A drug-disease association prediction method based on curvature optimization association

Abstract

The application discloses to the technical field of drug development, specifically a drug disease correlation prediction method based on curvature optimization correlation, comprising the following specific steps: obtaining a drug-disease correlation heterogeneous graph A, a drug similarity matrix DR and a disease similarity matrix DS; designing a curvature optimization correlation modification module, optimizing the drug-disease correlation heterogeneous graph A to obtain a drug-disease correlation heterogeneous graph M * ; using a GCN to perform feature extraction on the drug-disease correlation heterogeneous graph M * , obtaining a first feature matrix F1; designing a similarity perception hyperbolic graph neural network model to perform feature extraction on the matrix F1, obtaining a second feature matrix F2. The correlation modification module based on curvature optimization can optimize the drug-disease correlation graph, the optimized drug-disease correlation graph can effectively alleviate the over-compression problem in the GCN process, and the accuracy of feature representation is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of drug development, and particularly to a drug-disease association prediction method based on curvature optimization association. BACKGROUND

[0002] Traditional drug discovery is a time-consuming and labor-intensive process, usually taking more than a decade and costing between 500 million and 2 billion US dollars from drug discovery to clinical application. With the rapid development of artificial intelligence technology, drug repositioning (DR) as an alternative solution has received extensive attention. Drug repositioning has significant advantages in accelerating drug discovery and reducing duplication of work, which can greatly shorten the drug development time and reduce the waste of funds. Drug repositioning, also known as drug repurposing, refers to finding new uses for existing drugs, especially for the treatment of new diseases or symptoms. This approach is of great significance in the field of drug development, and its main way is to predict potential drug-disease associations.

[0003] Many researchers predict potential drug-disease associations through computational methods at a more efficient and economical cost. DR research based on computational methods has made significant progress and can identify new drug-disease associations (DDAs). These methods usually include the following two steps, first, extracting relevant features from biochemical and medical data related to drugs and diseases; then, putting these features into a trained model to facilitate DDA prediction. This type of method is mainly divided into two categories: machine learning (ML) based methods and deep learning (DL) based methods.

[0004] ML-based methods can extract features through various algorithms such as matrix decomposition, multi-kernel learning, support vector machines, and neural networks, and use these extracted embedding features to predict new DDAs. However, ML-based methods rely on shallow features and have limited ability to represent higher-level features. In order to overcome this limitation, DL-based methods (such as graph neural networks (GNN), hyperbolic graph neural networks, and recurrent neural networks) have been developed to use their powerful representation learning to obtain potential features of drugs and diseases.

[0005] However, in current research, the common way for DL-based methods to extract drug-disease related features is to construct a drug-disease association heterogeneous network from biomedical related data sources, and then use GNN or hyperbolic graph neural network to extract features from the network. However, GNN has the problem of over-compression, which affects the ability of message passing between graph nodes. Since GNN can only pass one distance of message per layer, this limits its ability to capture long-range dependencies.

[0006] In hyperbolic graph neural networks, computing neighborhood weights is a crucial step as it determines how information is aggregated in hyperbolic space. Common ways to compute neighborhood weights include attention-based mechanisms, curvature-based weights, and distance-based weights. Distance-based weights refer to computing weights based on the hyperbolic distance between nodes in hyperbolic space, with closer nodes having larger weights. This can be achieved by taking the inverse of the hyperbolic distance or a function thereof. However, this approach ignores the impact of node similarity on the network.

[0007] In drug-disease association prediction, self-attention mechanisms are often used to extract features of drugs and diseases. Self-attention, also known as intra-attention, is a deep learning technique that enhances the model's ability to process sequential data. It allows the model to dynamically focus on information at different positions in the sequence, capturing dependencies within the sequence. Semantic values of diseases refer to the richness of information or the level of detail in the description related to a specific disease, which is important in drug-disease association prediction. Therefore, improving the attention of self-attention mechanisms to semantic values is of great significance.

[0008] Based on the above, the current method has the following disadvantages:

[0009] 1. For GNN, over-compression is a common problem that affects the ability of the graph to pass messages between nodes; since GNN can only pass messages 1 distance per layer, this limits the ability of GNN to capture long-range dependencies;

[0010] 2. For hyperbolic graph neural networks, computing neighborhood weights is a crucial step; however, existing methods often ignore the impact of node similarity on the network;

[0011] 3. Traditional self-attention mechanisms allow the model to dynamically focus on information at different positions in the sequence when processing sequential data, capturing dependencies within the sequence; however, for drug-disease association prediction, the semantic nature of diseases has a more significant contribution to the association score; therefore, it is necessary to optimize traditional self-attention mechanisms to better capture disease semantic information.

[0012] Based on this, the present application provides a drug-disease association prediction method based on curvature optimization association. SUMMARY

[0013] To solve the above technical problems, according to one aspect of the present application, the present application provides the following technical solutions:

[0014] A drug-disease association prediction method based on curvature optimization association includes the following specific steps:

[0015] S1, obtaining a drug-disease association heterogeneous graph A, a drug similarity matrix DR, and a disease similarity matrix DS:

[0016] S11: obtaining drug-disease association data from existing public databases, constructing a drug-disease association heterogeneous graph and representing it as a matrix where m and d represent the number of drugs and diseases, respectively;

[0017] S12: obtaining the chemical structure of a drug from an existing public database, constructing a drug similarity matrix

[0018] S13: obtaining disease phenotype information from an existing public database, measuring disease similarity based on disease phenotype similarity, and constructing a disease similarity matrix

[0019] S2, designing a curvature-optimized association modification module to optimize the drug-disease association heterogeneous graph A, obtaining a drug-disease association heterogeneous graph M * :

[0020] S21: designing a curvature-optimized association modification module to alleviate the problem of over-compression in GCN;

[0021] S22: the drug-disease association heterogeneous graph A is processed by the association modification module to obtain the optimized drug-disease association heterogeneous graph M * ;

[0022] S3, using GCN to perform feature extraction on the drug-disease association heterogeneous graph M * to obtain a first feature matrix F1;

[0023] S4, designing a similarity-aware hyperbolic graph neural network model to perform feature extraction on the matrix F1 to obtain a second feature matrix F2;

[0024] S5, designing a gated signal self-attention mechanism to perform feature extraction on the feature matrix F2 to obtain a third feature matrix F3;

[0025] S6, based on the feature matrix F3, selecting MLP as the decoder to output the association prediction score S.

[0026] As a preferred scheme of the drug-disease association prediction method based on curvature-optimized association, in the S11, the definition of A is as follows:

[0027]

[0028] As a preferred scheme of the drug-disease association prediction method based on curvature-optimized association, in the S12, the specific steps are as follows:

[0029] S121: After obtaining the chemical structure of the drug from the existing public database, the chemical structure of the drug is converted into the topological fingerprint of the molecule using the RDKit toolkit;

[0030] S122: Calculate the Tanimoto similarity coefficient of each pair of drugs;

[0031] The formula for calculating the Tanimoto similarity coefficient is:

[0032]

[0033] Where R A and R B represent the set of two molecular fingerprints, and the calculated Tanimoto similarity coefficient of each pair of drugs is stored in the matrix DR, and the final DR matrix is the drug similarity matrix.

[0034] As a preferred scheme of the drug-disease association prediction method based on curvature optimization association according to the application, wherein the specific steps of S13 are as follows:

[0035] S131: Obtain disease phenotype information from existing public databases, and structure the disease phenotype information using human phenotype ontology, which provides the hierarchical relationship between diseases and phenotypes;

[0036] S132: Based on human phenotype ontology, the similarity between two diseases can be calculated, for this purpose, the specificity of the phenotype term can be measured using the information content method, and then the similarity between diseases is calculated, the specific formula is as follows:

[0037]

[0038] Where d i and d j represent diseases, T(d i ) and T(d j ) represent the set of phenotype terms of diseases d i and d j in human phenotype ontology, t represents the phenotype term, and IC(t) represents the information content of the phenotype term t. Store the phenotype similarity values of all disease pairs in the matrix DS, and the element DS(i,j) in the matrix represents the similarity between diseases d i and d j .

[0039] As a preferred scheme of the drug-disease association prediction method based on curvature optimization association according to the application, wherein the execution steps of the association modification module in S2 are as follows:

[0040] S211: Construct a new correlation heterogeneous network M using DS, DR and drug-disease correlation heterogeneous graph A, that is:

[0041]

[0042] S212: Calculate the Ollivier-Ricci curvature of all links in the entire drug-disease correlation heterogeneous graph M, find the n a edges with the smallest Ollivier-Ricci curvature value, and add virtual similarity links to these edges to alleviate the negative curvature problem, at the same time, find the n r edges with the largest Ollivier-Ricci curvature value, and remove them to reduce the positive curvature in the network, finally retain the edges connecting the drug nodes and disease nodes to obtain the optimized drug-disease correlation graph M * :

[0043]

[0044] Where A * is the matrix obtained by removing high-curvature edges and adding virtual similarity links to the drug-disease correlation heterogeneous graph A, A *T is the transpose matrix of A * .

[0045] As a preferred scheme of the drug-disease correlation prediction method based on curvature optimization correlation provided by the application, the specific steps of S3 are as follows:

[0046] Using GCN to perform feature extraction on the drug-disease correlation graph M * to obtain a feature matrix F1, and the definition formula is:

[0047]

[0048] Wherein, Wherein is an identity matrix, is a degree matrix of the drug-disease correlation graph, which is a diagonal matrix, represents taking the reciprocal of each diagonal element of the degree matrix and then taking the square root, represents the training parameter of the lth layer GCN, and LeakyReLU represents a nonlinear activation function, the input layer H (1) is M * , and L is the number of convolution layers.

[0049] As a preferred scheme of the drug-disease correlation prediction method based on curvature optimization correlation provided by the application, the specific steps of S4 are as follows:

[0050] S41: Using exponential mapping, map the Euclidean feature vector of each node in the drug-disease association feature matrix f1 to a hyperbolic space feature vector; for the drug-disease feature matrix F1, x represents a point in the hyperbolic space, Euclidean feature vector of node x, the mapping formula is as follows:

[0051]

[0052] wherein, represents the feature vector mapped to the hyperbolic space, represents the exponential mapping starting from x; c is the curvature of the hyperbolic space, and x represents a point in the hyperbolic space as the starting point of the exponential mapping; represents the Möbius addition in the Poincaré ball model, which is a distance measure in hyperbolic space; tanh represents the hyperbolic tangent function, which is used to map real numbers to the interval (-1, 1); is the absolute value of the square root of the curvature c, used to adjust the scale of the mapping; is a scale factor related to point x, which depends on the curvature c and the position of point x in the hyperbolic space; represents the Euclidean norm of the feature vector , indicating the length of the feature vector; represents the normalization operation, which normalizes the feature vector and adjusts it according to the curvature c, which maps the drug-disease association feature vector in Euclidean space to the feature vector in hyperbolic space;

[0053] S42: Calculate similarity-aware neighborhood weight α ij to make the hyperbolic graph neural network robust to feature aggregation of drug-disease features, α ij The calculation formula is as follows:

[0054]

[0055] wherein d i is the degree of node i;

[0056] S43: Feature aggregation of drug-disease features to obtain final output feature representation After calculating the neighborhood weight, the drug-disease features can be aggregated, and in the hyperbolic space, the feature aggregation can be realized in the following way:

[0057]

[0058] wherein L represents the number of layers, and l starts from 1, is the feature representation of node i at the l-th layer, is the neighbor set of node i, is the Möbius addition in hyperbolic space, is the aggregation operation on neighbor features, and ij is the weight between nodes i and j, and is the element-wise multiplication, and the final output feature representation is

[0059] S44: applying a nonlinear activation function to the feature Introducing a nonlinear characteristic; introducing the hyperbolic tangent function tanh as a nonlinear activation function to introduce a nonlinear characteristic, thereby enhancing the expression ability of the model, and the definition formula is:

[0060]

[0061] wherein, is the representation after the nonlinear function;

[0062] S45: using a logarithmic mapping to map the feature vector of the drug disease in the hyperbolic space back to the feature vector in the Euclidean space:

[0063]

[0064] wherein, represents the logarithmic mapping with q as the starting point; q is a point in the hyperbolic space, and the origin, i.e. the zero vector, is generally selected as the reference point of the logarithmic mapping; is another point in the hyperbolic space, and the goal is to find the tangent vector from q to ; c is the curvature of the hyperbolic space; is a scale factor depending on the curvature c and the position of the point q, and is specifically represents the Möbius addition in the Poincaré ball model; tanh -1 is the inverse function of the hyperbolic tangent function, i.e. the hyperbolic arctangent function; ||·||2 represents the Euclidean norm, and the geometric meaning of the formula is that given two points q and logarithmic mapping calculates the tangent vector at q of the geodesic from q to ; the tangent vector can be regarded as the Euclidean representation of the "direction" and "distance" between q and , and the feature matrix representation mapped back to the Euclidean space is

[0065] As a preferred scheme of the drug-disease association prediction method based on curvature optimization association according to the present application, wherein: the specific steps of S5 are as follows:

[0066] S51: A gating mechanism is introduced, so that the self-attention mechanism can pay more attention to those drug-disease features that are more important for the current drug repositioning task when processing drug-disease information, thereby improving the performance and generalization ability of the model, and the formula is defined as:

[0067] Q=F2W Q #(9)

[0068] K=F2W K #(10)

[0069] V=F2W V #(11)

[0070] wherein, and are learnable weight matrices;

[0071] S52: A gating signal needs to be calculated, which will be used to adjust the contribution of the value matrix V, the gating signal can be calculated by the dot product of the query matrix Q and the key matrix K, and then generated through a learnable weight matrix and a nonlinear activation function sigmoid;

[0072] GateSignal=sigmoid(QK T W G )#(12)

[0073] S53: Apply the gating signal to the value matrix V, which can be achieved by multiplying the gating signal with the value matrix V, thereby controlling the weight of each value vector in the final output;

[0074] GatedValues=GateSignal×V#(13)

[0075]

[0076] wherein d k is the dimension of the vector K, the Softmax function performs normalization operation, σ represents ReLU operation, and GateSignal represents the gating signal.

[0077] As a preferred scheme of the drug-disease association prediction method based on curvature optimization association provided by the application, wherein the specific steps of S6 are as follows:

[0078] based on the feature matrix F3, wherein Z i,j represents the drug i and disease j association feature in the feature matrix F3, S i,j is the drug m i and disease d jThe correlation score between the two is selected as the decoder, and a multi-layer linear perception (MLP) is selected as the decoder to predict the probability of each category:

[0079]

[0080] wherein and represent learnable parameters, and b r and b s are bias terms, and sigma is an optional activation function.

[0081] Compared with the prior art:

[0082] The correlation modification module based on curvature optimization can optimize the drug-disease correlation graph, and the optimized drug-disease correlation graph can effectively alleviate the problem of excessive compression in the GCN process, and improve the accuracy of feature representation; the similarity-aware hyperbolic graph neural network model not only considers whether the nodes are connected, but also considers the similarity degree of the features of the nodes themselves when extracting drug-disease features, so that the calculated neighborhood weight is more robust; the gating signal self-attention mechanism calculates a gating signal, which is used to adjust the contribution of the value matrix V, so that the gating signal self-attention mechanism can pay more attention to the more important features of the drug repositioning task when processing information, thereby improving the performance and generalization ability of the model. BRIEF DESCRIPTION OF DRAWINGS

[0083] Figure 1 The figure is a flowchart of the present application. DETAILED DESCRIPTION

[0084] To make the purpose, technical scheme and advantages of the present application clearer, the embodiments of the present application will be further described in detail below with reference to the drawings.

[0085] The present application provides a drug-disease correlation prediction method based on curvature optimization correlation, please refer to Figure 1 , including the following specific steps:

[0086] S1, obtaining a drug-disease correlation heterogeneous graph A, a drug similarity matrix DR and a disease similarity matrix DS:

[0087] S11: obtaining drug-disease correlation data from existing public databases, constructing a drug-disease correlation heterogeneous graph and representing it as a matrix wherein m and d represent the number of drugs and diseases respectively; wherein the definition of A in S11 is as follows:

[0088]

[0089] S12: obtaining the chemical structure of the drug from the existing public database, constructing the drug similarity matrix

[0090] The specific steps of S12 are as follows:

[0091] S121: After obtaining the chemical structure of the drug from the existing public database, the chemical structure of the drug is converted into the topological fingerprint of the molecule using the RDKit toolkit;

[0092] S122: Calculate the Tanimoto similarity coefficient of each pair of drugs;

[0093] The calculation formula of the Tanimoto similarity coefficient is:

[0094]

[0095] Wherein, R A and R B respectively represent the set of two molecular fingerprints, and the calculated Tanimoto similarity coefficient of each pair of drugs is stored in the matrix DR, and the final DR matrix is the drug similarity matrix

[0096] S13: Obtain disease phenotype information from the existing public database, measure disease similarity by disease phenotype similarity, and construct a disease similarity matrix

[0097] The specific steps of S13 are as follows:

[0098] S131: Obtain disease phenotype information from the existing public database, and structure the disease phenotype information using the human phenotype ontology, which provides the hierarchical relationship between diseases and phenotypes;

[0099] S132: Based on the human phenotype ontology, the phenotype similarity between two diseases can be calculated, for which the specificity of the phenotype term can be measured using the information content method, and then the similarity between diseases can be calculated, and the specific formula is as follows:

[0100]

[0101] Wherein, d i and d j represent diseases, T(d i ) and T(d j ) represent the set of phenotype terms of diseases d i and d j in the human phenotype ontology, t represents a phenotype term, and OC(t) represents the information content of the phenotype term t. Store the phenotype similarity values of all disease pairs in the matrix DS, and the element DS(i,j) in the matrix represents the similarity between diseases d i and d j ;

[0102] S1 includes but is not limited to the following embodiments:

[0103] 18,416 verified drug-disease associations obtained from the DrugBank database, drug-disease association is represented as drug-disease association heterogeneous graph A; the similarity of drug molecules is used to measure the similarity of drugs, drug fingerprint similarity is obtained from the DrugBank database based on RDKit and Tanimoto, and the drug fingerprint similarity matrix is represented as DR; disease similarity is measured by disease phenotype similarity, and disease similarity matrix is represented as DS, disease phenotype similarity is calculated by text mining analysis of biomedical information in OMIM database;

[0104] (1) RDKit can generate different types of fingerprints for molecules, which is crucial for comparing the similarity between molecules; fingerprint is a way to encode the chemical structure information of a molecule into binary or vector, which can be used for subsequent similarity calculation and search; Tanimoto coefficient is a measure method for measuring the similarity of two sets, which is commonly used in cheminformatics to calculate the similarity between two molecular fingerprints;

[0105] (2) DrugBank database and OMIM database are both publicly available databases;

[0106] DrugBank database is a comprehensive bioinformatics and cheminformatics database that combines detailed drug data (such as chemical information, pharmacological information, drug targets, etc.) and comprehensive drug target information, and is an important tool for drug research and development, clinical trials and safety monitoring;

[0107] OMIM (Online Mendelian Inheritance in Man) is an online database focusing on the relationship between human genes and genetic diseases, maintained by the National Library of Medicine (NLM) of the United States; it provides detailed descriptions of genetic diseases, gene mutations, clinical phenotypes, genetic patterns, and related literature information;

[0108] S2, design curvature optimization association modification module, optimize drug-disease association heterogeneous graph A to get drug-disease association heterogeneous graph M * :

[0109] S21: design curvature optimization association modification module to alleviate the problem of over-compression in GCN;

[0110] S22: drug-disease association heterogeneous graph A is processed by the association modification module to obtain the optimized drug-disease association heterogeneous graph M * ;

[0111] The execution steps of the association modification module in S2 are as follows:

[0112] S211: A new association heterogeneous network M is constructed using DS, DR and the drug-disease association heterogeneous graph A, that is:

[0113]

[0114] S212: The Ollivier-Ricci curvature of all links in the entire drug-disease association heterogeneous graph M is calculated, n a edges with the smallest Ollivier-Ricci curvature value are found, and virtual similarity links are added to these edges to alleviate the negative curvature problem, at the same time, n r edges with the largest Ollivier-Ricci curvature value are found, and they are removed to reduce the positive curvature in the network, finally, the edges connecting the drug nodes and the disease nodes are reserved, and the optimized drug-disease association graph M * is obtained:

[0115]

[0116] wherein A * is the matrix obtained by removing the edges with large curvature and adding virtual similarity links to the drug-disease association heterogeneous graph A, A *T is the transpose matrix of A * ;

[0117] wherein the over-compression problem refers to the phenomenon that in the graph neural network, multiple layers of propagation occur, causing the node features to become too similar in the information mixing process, thus losing the important differences between nodes and the complex structure characteristics of the graph, which reduces the expression ability and prediction accuracy of the model on the graph data; and since each layer can only transmit messages within a distance of 1, this means that two nodes with a distance of K can only transmit information to each other when the GNN has at least K layers; this phenomenon limits the ability of GNN to capture long-range dependencies;

[0118] The over-compression phenomenon is derived from the local structural characteristics of the graph; the local structural characteristics of the graph refer to the structural characteristics possessed by the subgraph formed by a node or a small part of nodes and their adjacent nodes, which can describe the topology of the graph and the relationship between nodes in a local range, corresponding to the global structural characteristics of the whole graph; it mainly focuses on the patterns and properties exhibited by the direct neighborhood of the nodes in the graph and the node set closely connected thereto; meanwhile, the positive and negative curvatures of the graph also affect the transmission process of information on the graph to some extent; therefore, the performance of the graph neural network (GNN) can be optimized by using the characteristics of the local graph; the optimization of the GNN by using the graph curvature can improve the size and performance of the graph structure to some extent; in the case of applying the traditional curvature theory to the discrete graph, the concept is no longer effective, and therefore the concept of Ollivier-Ricci curvature is introduced;

[0119] The Ollivier-Ricci curvature takes into account the cost paid by the node when migrating to other nodes according to a certain probability distribution; the transition probability μ u (x) of the node u∈V is defined as follows:

[0120]

[0121] Wherein, V is the node of the heterogeneous graph, x represents the neighborhood node of the node u, and x∈N u (deg(u) represents the degree of the node u, and u~x represents that there is a direct connection between the two nodes; then the Wasserstein distance between the two nodes u and v can be calculated as:

[0122]

[0123] Wherein, δ(x,y) represents the joint probability density between two nodes, and d(x,y) measures the geodesic distance between two points on the manifold; the Wasserstein distance W(μ u ,μ v ) measures the cost that the node u must move when reaching the node v through random walk;

[0124] According to the definition of Ollivier-Ricci, the Ollivier-Ricci curvature between the nodes u and v is finally calculated as:

[0125]

[0126] The concept of introducing virtual similarity links finds the links that really affect the message passing blocking; for two nodes that are not directly connected but have high similarity, it can be considered that they have a virtual link of similarity link, which has equivalent effect with the directly connected link in message passing; therefore, the virtual disease similarity link is constructed by selecting m most similar diseases for each disease from the DS, and the virtual drug similarity link is constructed by selecting m most similar drugs for each drug from the DR; the links that still maintain negative curvature after adding virtual similarity links can be considered as the cause of message passing blocking; reducing the number of these links can alleviate the over-smoothing problem in message passing process;

[0127] S3, using GCN to the drug-disease association heterogeneous graph M * feature extraction to obtain the first feature matrix F1;

[0128] The specific steps of S3 are as follows:

[0129] using GCN to the drug-disease association graph M * feature extraction to obtain the feature matrix F1, and the definition formula is:

[0130]

[0131] wherein, wherein is the unit matrix, is the degree matrix of the drug-disease association graph, which is a diagonal matrix, represents taking the reciprocal of each diagonal element of the degree matrix and then taking the square root, represents the training parameters of the lth layer GCN, and LeakyReLU represents a nonlinear activation function, and the input layer H (1) is M * , and L is the number of convolution layers;

[0132] The core idea of GCN (graph neural network) is to aggregate the neighbor information of the node into the representation of the node itself through convolution operation, which is similar to the convolution operation of traditional convolutional neural network (CNN) on image;

[0133] S4, designing a similarity-aware hyperbolic graph neural network model to perform feature extraction on the matrix F1 to obtain a second feature matrix F2;

[0134] The specific steps of S4 are as follows:

[0135] S41: using exponential mapping to map the Euclidean feature vector of each node in the drug-disease association feature matrix F1 into a hyperbolic space feature vector; for the drug-disease feature matrix F1, x represents a point in the hyperbolic space, Represents the Euclidean eigenvector of node x. The mapping formula is as follows:

[0136]

[0137] in, express The eigenvector after being mapped to the hyperbolic space, represents an exponential mapping starting from x; c is the curvature of the hyperbolic space, and x represents a point in the hyperbolic space as the starting point of the exponential mapping; represents the Möbius addition in the Poincaré sphere model, which is a distance metric in hyperbolic space; tanh represents the hyperbolic tangent function, which is used to map real numbers to the interval (-1,1); is the absolute value of the square root of the curvature c, which is used to adjust the scale of the mapping; is a scaling factor associated with point x, which depends on the curvature c and the position of point x in hyperbolic space; Representative feature vector The Euclidean norm of , which represents the length of the eigenvector; Represents the normalization operation, which transforms the feature vector Normalized and adjusted according to the curvature c, the formula maps the eigenvector of the drug-disease association in Euclidean space to the eigenvector in hyperbolic space;

[0138] S42: Calculate the similarity-aware neighborhood weight α ij , making the hyperbolic graph neural network robust to the feature aggregation of drug-disease features, α ij The calculation formula is as follows:

[0139]

[0140] in d i is the degree of node i;

[0141] Among them, traditional graph neural networks may only consider the structural information between nodes when calculating neighborhood weights, such as the connection relationship or distance information between nodes. Similarity-aware neighborhood weights introduce the cosine similarity function, which can more comprehensively consider the intrinsic similarity between nodes. This means that it not only considers whether the nodes are connected, but also the degree of feature similarity between the nodes themselves.

[0142] S43: Perform feature aggregation on drug-disease features to obtain the final output feature representation After calculating the neighborhood weights, we can perform feature aggregation on the drug-disease features. In hyperbolic space, feature aggregation can be achieved in the following ways:

[0143]

[0144] where L represents the number of layers, l is counted from 1, is the feature representation of node i at the l-th layer, is the neighbor set of node i, is the Möbius addition in hyperbolic space, is the aggregation operation on neighbor features, a ij is the weight between node i and j, ⊙ represents element-wise multiplication, and the final output feature representation is

[0145] S44: applying a nonlinear activation function to the feature Introducing nonlinear characteristics; introducing the hyperbolic tangent function tanh as a nonlinear activation function to introduce nonlinear characteristics, thereby enhancing the expression ability of the model, and the definition formula is:

[0146]

[0147] where, is the representation after the nonlinear function;

[0148] S45: using logarithmic mapping to map the feature vector of drug disease in hyperbolic space back to the feature vector in Euclidean space:

[0149]

[0150] where, represents the logarithmic mapping with q as the starting point; q is a point in hyperbolic space, and the origin, i.e. the zero vector, is generally selected as the reference point of the logarithmic mapping; is another point in hyperbolic space, and the goal is to find the tangent vector from q to ; c is the curvature of the hyperbolic space; is a scale factor depending on the curvature c and the position of the point q, and specifically represents the Möbius addition in the Poincaré ball model; tanh -1 is the inverse function of the hyperbolic tangent function, i.e. the hyperbolic arctangent function; ||·||2 represents the Euclidean norm, and its geometric meaning is that given two points q and logarithmic mapping calculates the tangent vector at q of the geodesic from q to ; the tangent vector can be regarded as the Euclidean representation of the "direction" and "distance" between q and , and the feature matrix representation mapped back to the Euclidean space is

[0151] Among them, the hyperbolic graph neural network is a deep learning architecture that combines graph neural networks with hyperbolic geometry, aiming to utilize the characteristics of hyperbolic space to process graph data, especially for data with hierarchical or tree-like structure, hyperbolic space can better represent the inherent geometric characteristics, because hyperbolic space has higher expressive power than Euclidean space, and can more effectively represent data with complex structure in lower dimensions;

[0152] S5, a gating signal self-attention mechanism is designed to extract features from the feature matrix F2 to obtain a third feature matrix F3;

[0153] Among them, the specific steps of S5 are as follows:

[0154] S51: The gating mechanism is introduced, so that the self-attention mechanism can pay more attention to the drug-disease features that are more important for the current drug repositioning task when processing drug-disease information, thereby improving the performance and generalization ability of the model, and the definition formula is:

[0155] Q=F2W Q #(9)

[0156] K=F2W K #(10)

[0157] V=F2W V #(11)

[0158] Among them, and are learnable weight matrices;

[0159] S52: A gating signal needs to be calculated, which will be used to adjust the contribution of the value matrix V, the gating signal can be calculated by the dot product of the query matrix Q and the key matrix K, and then generated through a learnable weight matrix and a nonlinear activation function sigmoid;

[0160] GateSignal=sigmoid(QK T W G )#(12)

[0161] S53: Apply the gating signal to the value matrix V, which can be achieved by multiplying the gating signal with the value matrix V, thereby controlling the weight of each value vector in the final output;

[0162] GatedValues=GateSignal×V#(13)

[0163]

[0164] where d kis the dimension of vector K, the Softmax function performs normalization operation, and represents the ReLU operation GateSignal represents the gating signal;

[0165] Wherein, the gating signal self-attention mechanism can dynamically weight different features according to the requirements of the drug repositioning task by introducing a gating signal, which enables the model to pay more attention to more important features when processing information.

[0166] S6, based on the feature matrix F3, an MLP is selected as the decoder to output the association prediction score S;

[0167] Wherein, based on the feature matrix F3, wherein Z i,j represents the association feature of drug i and disease j in the feature matrix F3, S i,j is the association score between drug m i and disease d j , and a multi-layer linear perception MLP is selected as the decoder to predict the probability of each category:

[0168]

[0169] Wherein and represent learnable parameters, b r and b s are bias terms, and sigma is an optional activation function.

[0170] In summary, the application designs an association modification module based on curvature optimization to alleviate the over-compression problem in GCN; specifically, the Ollivier-Ricci curvature of all links in the entire drug-disease association heterogeneous graph is calculated, n a The edges with the smallest Ollivier-Ricci curvature value are found, and virtual similarity links are added to these edges to alleviate the negative curvature problem, and n r The edges with the largest Ollivier-Ricci curvature value are found, and they are removed to reduce the positive curvature in the network; finally, the edges connecting the drug nodes and the disease nodes are retained to obtain the optimized drug-disease association graph, which can alleviate the over-compression problem in GCN.

[0171] The application designs a similarity-aware hyperbolic graph neural network model, which introduces a cosine similarity function when calculating the neighborhood weight, so that the model not only considers whether the nodes are connected when extracting drug and disease features, but also considers the similarity degree of the features of the nodes themselves.

[0172] The application designs a gating signal self-attention mechanism, by calculating a gating signal, the gating signal will be used to adjust the contribution of the value matrix V; so that the gating signal self-attention mechanism can pay more attention to the more important features of the drug redirection task when processing information, thereby improving the performance and generalization ability of the model.

[0173] Although the present application has been described with reference to the embodiments above, various improvements can be made thereto and components thereof can be substituted with equivalents without departing from the scope of the present application. In particular, features in the disclosed embodiments of the present application can be combined together in any manner as long as there is no structural conflict, and the combinations are not exhaustively described in the specification only for the purpose of omitting the length and saving resources. Therefore, the present application is not limited to the specific embodiments disclosed herein, but includes all technical solutions falling within the scope of the claims.

Claims

1. A drug-disease association prediction method based on curvature optimization association, characterized in that, The specific steps include the following: S1, obtaining a drug-disease association heterogeneous graph A, a drug similarity matrix DR, and a disease similarity matrix DS: S11: Obtain drug-disease association data from existing public databases, construct drug-disease association heterogeneous graph and represent as matrix where m and d represent the number of drugs and diseases, respectively; S12: Obtain the chemical structure of the drug from the existing public database, and construct a drug similarity matrix S13: Obtain disease phenotype information from existing public databases, measure disease similarity by disease phenotype similarity, and construct a disease similarity matrix S2, a curvature-optimized association modification module is designed to optimize the drug-disease association heterogeneous graph A to obtain a drug-disease association heterogeneous graph M * The execution steps are as follows: S211: Construct a new association heterogeneous network M using DS, DR, and the drug-disease association heterogeneous graph A, that is: S212: Calculate the Ollivier-Ricci curvature of all links in the whole drug-disease association heterogeneous graph M by M, find the n with the minimum Ollivier-Ricci curvature value a S213: Add virtual similarity links to the edges with negative curvature to alleviate the problem of negative curvature, and find the n with the maximum Ollivier-Ricci curvature value r S214: Remove the edges with positive curvature to reduce the positive curvature in the network, and finally retain the edges connecting the drug nodes and disease nodes to obtain the optimized drug-disease association graph M * : where A * is the matrix obtained by removing large-curvature edges and adding virtual similarity links to the drug-disease association heterogeneous graph A, A *T is the transpose matrix of A * . S3, using the GCN on the drug-disease association heterogeneous graph M * performing feature extraction to obtain a first feature matrix F1; S4, designing a similarity-aware hyperbolic graph neural network model to extract features of the matrix F1 to obtain a second feature matrix F2, and the similarity-aware neighborhood weight introduces a cosine similarity function, which can more comprehensively consider the inherent similarity between nodes; S5, designing a gated signal self-attention mechanism to extract features of the feature matrix F2 to obtain a third feature matrix F3; S6, based on the feature matrix F3, selecting an MLP as a decoder to output an association prediction score S.

2. The drug-disease association prediction method based on curvature optimization association according to claim 1, characterized in that, The definition of A in S11 is as follows: 3.The drug-disease association prediction method based on curvature optimization correlation according to claim 1, characterized in that, The specific steps of S12 are as follows: S121: After obtaining the chemical structure of the drug from the existing public database, the chemical structure of the drug is converted into a molecular topological fingerprint using the RDKit toolkit; S122: Calculate the Tanimoto similarity coefficient of each pair of drugs; The calculation formula of the Tanimoto similarity coefficient is as follows: where R A and R B represent the set of two molecular fingerprints, respectively. The calculated Tanimoto similarity coefficient for each pair of drugs is stored in a matrix DR, and the resulting DR matrix is the drug similarity matrix.

4. The drug-disease association prediction method based on curvature optimization association according to claim 1, characterized in that, The specific steps of S13 are as follows: S131: Obtain disease phenotype information from an existing public database, and structure the disease phenotype information using the human phenotype ontology, which provides a hierarchical relationship between diseases and phenotypes; S132: Based on the human phenotype ontology, the similarity between two diseases can be calculated. For this purpose, the specificity of the phenotype term can be measured using the information content method, and then the similarity between diseases can be calculated. The specific formula is as follows: where d i and d j represent diseases, T(d i ) and T(d j ) represent the information content of diseases d i and d j respectively, and t represents a phenotype term in the set of phenotype terms in the Human Phenotype Ontology, IC(t) represents the information content of phenotype term t. The phenotype similarity values of all disease pairs are stored in a matrix DS, where the element DS(i,j) in the matrix represents the similarity between diseases d i and d j .

5. The drug-disease association prediction method based on curvature optimization association according to claim 1, characterized in that, The specific steps of S3 are as follows: Using GCN on drug-disease association graph M * Feature extraction is performed to obtain a feature matrix F1, and a definition formula is as follows: wherein wherein is the identity matrix, is the degree matrix of the drug-disease association graph, which is a diagonal matrix, represents taking the reciprocal of each diagonal element of the degree matrix and then taking the square root, represents the training parameters of the l-th layer GCN, LeakyReLU represents a nonlinear activation function, and the input layer H (1) is M * , and L is the number of convolutional layers.

6. The drug-disease association prediction method based on curvature optimization association according to claim 1, characterized in that, The specific steps of S4 are as follows: S41: using exponential mapping, mapping the Euclidean feature vector of each node in the drug-disease association feature matrix F1 into a hyperbolic space feature vector; for the drug-disease feature matrix F1, x represents a point in the hyperbolic space, the Euclidean feature vector of the representative node x, the mapping formula is as follows: wherein, represents the feature vector mapped to hyperbolic space, represents the exponential map with x as the starting point; c is the curvature of the hyperbolic space, x represents a point in the hyperbolic space as the starting point of the exponential map; ⊕ c represents the Möbius addition in the Poincaré ball model, which is a distance metric in hyperbolic space; tanh represents the hyperbolic tangent function, which is used to map real numbers to the interval (-1, 1); is the absolute value of the square root of the curvature c, used to adjust the scale of the mapping; is a scaling factor related to the point x, which depends on the curvature c and the position of the point x in the hyperbolic space; represents the Euclidean norm of the feature vector , indicating the length of the feature vector; represents the normalization operation, which normalizes the feature vector and adjusts it according to the curvature c, the formula maps the feature vector of the drug-disease association in the Euclidean space to the feature vector in the hyperbolic space; S42: Calculate the neighborhood weight α of similarity perception ij , making the hyperbolic graph neural network robust to feature aggregation of drug disease characteristics, α ij The calculation formula is as follows: wherein d i is the degree of node i; S43: Feature aggregation is performed on the features of the drug disease to obtain a final output feature representation After the neighborhood weights are calculated, feature aggregation can be performed on the features of the drug disease. In hyperbolic space, feature aggregation can be implemented in the following manner: where L represents the number of layers, l is counted from 1, is the feature representation of node i at the l-th layer, is the neighbor set of node i, is the Möbius addition in hyperbolic space, is the aggregation operation on neighbor features, a ij is the weight between node i and j, ⊙ represents element-wise multiplication, and the final output feature representation is S44: using a nonlinear activation function for the features Introducing nonlinear characteristics; introducing the hyperbolic tangent function tanh as a nonlinear activation function to introduce nonlinear characteristics, thereby enhancing the expression ability of the model, and the definition formula is: wherein is representation after a non-linear function; S45: Use logarithmic mapping to map the drug-disease feature vector in the hyperbolic space back to the feature vector in the Euclidean space: in, represents a logarithmic mapping starting from q; q is a point in the hyperbolic space, and the origin, i.e., the zero vector, is selected as the reference point of the logarithmic mapping; is another point in the hyperbolic space, and the goal is to find the distance from q to The tangent vector of ; c is the curvature of the hyperbolic space; is a scaling factor that depends on the curvature c and the position of the point q, specifically ⊕ c represents the Möbius addition in the Poincaré sphere model; tanh -1 Is the inverse function of the hyperbolic tangent function, that is, the hyperbolic inverse tangent function; ||·||2 represents the Euclidean norm, and the geometric meaning of its formula is that, given two points q and Logarithmic mapping Calculate from q to The tangent vector of the geodesic at q can be regarded as the tangent vector of q and The Euclidean representation of "direction" and "distance" between them, mapped back to the Euclidean space, is represented by the characteristic matrix 7. The drug-disease association prediction method based on curvature optimization association according to claim 1, characterized in that, The specific steps of S5 are as follows: S51: Introducing a gating mechanism allows the self-attention mechanism to pay more attention to drug-disease features that are more important for the current drug repositioning task when processing drug-disease information, thereby improving the performance and generalization ability of the model. The definition formula is as follows: Q = F2W Q (9) K = F2W K (10) V = F2W V (11) wherein, and are learnable weight matrices; S52: A gating signal needs to be computed, which will be used to modulate the contribution of the value matrix V, the gating signal can be computed by the dot product of the query matrix Q and the key matrix K, then by a learnable weight matrix and a non-linear activation function sigmoid to generate; GateSignal = sigmoid(QK T W G ) (12) S53: Apply the gating signal to the value matrix V, which can be achieved by multiplying the gating signal with the value matrix V, thereby controlling the weight of each value vector in the final output; GatedValues=GateSignal×V (13) where d k is the dimension of the vector K, the Softmax function performs a normalization operation, σ denotes a ReLU operation, and GateSignal denotes a gating signal.

8. The drug-disease association prediction method based on curvature optimization association according to claim 1, characterized in that, The specific steps of S6 are as follows: Based on the feature matrix F3, where Z i,j represents the association feature between drug i and disease j in the feature matrix F3, S i,j is the association score between drug m i and disease d j , a multi-layer perceptron (MLP) is selected as the decoder to predict the probability of each class: where and represent learnable parameters, b r and b s is a bias term, and σ is an optional activation function.

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