case of fixing the prior expectations, the posterior expectations and covariance matrices of latent factor matrices are inferred based on the association tensor;

[0014] An M-step is performed, and in the case of fixing the posterior expectations and covariance matrices, the joint probability model parameters and the deep learning mappings are updated using an Adam optimizer, and the E-step and the M-step are alternately performed until an optimal balance is reached, the optimal posterior distributions of all latent factor matrices are obtained, and the final posterior expectation values of the latent factor matrices are extracted as the final joint probability model output.

[0015] The predicted association probability is calculated for any drug-microbe-disease triple based on the final posterior expected value. The predicted association probabilities are then sorted in descending order to generate a recommendation list.

[0016] The present invention also provides a high-order interaction prediction device with hybrid graph deep learning, comprising:

[0017] The data extraction unit is used to extract drug data, microbial data, disease data, and auxiliary information from multiple preset databases, and to construct a hybrid graph structure and correlation tensor based on the extracted data;

[0018] The prior expectation calculation unit is used to extract features from the hybrid graph structure using graph convolutional networks and hypergraph convolutional networks, introduce the corresponding attention factors and deep learning mappings, calculate the prior expectation and multivariate Gaussian distribution, and calculate the joint likelihood probability based on the correlation tensor. Combining the joint likelihood probability and multivariate Gaussian distribution, the joint probability model is obtained.

[0019] The E-step unit is used to perform the E-step, which, with a fixed prior expectation, infers the posterior expectation and covariance matrix of the latent factor matrix by combining the correlation tensor.

[0020] The M-step unit is used to execute the M-step. With the posterior expectation and covariance matrix fixed, the Adam optimizer is used to update the joint probability model parameters and deep learning mapping, and the E-step and M-step are executed alternately until the optimal balance is reached. The optimal posterior distribution of all latent factor matrices is obtained, and the final posterior expectation of each latent factor matrix is ​​extracted as the final joint probability model output.

[0021] The prediction unit is used to calculate the predicted association probability for any drug-microbe-disease triple based on the final posterior expected value, and then sort the predicted association probabilities in descending order to generate a recommendation list.

[0022] In summary, this invention provides a high-order interaction prediction method with hybrid graph deep learning, mainly used to process multi-source heterogeneous data of drugs, microorganisms and diseases, and predict high-order potential associations between them. It can effectively integrate multi-source heterogeneous data such as drug molecular structure, microbial phylogenetic tree and disease semantic network, improve the accuracy and robustness of drug-microbe-disease (DMD) high-order association prediction, and effectively solve the limitations of traditional experimental costs and existing computational models in terms of nonlinear feature mining and negative sampling noise. Attached Figure Description

[0023] Figure 1This is a flowchart illustrating the high-order interactive prediction method with hybrid graph deep learning provided in the first embodiment of the present invention.

[0024] Figure 2 This is a schematic diagram of a module of a high-order interaction prediction device with hybrid graph deep learning provided in the second embodiment of the present invention. Detailed Implementation

[0025] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0026] refer to Figure 1 As shown, the first embodiment of the present invention discloses a high-order interaction prediction method with hybrid graph deep learning, which can be executed by a high-order interaction prediction device with hybrid graph deep learning (hereinafter referred to as the prediction device), specifically, by one or more processors within the prediction device, to implement the following method:

[0027] S1 extracts drug data, microbial data, disease data, and auxiliary information from multiple pre-set databases, and constructs a hybrid graph structure and correlation tensor based on the extracted data;

[0028] Specifically, step S1 further includes: extracting drug data, microbial data, disease data, and auxiliary information from multiple preset databases;

[0029] The SMILES string in the drug data is transformed to construct the drug molecule map. ,in, Let R be the atomic attribute matrix, where R is the feature dimension and n is the number of atoms. Let A be the adjacency matrix, representing atomic properties. If the i-th and j-th atoms are connected by a chemical bond, then... ;

[0030] Microbial weighted graphs were constructed based on microbial and disease data, respectively. Disease-weighted graph ,in, As the apex of microorganisms, For the edge of microorganisms, Let be the weight corresponding to the edge representing the microorganism. At the peak of the disease, For the edge of disease, The weights corresponding to the edges representing diseases; for example, microorganisms are used, utilizing phylogenetic similarity. As edge weight, i.e. when At that time, edge weight .

[0031] A DMD hypermap is constructed based on drug data, microbial data, disease data, and auxiliary information. , This is a vertex set containing all drug data, microbial data, and disease data. Let be a set of superedges; where each superedge It contains three vertices (a drug, a microorganism, and a disease), corresponding to known DMD triple associations.

[0032] A hybrid graph structure was constructed based on the drug molecule graph, microbial weighted graph, disease weighted graph, and DMD hypergraph, and a hypergraph association matrix was defined. Wherein, when the v-th vertex is in the e-th hyperedge, the corresponding hypergraph incidence matrix is... When the v-th vertex is not in the e-th hyperedge, the corresponding hypergraph incidence matrix is... , , ;

[0033] Establish the drug-microbe-disease association tensor Where I represents the number of drugs, J represents the number of microorganisms, and K represents the number of diseases. The elements (i,j,k) are denoted as... Let represent the association between the i-th drug, the j-th microorganism, and the k-th disease. If an association exists, Otherwise, it is 0 (or unknown).

[0034] In this embodiment, a hybrid graph is constructed to transform multi-source heterogeneous biological data into computer-processable graph structure data. First, validation is performed using two pre-defined benchmark datasets (DataI and DataII). DataI contains 2763 known triplet relationships involving 270 drugs, 58 microorganisms, and 167 diseases. DataII, to expand the data scale, was re-collected and reorganized from databases such as MDAD, MASI, HMDAD, and Disbiome. Ultimately, 4276 known associations among 345 drugs, 200 microorganisms, and 155 diseases are obtained.

[0035] Because traditional similarity matrices lose information about the internal topological structure of drug molecules, it is necessary to construct a DrugMolecularGraph. This graph uses the SMILES strings of drugs to describe structural information and builds a set of drugmolecular graphs. In other words, through molecular graphs, graph convolution can capture the chemical environment features between atoms. Secondly, to further preserve the semantic or evolutionary similarity between biological entities, nearest neighbor relationships are constructed to provide a structural foundation for subsequent information dissemination. This involves obtaining the taxonomic hierarchy structure based on NCBITaxID, calculating phylogenetic similarity, and constructing weighted graphs of microorganisms. Similarly, a hierarchical directed acyclic graph (DAG) of diseases is extracted based on MeSHID, and semantic similarity is calculated to construct a weighted graph of diseases. Furthermore, since existing binary networks cannot directly express ternary interactions, a hypergraph is constructed using known triple associations, where each hyperedge connects the drug, microorganism, and disease nodes; this is called the Drug-Microorganism-Disease Hypergraph (DMDHypergraph). Hypergraphs can naturally model higher-order associations between drugs, microorganisms, and diseases, avoiding the information loss caused by decomposing triples into binary pairs. In addition, it is necessary to construct a drug-microbe-disease association tensor.

[0036] S2 uses graph convolutional networks and hypergraph convolutional networks to extract features from the hybrid graph structure, introduces the corresponding attention factor and deep learning mapping, calculates the prior expectation and multivariate Gaussian distribution, and calculates the joint likelihood probability based on the correlation tensor. Combining the joint likelihood probability and multivariate Gaussian distribution, the joint probability model is obtained.

[0037] Specifically, step S2 further includes: applying multi-layer GCN propagation to the microbial weighted map and the disease weighted map to obtain propagation characteristics, wherein the calculation formula for the propagation characteristics of the (t+1)th layer is: , For degree matrix, Let be the learnable parameter matrix of the t-th layer. For the propagation characteristics of layer t, It is a non-linear activation function. This is a phylogenetic similarity matrix for microorganisms, which describes the similarity relationship between any two microorganisms;

[0038] A graph convolutional network is applied to the drug molecule graph, and global max pooling is used to aggregate atomic-level features into a drug-level feature vector. This feature vector and propagation features are then combined to obtain GCN features.

[0039] Applying a hypergraph convolutional network to the DMD hypergraph, performing vertex-hyperedge-vertex information propagation, and extracting hypergraph convolutional network features, wherein the propagation rule is as follows: , Let be the degree matrix of the vertices. Let be the degree matrix of the hyperedge. Let T be the hyperedge weight matrix, and T be the transpose. For the drug characteristics of layer t+1, For the characteristics of the drug in layer t, The projection matrix;

[0040] The drug features in the GCN feature set are fused with the drug features in the hypergraph convolutional network feature set to obtain the drug set. And introduce learnable drug attention factors. The prior expectation of the drug is obtained by normalization calculation using the Softmax function. , , As a learnable drug attention factor, The number of drug characteristics, It is an exponential function;

[0041] Microbial features from GCN features are fused with microbial features from hypergraph convolutional network features to obtain a microbial set. Introducing learnable microbial attention factors To obtain the prior expectations of microorganisms , , The number of microbial characteristics, A learnable microbial attention factor;

[0042] The disease features in the GCN feature set are fused with the disease features in the hypergraph convolutional network feature set to obtain the disease set. Introducing learnable disease attention factors To obtain the prior expectation of the disease , , The number of disease characteristics, It is a learnable disease attention factor.

[0043] set up , , These are drug latent factor matrices, microbial latent factor matrices, and disease latent factor matrices, using... Represents the set of latent factor matrices;

[0044] By introducing a deep learning mapping F, and based on the prior expectations of drugs, microorganisms, and diseases, the multivariate Gaussian distribution of the drug latent factor matrix G is calculated. , It is a diagonal matrix. For the a priori expectation of the drug The i-th row, For the i-th row of the drug potential factor matrix G, It follows a normal distribution. Here are the parameters of the joint probability model; the expectation of this multivariate Gaussian distribution satisfies The accuracy is ;in, It can also be interpreted as the drug prior features calculated through the hybrid graph deep learning module (which integrates the attention mechanism output of GCN and HGCN features).

[0045] Similarly, H and W are also row-independent, and their a priori expectations are determined by... and generate;

[0046] Calculate the multivariate Gaussian distribution of the microbial latent factor matrix H , For microbial prior expectations The j-th row, Let H be the j-th row of the microbial latent factor matrix H; where the expectation of this Gaussian distribution satisfies The accuracy is .

[0047] Calculate the multivariate Gaussian distribution of the disease latent factor matrix W. , a priori expectations for disease The kth row, Let W be the k-th row of the disease latent factor matrix; where the expectation of this Gaussian distribution satisfies The accuracy is .

[0048] Based on correlation tensor Calculate the correlation tensor joint likelihood probability , , c is the importance level parameter. Let (i,r) be the (i,r)th element of the drug potential factor matrix G. Let (j,r) be the (j,r)th element of the microbial potential factor matrix H. Let be the (k,r)th element of the potential factor matrix W for disease substances. For correlation tensors The (i,j,k)th element;

[0049] Associated tensors The joint likelihood probability is combined with the multivariate Gaussian distribution to obtain the formula for the joint probability model: , Let the a priori expectation set represent the projected mappings of drugs, microorganisms, and diseases. For parameters and correlation tensor The joint likelihood function, For correlation tensors The likelihood function, For parameters The likelihood function;

[0050] Through optimization of log-likelihood, the parameters of the joint probability model are... Prior expectation set The adaptive evaluation is performed using the following formula: , These are the optimal hyperparameters of the model. This is the set of optimal projection mappings for the model. For correlation tensors The likelihood function, The derivative of the matrix with respect to all latent factors;

[0051] The posterior probability distribution of the latent factor matrix set is inferred. , Let be the joint likelihood function of parameters and variables based on optimal hyperparameters and projections. It is the likelihood function based on the optimal hyperparameters and projection.

[0052] In this embodiment, a probabilistic graphical model is established based on the constructed hybrid graph structure and association tensor. Key technologies include: using hybrid graph deep learning (GCN and HGCN) to extract nonlinear features as the prior expectation of the latent factor matrix, and using logistic tensor decomposition to model the association probability. That is, this stage uses deep learning to extract nonlinear features to provide an informative prior for the subsequent Bayesian model, rather than directly outputting prediction results.

[0053] Specifically, a priori method for generating latent factor matrices using deep learning mapping is introduced. First, graph convolutional network (GCN) features are extracted from drug molecule graphs, microbial weighted graphs, and disease weighted graphs. Hypergraph convolutional network (HGCN / HGNN) features are extracted from the DMD hypergraph construction. GCN captures the internal structural features of single-class entities, while HGCN captures global high-order interaction features across entities. The combination of the two achieves complementarity between local and global information.

[0054] For each entity (e.g., drug, microorganism, disease), the feature sequences from GCN and HGCN are fused, and a corresponding learnable attention factor is introduced. After Softmax normalization, the final fused feature (i.e., prior expectation) is calculated. Since different data sources (e.g., graph structures, hypergraph structures) contribute differently to the prediction task and contain different levels of noise, this step uses an attention mechanism to adaptively select key features and suppress noise.

[0055] It should be noted that in this embodiment, a Graph Convolutional Network (GCN) is used to process binary graphs (drug molecule graph, similarity graph), and a HyperGraph Convolutional Network (HGCN) is used to process ternary hypergraphs. In other feasible embodiments, Graph Attention Networks (GAT / HyperGAT) can be used, where Graph Attention Networks (GAT) can replace GCN, and HyperGraph Attention Networks (HyperGAT) can replace HGCN. During feature propagation, instead of using a fixed normalized Laplacian matrix to aggregate neighbor information, features are dynamically weighted and aggregated by calculating the attention coefficients between nodes and their neighbors. This approach can still extract nonlinear structural features of drugs, microorganisms, and diseases, and can further distinguish the importance of different neighbor nodes.

[0056] In addition, GraphSAGE or GIN can be used. Specifically, GraphSAGE (GraphSampleandAggregate) or Graph Isomorphic Network (GIN) can be used instead of GCN. GraphSAGE generates node embeddings by sampling neighbors and using aggregation functions (such as Mean, LSTM, Pooling); GIN enhances the discriminative power of the graph through Multilayer Perceptron (MLP) and summation aggregation. Both achieve a nonlinear mapping from graph-structured data to low-dimensional dense vectors, serving as prior inputs to the Bayesian model.

[0057] This embodiment employs an attention mechanism to fuse multi-view features. In other feasible embodiments, GRU-like gating or simple concatenation followed by a fully connected layer can be used instead of attention fusion. The features output by the GCN and HGCN are concatenated and input into a multilayer perceptron (MLP) for dimensionality reduction and fusion. Alternatively, a learnable "gate" parameter can be set to control the information throughput of different feature streams. This also achieves the integration of multi-source heterogeneous features, generating a unique prior feature vector.

[0058] S3, execute E-step, and under the condition of fixed prior expectation, infer the posterior expectation and covariance matrix of the latent factor matrix by combining the correlation tensor;

[0059] Specifically, step S3 further includes: calculating the i-th row of the disease microbial latent factor matrix G based on variational inference and mean-field approximation. posterior expectation It satisfies a multivariate Gaussian distribution. , and covariance matrix , The product of Khatri–Rao, for Expectations for Expectations For Hadamard product, Let W be the posterior expectation of the disease latent factor matrix. Let H be the posterior expectation of the microbial latent factor matrix. for transpose multiplied by , for transpose multiplied by , for The i-th row, For tensor Mode-1 matrixing, , Let be the local variational parameter of the ijkth term;

[0060] Calculate the j-th row of the microbial latent factor matrix H posterior expectation It satisfies a multivariate Gaussian distribution. , and covariance matrix , for Expectations for transpose multiplied by , express The j-th row, Tensor mode-2 matrixing, Let G be the posterior expectation of the drug potential factor matrix;

[0061] Calculate the k-th row of the disease latent factor matrix W posterior expectation It satisfies a multivariate Gaussian distribution. , and covariance matrix , express The j-th row, Tensor Mode-3 matrixing;

[0062] The ijk-th local variational parameter satisfy , It is a generalized inner product symbol. For the desired label, Product of latent factors .

[0063] In this embodiment, to avoid tedious hyperparameter tuning and handling complex posterior distributions, a variational inference framework is used to alternately infer the posterior distribution of the latent factor matrix and update the deep learning network parameters. Specifically, features extracted by deep learning are integrated into a Bayesian framework, and model parameters are solved using an iterative algorithm. Firstly, performing Bayesian inference using the above formula is challenging because of the marginal likelihood... Calculating the marginal values ​​of all latent variables is extremely difficult. To address the problem of Bayesian inference while ensuring the efficiency of model solution, a variational expectation-maximization algorithm is used for approximate Bayesian inference. To apply Bayesian approximation, firstly... Defined as posterior The approximate distribution is given. At this point, the logarithm of the marginal likelihood is: Among them, Jason's inequality is used to obtain evidencelowerbound(ELBO). This is true if and only if... Accurate equals This inequality holds when the variational posterior q is given by the model parameters. and mixed image projection (i.e., the prior expectation set) is used to iteratively maximize the ELBO, instead of maximizing the marginal likelihood logarithm, as shown in the formula: Using terminology from the EM algorithm, maximizing ELBO with respect to q is called the E-step, and ELBO with respect to... and Maximizing this is called the M-step.

[0064] Specifically, the E-step involves inferring the posterior distribution of latent variables using priors and updating the approximate posterior of these variables. Since the sigmoid function of the logistic model makes integration difficult, local variational parameters are introduced to construct a lower bound approximation (Jaakkola & Jordanbound). That is, the posterior expectation of the latent variables is calculated analytically; due to the sigmoid form of the logistic function making integration difficult, local variational parameters are introduced to construct a lower bound. The approximate posterior of the latent variables (taking drugs as an example) follows a multivariate normal distribution, and its expectation and covariance are iteratively updated using analytical formulas. In the E-step, the goal is to find the optimal solution for the approximate posterior based on the current estimates of the model parameters and the prior expectation set. Based on the mean-field approximation, assuming that the posteriors of all latent variables are independent, a decomposition of the latent variable distribution can be obtained. This step, through variational approximation, transforms the complex non-conjugate Bayesian inference into an analytical Gaussian update, significantly improving computational efficiency.

[0065] S4, execute M-step. With the posterior expectation and covariance matrix fixed, use the Adam optimizer to update the joint probability model parameters and deep learning mapping, and alternately execute E-step and M-step until the optimal balance is reached. Obtain the optimal posterior distribution of all latent factor matrices, and extract the final posterior expectation of each latent factor matrix as the final joint probability model output.

[0066] Specifically, step S4 further includes: using the Adam optimizer to perform backpropagation to update the joint probability model parameters, wherein the variational approximate posterior is fixed. And based on the joint probability model parameters and prior expectation set Maximize ELBO (ELBO is preserved in this article) The relevant items are as follows) and the formula is: , , , ,in, As a lower bound for approximate evidence, For the posterior of q, Let r be the latent factor matrix. To perform trajectory calculations, For G, H, W and a quadratic function, It is a quadratic function The exponent power, For local variational parameters, For local variational parameters, is a constant (where is a likelihood function, which needs to be differentiated with respect to the parameter later; the constant derivative is 0 because this term is a parameter, so it is not necessary to write out the constant expression or magnitude, and it does not affect the subsequent differentiation).

[0067] Fixed prior expectation set ,Will about Taking the derivative and setting it to zero, we get... ,(because (Non-negative) and maximize The prior expectation set is obtained. Objective function: , , , For matrix Elements on the diagonal For matrix Elements on the diagonal For matrix Elements on the diagonal;

[0068] By combining the posterior expectation of the latent factor matrix of generation l with the objective function, the prior expectation of generation l+1 is obtained using the Adam optimizer.

[0069] The E-step and M-step processes are executed alternately until an optimal balance is reached, obtaining the optimal posterior distribution of all latent factor matrices, and then the final posterior expectation of each latent factor matrix is ​​extracted. , , This serves as the final output of the joint probability model.

[0070] In this embodiment, the deep learning network (prior generator) is updated by back-updating the latent variable posterior distribution, maximizing the lower bound of evidence (ELBO) to update the model parameters and the deep learning mapping F. By maximizing the lower bound of evidence (ELBO), the weight parameters of GCN and HGCN are updated using the Adam optimizer (learning rate set to 0.01), making the deep learning output F approximate the posterior expectation of the latent variable. Specifically, maximizing the lower bound of evidence (ELBO) updates the precision parameters and deep learning projection, and updates the deep learning mapping (i.e., training GCN / HGCN): the goal is to minimize the Euclidean distance between the deep learning output F and the posterior expectation of the latent variable. This step achieves bidirectional facilitation—tensor decomposition uses global information to correct the latent variable, and the corrected latent variable then serves as a label to guide the training of the deep learning network (F).

[0071] Subsequently, through alternating E-step and M-step iterations until ELBO converges, the "prior" provided by deep learning and the "posterior" obtained by Bayesian inference continuously correct each other until the optimal balance is reached, obtaining the optimal posterior distribution of all latent variables, and extracting the expected value of the posterior distribution of each latent variable as the final model output.

[0072] It should be noted that this embodiment employs a logical tensor decomposition based on CP decomposition (CANDECOMP / PARAFAC). In other feasible embodiments, Tucker decomposition can be used. Specifically, the Tucker decomposition model can replace the CP decomposition model, decomposing the correlated tensor into a core tensor. The product of the three factor matrices is the sum of the product of the two factors. Tucker decomposition is a generalization of CP decomposition, which has a stronger ability to express feature interactions. It can also introduce deep learning priors within the Bayesian framework for probabilistic prediction.

[0073] Furthermore, this embodiment employs the Variational Expectation-Maximization (VEM) algorithm to solve for the posterior distribution. In other feasible embodiments, Gibbs sampling based on Markov Chain Monte Carlo (MCMC) can be used instead of variational inference. Instead of explicitly optimizing the lower bound of evidence (ELBO), it performs cyclic sampling based on the conditional posterior distribution of the latent variables, estimating the expectation and variance of the latent variables through a large number of sample statistics. This still achieves parameter estimation of the Bayesian model and, theoretically, can converge to the accurate posterior distribution (although the computation speed may be slower). A simplified Bayesian inference process can also be used, employing Maximum A posteriori estimation (MAP) combined with stochastic gradient descent (SGD / Adam). Instead of calculating the complete posterior distribution (i.e., ignoring variance / uncertainty), it directly maximizes the logarithm of the posterior probability and uses automatic differentiation tools to directly update the latent variables and deep network parameters. Although it sacrifices some uncertainty modeling capabilities, it can still use deep priors to complete association prediction, and the implementation is simpler.

[0074] S5. Calculate the predicted association probability (range 0-1) for any drug-microbe-disease triple based on the final posterior expected value, and then sort the predicted association probabilities in descending order to generate a recommendation list.

[0075] Specifically, step S5 further includes: the formula for calculating the predicted association probability is: .

[0076] In this embodiment, the posterior expectation of the latent variables obtained after the convergence of variational inference in step S4 is extracted, the predicted association probability of any triple is calculated, and the predicted probabilities of all unknown associations are sorted in descending order to generate a recommendation list. Through the above steps, this invention cleverly combines the nonlinear feature extraction capability of graph deep learning with the global modeling capability of Bayesian tensor decomposition. This design not only avoids the negative sampling operation in traditional deep learning (because the Bayesian model utilizes all observed and unobserved data), but also endows tensor decomposition with the ability to handle complex molecular structures and nonlinear relationships.

[0077] Specifically, in this embodiment, to further illustrate the beneficial effects of this method, its effectiveness is verified through comparative experiments and case studies on DataI and DataII. First, 5-fold cross-validation is employed, setting up four experimental scenarios: CV... triplet : Evaluate the predictive power for unknown triples. CV drug / CV micro / CV dis The model's predictive capabilities for new drugs, new microorganisms, and new diseases (i.e., cold-start scenarios) were evaluated. Evaluation metrics were: for imbalanced datasets, AUPR (Area Under the Precision-Recall Curve), AUC, and F1 scores were used; for new entity prediction, HitRatio (HR@N) and NDCG@N were used.

[0078] To demonstrate the advancement of this invention, the following state-of-the-art methods were selected for comparison: TDRC: Tensor decomposition with relational constraints; WeightTDAIGN: CP decomposition with positive sample weighting and graph regularization; SPLDHyperAWNTF: Non-negative tensor decomposition combining self-organizing learning and hypergraph regularization; KBLTDARD: Kernel Bayesian logic tensor decomposition with automatic rank determination; MCHNN: Hypergraph Neural Network with Multi-View Adversarial Learning.

[0079] The experimental results are analyzed as follows: (1) CV triplet Performance comparison in different scenarios: For DataI and DataII, this invention tested different ratios of positive and negative samples. Performance at lower levels, with a focus on extreme imbalance ( In the case where negative examples are 100 times more than positive examples, the results show that on extremely imbalanced datasets, the AUPR value of this invention reaches 0.9408 on DataI, which is much higher than MCHNN (0.6647) and other tensor decomposition methods. This indicates that this invention avoids negative sampling by using Bayesian full tensor modeling, which significantly improves robustness under sparse data. (2) Performance comparison in the scenario of new entity prediction (cold start): In DataI CV drugIn the scenario of predicting new drug associations, the performance advantage of this invention is also significant: HR@10: This invention achieves 0.7382, a 3.61% improvement over the second-ranked KBLTDARD. NDCG@10: This invention achieves 0.6666, a 4.84% improvement over the second-ranked KBLTDARD. This demonstrates that this invention, by utilizing hybrid graph deep learning to extract molecular structural features as priors, can effectively solve the cold-start prediction problem for new drugs.

[0080] Furthermore, to verify the biological significance of the prediction results, this invention was used to predict potential drugs for the microbe-disease pair "(Firmicutes, Breast Neoplasms)". The prediction results showed that 9 out of the top 10 drugs were supported by literature. The top-ranked drug was Cyclophosphamide, with a prediction score as high as 0.97. Previous studies have shown that the anticancer effect of this drug is closely related to gut microbiota (such as Firmicutes), further confirming the reliability of the prediction results of this invention.

[0081] In summary, this invention provides a high-order interaction prediction method with hybrid graph deep learning (BLTDMGDL) for predicting high-order associations between drugs, microorganisms, and diseases. By introducing hybrid graph deep learning to mine nonlinear features and utilizing a Bayesian framework to avoid negative sampling noise, this invention demonstrates superior performance compared to state-of-the-art methods on balanced and extremely imbalanced datasets, as well as on novel entity prediction tasks, and has extremely high application value. Specifically, its core technical principle is as follows: First, a hybrid graph structure is constructed based on the natural attributes of multi-source data, including a drug molecule graph, a microorganism / disease weighted graph, and a drug-microorganism-disease hypergraph. A hybrid graph deep learning model (combining Graph Convolutional Network (GCN) and Hypergraph Neural Network (HGCN)) is used to mine nonlinear features of single entities and high-order interactions, and an attention mechanism is used to achieve adaptive fusion of multi-source features. Then, the fused deep nonlinear features are mapped to the prior expectations of latent variables in a Bayesian logistic tensor decomposition model, constructing a probabilistic graphical model. Finally, a Variational Expectation Maximization (VEM) algorithm is developed to perform joint adaptive inference of model parameters, latent variables, and nonlinear projections, thereby accurately predicting the probability of potential ternary associations between drugs, microorganisms, and diseases using full tensor information without the need for negative sampling. Aiming to overcome the limitation of existing tensor decomposition models that can only perform linear feature fusion, this study mines nonlinear structural features of multi-source data through hybrid graph deep learning; it addresses the false negative noise problem caused by negative sampling in existing deep learning methods by introducing prior expectations using a Bayesian probabilistic graphical model to cover the entire sample space without negative sampling; and it solves the problem of difficult model parameter tuning by achieving adaptive parameter inference through a variational expectation maximization algorithm, thereby improving the accuracy and generalization ability of predicting higher-order associations between drugs, microorganisms, and diseases.

[0082] Compared with existing technologies, this invention has the following advantages: 1. Eliminating false negative noise introduced by "negative sampling" and significantly improving prediction robustness under sparse data: A joint likelihood probability model based on full tensors is established, and variational inference is used to globally update all latent variables (regardless of whether they are observed or not); by using the above full tensor modeling steps, this invention completely abandons the negative sampling operation, fundamentally solving the problem of false negative noise introduced by mislabeling "undiscovered true associations" as negative samples. Experimental data shows that in a scenario with an extremely unbalanced ratio of positive to negative samples (1:100), the AUPR value of this scheme (0.9408) is much higher than that of the MCHNN model that relies on negative sampling (0.6647), demonstrating its superior robustness on extremely sparse biological data. 2. Overcoming the limitations of linear models and deeply mining the nonlinear features of multi-source data: A drug molecule graph and DMD hypergraph that retain the original topological information are constructed. Nonlinear features are extracted using GCN and HGCN networks and injected into the Bayesian model as prior expectations. Utilizing the above hybrid graph learning steps, this invention can capture the complex chemical structural features within drug molecules and the high-order nonlinear interactions between biological entities, solving the problem of insufficient feature representation capabilities of traditional linear models. This directly improves the model's accuracy in complex prediction tasks (e.g., Top-1 accuracy is improved by approximately 3%). 3. Achieving adaptive fusion of multi-source heterogeneous information and avoiding information bias from a single view: In the process of generating latent variable priors, instead of simply concatenating the outputs of GCN and HGCN, a learnable attention mechanism is introduced to weight the features of different views. This step automatically assigns weights based on the contribution of different data sources (e.g., drug structure view vs. disease semantic view) to the prediction task. This effectively filters noise from low-quality data sources and avoids information bias caused by simple fusion, thereby generating a higher-quality latent variable prior distribution. 4. Solving the "cold start" prediction problem and achieving effective screening of new drugs / microorganisms: Even for "new drugs" without any records in the historical interaction tensor, a molecular graph can still be constructed based on their SMILES strings. The deep network can still generate effective prior features based on this, and then calculate the association probability. By utilizing this attribute learning step, this invention solves the defect of traditional collaborative filtering methods that rely on historical interaction records and cannot predict new entities (cold start). Experiments show that in the new drug prediction scenario, the NDCG@10 index of this scheme is improved by 4.84% compared with the suboptimal method, which greatly expands the application scope of the model in drug relocation and early-stage new drug development. 5. Achieving adaptive hyperparameter inference and improving the model's generalization ability and solution efficiency: In the iteration process of the variational EM algorithm, the M-step updates the model accuracy parameters and deep network weights by maximizing the evidence lower bound (ELBO). Using this adaptive update step, this invention achieves automatic optimization of hyperparameters, avoiding the tedious and experience-dependent manual parameter tuning process in existing methods.This not only improves the convergence efficiency of the algorithm, but also ensures that the model can maintain stable high performance when facing datasets with different distributions (such as DataI and DataII), significantly enhancing its generalization ability.

[0083] Please see Figure 2 A second embodiment of the present invention provides a high-order interaction prediction device with hybrid graph deep learning, comprising:

[0084] The data extraction unit 101 is used to extract drug data, microbial data, disease data and auxiliary information from multiple preset databases, and to construct a hybrid graph structure and correlation tensor based on the extracted data;

[0085] The prior expectation calculation unit 102 is used to extract features from the hybrid graph structure using graph convolutional networks and hypergraph convolutional networks, introduce the corresponding attention factors and deep learning mappings, calculate the prior expectation and multivariate Gaussian distribution, and calculate the joint likelihood probability based on the correlation tensor. Combining the joint likelihood probability and multivariate Gaussian distribution, the joint probability model is obtained.

[0086] E-step unit 103 is used to perform E-step, which, with a fixed prior expectation, infers the posterior expectation and covariance matrix of the latent factor matrix by combining the correlation tensor.

[0087] M-step unit 104 is used to execute M-step. With the posterior expectation and covariance matrix fixed, it uses the Adam optimizer to update the joint probability model parameters and deep learning mapping, and alternately executes E-step and M-step until the optimal balance is reached. It obtains the optimal posterior distribution of all latent factor matrices and extracts the final posterior expectation of each latent factor matrix as the final joint probability model output.

[0088] The prediction unit 105 is used to calculate the predicted association probability for any drug-microbe-disease triple based on the final posterior expected value, and to sort the predicted association probabilities in descending order to generate a recommendation list.

[0089] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications are also considered to be within the scope of protection of the present invention.

Claims

1. A high-order interaction prediction method with hybrid graph deep learning, characterized in that, include: Drug data, microbial data, disease data, and auxiliary information are extracted from multiple pre-defined databases, and a hybrid graph structure and correlation tensor are constructed based on the extracted data; We employ graph convolutional networks and hypergraph convolutional networks to extract features from hybrid graph structures, introduce corresponding attention factors and deep learning mappings, calculate prior expectations and multivariate Gaussian distributions, and calculate joint likelihood probabilities based on correlation tensors. By combining the joint likelihood probabilities with the multivariate Gaussian distribution, we obtain a joint probability model. Perform the E-step, and with the prior expectation fixed, infer the posterior expectation and covariance matrix of the latent factor matrix by combining the correlation tensor; The M-step is executed. With the posterior expectation and covariance matrix fixed, the Adam optimizer is used to update the joint probability model parameters and deep learning mapping. The E-step and M-step are executed alternately until the optimal balance is reached, the optimal posterior distribution of all latent factor matrices is obtained, and the final posterior expectation of each latent factor matrix is ​​extracted as the final joint probability model output. The predicted association probability is calculated for any drug-microbe-disease triple based on the final posterior expected value. The predicted association probabilities are then sorted in descending order to generate a recommendation list. Drug data, microbial data, disease data, and auxiliary information are extracted from multiple pre-defined databases. A hybrid graph structure and correlation tensor are then constructed based on the extracted data, specifically: Extract drug data, microbial data, disease data, and auxiliary information from multiple pre-set databases; The SMILES string in the drug data is transformed to construct the drug molecule map. ,in, Let R be the atomic attribute matrix, where R is the feature dimension and n is the number of atoms. Let A be the atomic attribute dimension and A be the adjacency matrix. Microbial weighted graphs were constructed based on microbial and disease data, respectively. Disease-weighted graph ,in, As the apex of microorganisms, For the edge of microorganisms, Let be the weight corresponding to the edge representing the microorganism. At the peak of the disease, For the edge of disease, The weights corresponding to the edges of the disease; A DMD hypermap is constructed based on drug data, microbial data, disease data, and auxiliary information. , This is a vertex set containing all drug data, microbial data, and disease data. It is a super-edge set; A hybrid graph structure was constructed based on the drug molecule graph, microbial weighted graph, disease weighted graph, and DMD hypergraph, and a hypergraph association matrix was defined. Wherein, when the v-th vertex is in the e-th hyperedge, the corresponding hypergraph incidence matrix is... When the v-th vertex is not in the e-th hyperedge, the corresponding hypergraph incidence matrix is... , , ; Establish the drug-microbe-disease association tensor Where I represents the number of drugs, J represents the number of microorganisms, and K represents the number of diseases.

2. The high-order interaction prediction method with hybrid graph deep learning according to claim 1, characterized in that, Feature extraction of the hybrid graph structure is performed using graph convolutional networks and hypergraph convolutional networks. Corresponding attention factors and deep learning mappings are introduced, prior expectations and multivariate Gaussian distributions are calculated, and joint likelihood probabilities are calculated based on the association tensor. Combining the joint likelihood probabilities with the multivariate Gaussian distribution, a joint probability model is obtained, specifically: For the microbial weighted graph and the disease weighted graph, a multi-layer GCN propagation method is used to obtain propagation characteristics. The formula for calculating the propagation characteristics of the (t+1)th layer is as follows: , For degree matrix, Let be the learnable parameter matrix of the t-th layer. For the propagation characteristics of layer t, It is a non-linear activation function. A phylogenetic similarity matrix for microorganisms; A graph convolutional network is applied to the drug molecule graph, and global max pooling is used to aggregate atomic-level features into a drug-level feature vector. This feature vector and propagation features are then combined to obtain GCN features. Applying a hypergraph convolutional network to the DMD hypergraph, performing vertex-hyperedge-vertex information propagation, and extracting hypergraph convolutional network features, wherein the propagation rule is as follows: , Let be the degree matrix of the vertices. Let be the degree matrix of the hyperedge. Let T be the hyperedge weight matrix, and T be the transpose. For the drug characteristics of layer t+1, For the characteristics of the drug in layer t, The projection matrix; The drug features in the GCN feature set are fused with the drug features in the hypergraph convolutional network feature set to obtain the drug set. And introduce learnable drug attention factors. The prior expectation of the drug is obtained by normalization calculation using the Softmax function. , , As a learnable drug attention factor, The number of drug characteristics, It is an exponential function; Microbial features from GCN features are fused with microbial features from hypergraph convolutional network features to obtain a microbial set. Introducing learnable microbial attention factors To obtain the prior expectations of microorganisms , , The number of microbial characteristics, A learnable microbial attention factor; The disease features in the GCN feature set are fused with the disease features in the hypergraph convolutional network feature set to obtain the disease set. Introducing learnable disease attention factors To obtain the prior expectation of the disease , , The number of disease characteristics, It is a learnable disease attention factor.

3. The high-order interaction prediction method with hybrid graph deep learning according to claim 2, characterized in that, Also includes: set up , , These are drug latent factor matrices, microbial latent factor matrices, and disease latent factor matrices, using... Represents the set of latent factor matrices; By introducing a deep learning mapping F, and based on the prior expectations of drugs, microorganisms, and diseases, the multivariate Gaussian distribution of the drug latent factor matrix G is calculated. , It is a diagonal matrix. For the a priori expectation of the drug The i-th row, For the i-th row of the drug potential factor matrix G, It follows a normal distribution. These are the parameters of the joint probability model; Calculate the multivariate Gaussian distribution of the microbial latent factor matrix H , For microbial prior expectations The j-th row, This represents the j-th row of the microbial potential factor matrix H; Calculate the multivariate Gaussian distribution of the disease latent factor matrix W. , a priori expectations for disease The kth row, This represents the k-th row of the disease potential factor matrix W; Based on correlation tensor Calculate the correlation tensor joint likelihood probability , , c is the importance level parameter. Let (i,r) be the (i,r)th element of the drug potential factor matrix G. Let (j,r) be the (j,r)th element of the microbial potential factor matrix H. Let be the (k,r)th element of the potential factor matrix W for disease substances. For correlation tensors The (i,j,k)th element; Associated tensors The joint likelihood probability is combined with the multivariate Gaussian distribution to obtain the formula for the joint probability model: , For the a priori expectation set, For parameters and correlation tensor The joint likelihood function, For correlation tensors The likelihood function, For parameters The likelihood function; By optimizing the log-likelihood, the parameters of the joint probability model are... Prior expectation set The adaptive evaluation is performed using the following formula: , These are the optimal hyperparameters of the model. This is the set of optimal projection mappings for the model. For correlation tensors The likelihood function, For the derivative of all latent factor matrices; The posterior probability distribution of the latent factor matrix set is inferred. , Let be the joint likelihood function of parameters and variables based on optimal hyperparameters and projections. It is the likelihood function based on the optimal hyperparameters and projection.

4. The high-order interaction prediction method with hybrid graph deep learning according to claim 3, characterized in that, Performing the E-step, with a fixed prior expectation, infers the posterior expectation and covariance matrix of the latent factor matrix by combining the correlation tensor, specifically as follows: Based on variational inference and mean-field approximation, the i-th row of the drug latent factor matrix G is calculated. posterior expectation It satisfies a multivariate Gaussian distribution. , and covariance matrix , The product of Khatri–Rao, for Expectations for Expectations For Hadamard product, Let W be the posterior expectation of the disease latent factor matrix. Let H be the posterior expectation of the microbial latent factor matrix. for transpose multiplied by , for transpose multiplied by , for The i-th row, For tensor Mode-1 matrixing, , Let be the local variational parameter of the ijkth term; Calculate the j-th row of the microbial latent factor matrix H posterior expectation It satisfies a multivariate Gaussian distribution. , and covariance matrix , for Expectations for transpose multiplied by , express The j-th row, Tensor mode-2 matrixing, Let G be the posterior expectation of the drug potential factor matrix; Calculate the k-th row of the disease latent factor matrix W posterior expectation It satisfies a multivariate Gaussian distribution. , and covariance matrix , express The j-th row, Tensor Mode-3 matrixing; The ijk-th local variational parameter satisfy , It is a generalized inner product symbol. For the desired label, Product of latent factors .

5. The high-order interaction prediction method with hybrid graph deep learning according to claim 4, characterized in that, The M-step process is executed. With the posterior expectation and covariance matrix fixed, the Adam optimizer is used to update the joint probability model parameters and deep learning mapping. The E-step and M-step processes are then executed alternately until an optimal balance is reached, obtaining the optimal posterior distribution of all latent factor matrices. The final posterior expectation of each latent factor matrix is ​​then extracted as the final joint probability model output. Specifically: The Adam optimizer is used for backpropagation to update the joint probability model parameters, where the variational approximate posterior is fixed. And based on the joint probability model parameters and prior expectation set To maximize ELBO, the formula is: , , , ,in, As a lower bound for approximate evidence, For the posterior of q, Let r be the latent factor matrix. To perform trajectory calculations, For G, H, W and a quadratic function, It is a quadratic function The exponent power, For local variational parameters, It is a constant; Fixed prior expectation set ,Will about Taking the derivative and setting it to zero, we get... and maximize The prior expectation set is obtained. Objective function: , , , For matrix Elements on the diagonal For matrix Elements on the diagonal For matrix Elements on the diagonal; By combining the posterior expectation of the latent factor matrix of generation l with the objective function, the prior expectation of generation l+1 is obtained using the Adam optimizer. The E-step and M-step processes are executed alternately until an optimal balance is reached, obtaining the optimal posterior distribution of all latent factor matrices, and then the final posterior expectation of each latent factor matrix is ​​extracted. , , This serves as the final output of the joint probability model.

6. The high-order interaction prediction method with hybrid graph deep learning according to claim 5, characterized in that, The formula for calculating the predicted association probability is as follows: .

7. A high-order interactive prediction device with hybrid graph deep learning, characterized in that, include: The data extraction unit is used to extract drug data, microbial data, disease data, and auxiliary information from multiple preset databases, and to construct a hybrid graph structure and correlation tensor based on the extracted data; The prior expectation calculation unit is used to extract features from the hybrid graph structure using graph convolutional networks and hypergraph convolutional networks, introduce the corresponding attention factors and deep learning mappings, calculate the prior expectation and multivariate Gaussian distribution, and calculate the joint likelihood probability based on the correlation tensor. Combining the joint likelihood probability and multivariate Gaussian distribution, the joint probability model is obtained. The E-step unit is used to perform the E-step, which, with a fixed prior expectation, infers the posterior expectation and covariance matrix of the latent factor matrix by combining the correlation tensor. The M-step unit is used to execute the M-step. With the posterior expectation and covariance matrix fixed, the Adam optimizer is used to update the joint probability model parameters and deep learning mapping, and the E-step and M-step are executed alternately until the optimal balance is reached. The optimal posterior distribution of all latent factor matrices is obtained, and the final posterior expectation of each latent factor matrix is ​​extracted as the final joint probability model output. The prediction unit is used to calculate the predicted association probability for any drug-microbe-disease triple based on the final posterior expected value, and then sort the predicted association probabilities in descending order to generate a recommendation list. Drug data, microbial data, disease data, and auxiliary information are extracted from multiple pre-defined databases. A hybrid graph structure and correlation tensor are then constructed based on the extracted data, specifically: Extract drug data, microbial data, disease data, and auxiliary information from multiple pre-set databases; The SMILES string in the drug data is transformed to construct the drug molecule map. ,in, Let R be the atomic attribute matrix, where R is the feature dimension and n is the number of atoms. Let A be the atomic attribute dimension and A be the adjacency matrix. Microbial weighted graphs were constructed based on microbial and disease data, respectively. Disease-weighted graph ,in, As the apex of microorganisms, For the edge of microorganisms, Let be the weight corresponding to the edge representing the microorganism. At the peak of the disease, For the edge of disease, The weights corresponding to the edges of the disease; A DMD hypermap is constructed based on drug data, microbial data, disease data, and auxiliary information. , This is a vertex set containing all drug data, microbial data, and disease data. It is a super-edge set; A hybrid graph structure was constructed based on the drug molecule graph, microbial weighted graph, disease weighted graph, and DMD hypergraph, and a hypergraph association matrix was defined. Wherein, when the v-th vertex is in the e-th hyperedge, the corresponding hypergraph incidence matrix is... When the v-th vertex is not in the e-th hyperedge, the corresponding hypergraph incidence matrix is... , , ; Establish the drug-microbe-disease association tensor Where I represents the number of drugs, J represents the number of microorganisms, and K represents the number of diseases.

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