Drug-disease association prediction method based on matrix completion and double-strategy graph reasoning

Abstract

The invention belongs to the technical field of biological information and computers, and particularly relates to a medicine-disease association prediction method based on matrix completion and double-strategy graph reasoning. The method comprises the following steps: firstly, calculating the similarity of Gaussian kernels and Laplacian kernels of drugs and diseases, and then fusing the Gaussian kernels and the Laplacian kernels by using a nonlinear fusion technology. According to the method, an adjacent matrix of a drug-disease heterogeneous network is taken as a target matrix, and the robustness and formability of the edge of a drug-disease association network are enhanced through truncation arc tangent rank minimization. The method mainly focuses on adjacent nodes of drugs and diseases, and potential noise of farther nodes is filtered out. In addition, the method adopts top-down and bottom-up strategies to predict the drug-disease association based on the drug-disease heterogeneous network. The cooperative effect of the double strategies can enhance the comprehensive processing capability of a complex structure and cross-domain association in the heterogeneous graph, and sufficient utilization of rich information in the network is ensured.

Description

Technical Field

[0001] The invention belongs to the field of bioinformatics and computer technology, and particularly relates to a drug-disease association prediction method based on matrix completion and dual-strategy graph reasoning. Background Art

[0002] In the traditional drug development process, a lot of resources are often wasted on drugs that ultimately prove to be ineffective. Therefore, new strategies are urgently needed to reduce the time and cost of drug development. One such approach is drug repositioning, which is finding new therapeutic uses for existing drugs. This strategy has gained a lot of attention because it focuses on repurposing already developed or approved drugs, offering the potential to treat new diseases.

[0003] Drug repositioning leverages existing safety and efficacy data from approved drugs, allowing for faster clinical translation and significantly reducing development costs compared to developing drugs from scratch. Identifying drug-disease associations (DDAs) is critical for drug discovery and repositioning. By predicting these associations, medical researchers can prioritize the most promising therapeutic candidates, streamlining resource allocation and increasing the likelihood of success.

[0004] Advances in bioassays and screening technologies have expanded our understanding of drugs and diseases, providing more possibilities for discovering treatments. Identifying drug-disease associations can leverage this valuable data to explore new areas of therapeutic options. However, traditional biological experiment-based drug-disease association predictions are often labor-intensive and time-consuming, greatly limiting the efficiency of the prediction process. Therefore, the development of efficient computational methods is critical to accelerating progress in this prediction process.

[0005] Graph reasoning techniques are widely used in association prediction due to their high efficiency and interpretability. However, existing methods often fail to adequately address the large number of missing edges in drug-disease networks. Matrix completion can effectively fill these gaps. For example, the SLHGISMMA algorithm uses a sparse learning method based on the kernel norm to supplement the missing values ​​in the correlation matrix, and then obtains the prediction score through heterogeneous graph reasoning. Similarly, the TSPN algorithm constructs a heterogeneous network using rich biological information and achieves prediction based on the adjacency matrix of the network by minimizing the truncated schatten p-norm. However, current matrix completion techniques have difficulty in effectively approximating the rank function, often resulting in suboptimal solutions.

[0006] In addition, existing graph reasoning techniques usually rely on local network reasoning or unidirectional reasoning, which has some limitations. For example, the NetPro algorithm predicts DDAs by first preprocessing the similarity and association matrices before using label propagation. In contrast, the DR-IBRW algorithm uses double random walks for association prediction. Both methods are local reasoning, wandering the similarity network to the association network, and cannot fully utilize the available information from the entire heterogeneous network. Although the HGIMC algorithm uses heterogeneous graph reasoning technology to generate prediction scores on a comprehensive heterogeneous network, it only considers a unidirectional reasoning path and lacks a holistic perspective. In addition, these existing methods are easily affected by remote nodes during the reasoning process.

[0007] In summary, accurately identifying new therapeutic uses of drugs is crucial to advance drug research and development. Graph reasoning techniques have shown great promise in predicting drug-disease associations, providing high convergence accuracy and efficiency. However, most existing methods cannot adequately address the problem of large amounts of missing information in drug-disease association networks. In addition, existing methods are often constrained by local or unidirectional reasoning. Summary of the invention

[0008] The present invention proposes a drug-disease association prediction method based on matrix completion and dual-strategy graph reasoning, and proposes a new matrix completion method and bidirectional neighborhood constraint graph reasoning, which solves the problem in the prior art that a large amount of missing information in the drug-disease association network has not been fully supplemented, and the graph reasoning technology is limited by locality and unidirectional reasoning, resulting in insufficient prediction accuracy.

[0009] The technical solution of the present invention is achieved in this way: The drug-disease association prediction method based on matrix completion and dual-strategy graph reasoning includes the following steps: S1. Calculate the Gaussian kernel and Laplace kernel similarities between drugs and diseases, and fuse them using nonlinear fusion technology to obtain integrated drug similarity and disease similarity; S2. Use the truncated inverse tangent rank minimization method to enhance the robustness and structural integrity of the drug-disease network edge; Step S2 specifically includes the following contents: S21, integrating the drug-disease association network with the similarity network to construct a drug-disease heterogeneous network; S22, taking the adjacency matrix of the heterogeneous network as the target matrix for minimizing the truncated inverse tangent rank; S23, then solving the corresponding objective function using the alternating direction multiplier method; S3, design a dual-strategy neighborhood constraint graph reasoning to complete the prediction; Step S3 specifically includes the following contents: S31, calculating the neighborhood similarity of drugs and diseases based on adjacent nodes; S32, integrating the established drug and disease neighborhood similarity networks and the well-established drug-disease association network into a comprehensive heterogeneous network; S33, uses top-down and bottom-up methods to perform reasoning on this network, effectively capturing key associations.

[0010] Optionally, in step S1, the Gaussian kernel similarity between drugs and diseases is calculated as follows: The vector stores the drug vector of row i of the association matrix, Represents the disease vector of the jth column of the storage association matrix, and the calculation formula is as follows: ; ; Among them, the variable Indicates drug Gaussian kernel similarity, variable Indicates disease and Gaussian kernel similarity, To store the disease vector of column i of the association matrix, To store the drug vector of row j of the association matrix, the adjustable parameter and Control the bandwidth of the kernel function. The specific calculation formula is as follows: ; .

[0011] Optionally, in step S1, the Laplace kernel similarity between drugs and diseases is calculated as follows: ; ; Among them, the variable Represents the Laplace kernel similarity of drugs, variable represents the Laplace kernel similarity of the disease, Represents the bandwidth of the control function.

[0012] Optionally, in step S1, the method of using nonlinear fusion technology to fuse them to obtain integrated drug similarity and disease similarity is as follows: In the first step, the drug similarity matrix is ​​normalized one by one, as shown below: ; in, represents the h-th drug similarity matrix, is the h-th normalized drug similarity matrix; The second step is to introduce the k nearest neighbor method; ; in, represents the neighborhood constraint matrix, Indicates drug The neighbor set consisting of the k most similar drugs; The third step is to normalize the similarity matrix and the neighbor constraint matrix Merge as follows: ; in, Indicates The h-th matrix after iterations, is the initial value, is the weight parameter, α represents the initial normalized matrix of the network to be fused, represents the hth neighborhood constraint matrix, represents the fusion of different drug normalized matrices, represents the transpose of the h-th neighborhood constraint matrix, The final matrix after iterations is as follows: ; The fourth step is to embed the weighted matrix into the nonlinear fusion. The weighted matrix embeds additional neighbor information. The weighted matrix is: ; Step 5: Get the final drug similarity matrix As shown below: ; Similarly, the final disease similarity matrix can be obtained .

[0013] Optionally, in step S21, the method of constructing a drug-disease heterogeneous network is as follows: Integrate the similarity matrix and the association matrix to construct a drug-disease heterogeneous network rich in biological information. The network includes two types of nodes: drug nodes and disease nodes. , represents m drug nodes, Represents n disease nodes. The similarity scores between drugs and between diseases are used as edge weights in the drug and disease similarity networks, respectively. When there is a drug-disease association in the dataset, an edge is established between the corresponding drug and disease nodes, and the association score is used as the weight of the edge. They are defined as the edge sets representing drug-drug, disease-disease, and drug-disease relationships, respectively, and the weights on these edges are expressed as , and They correspond to drug-drug, disease-disease and drug-disease networks respectively. The drug-disease heterogeneous network can be expressed as ; The adjacency matrix of the heterogeneous network The construction form is as follows; ; Among them, RR represents the integrated drug similarity matrix, DD represents the integrated basic similarity matrix, represents the drug-disease association matrix, Represents the transpose of the drug-disease association matrix.

[0014] Optionally, in step S22, the method of constructing the truncated inverse tangent rank minimization target matrix is ​​as follows: The underlying model of matrix completion is summarized as follows: ; in, represents the rank function, Ω represents the coordinate index set of the elements in L, and the operator represents the orthogonal projection operator applied to Ω; ; Minimizing the rank function is an NP-hard problem. The problem can be solved by approximating the rank function based on the nuclear norm. The formula is as follows: ; , represents the nuclear norm of matrix X; Use the inverse tangent function instead of the rank function; ; in, is the i-th singular value of the matrix X, It is differentiable, concave, monotonically increasing, and unitarily invariant on [0,1]; ; in, , and represents the identity matrix, represents the projection matrix of matrix X applied to Ω, represents the projection matrix of matrix L applied to Ω, Indicates the truncation property. , indicating that the matrix A is an orthogonal matrix, Indicates that the matrix B is an orthogonal matrix; ; Among them, if is a balance parameter, and This means that all elements in X are in the range [0,1].

[0015] Optionally, in step S23, the method of efficiently solving the truncated inverse tangent rank minimization using the alternating direction multiplier method is as follows: The directions are updated alternately in each iteration as follows: ; The augmented Lagrangian form can be expressed as: ; Among them, Z represents the Lagrange multiplier, β represents the penalty parameter, represents the objective function to be minimized, Indicates the truncation property. represents the Lagrangian parameter term, Represents the penalty term, all matrices Initialized as L matrix, during k iterations, calculate .

[0016] Optionally, in step S31, the neighborhood similarity between drugs and diseases is calculated as follows: Assumed disease and medications The possibility of association between and Adjacent association scores correspond closely, and for a given drug ,choose Based on the most similar drugs, the comprehensive drug similarity indicates that this neighbor set , define the neighborhood similarity matrix , which is calculated as follows: ; disease The nearest neighbors of , expressed as , disease neighborhood similarity matrix Calculated in a similar manner; .

[0017] Optionally, in step S32 and step S33, the method of performing dual-strategy neighborhood constraint graph reasoning based on heterogeneous networks is as follows: Top-down graph reasoning strategy: ; Bottom-up graph reasoning strategy: ; in, and Represent the prediction results of top-down and bottom-up graph reasoning strategies respectively, where and Corresponding to the weights of the top-down and bottom-up strategies, respectively, before starting the reasoning process, the neighborhood similarity matrix must be and Perform normalization; ; ; The final prediction score matrix : ; and Represent the prediction results of top-down and bottom-up graph reasoning strategies respectively.

[0018] After adopting the above technical solution, the beneficial effects of the present invention are: The present invention proposes a new method of truncated inverse tangent rank minimization and dual-strategy neighborhood constrained graph inference (TARMDNGI) to predict drug-disease associations. First, the Gaussian kernel and Laplacian kernel similarities of drugs and diseases are calculated, and then they are integrated using nonlinear fusion techniques. The present invention introduces a new matrix completion technique, called truncated inverse tangent rank minimization (TARM). TARM uses the adjacency matrix of the drug-disease heterogeneous network as the target matrix and enhances the robustness and formability of the edges of the drug-disease association network by minimizing the truncated inverse tangent rank. In addition, the present invention proposes a dual-strategy neighborhood constrained graph inference method to predict drug-disease associations. This technique focuses on the neighboring nodes of drugs and diseases and filters out the potential noise of more distant nodes. In addition, the dual-strategy neighborhood constrained graph inference (DNGI) method uses top-down and bottom-up strategies to infer the associations of the entire drug-disease heterogeneous network. The synergy of the dual strategies can enhance the comprehensive processing capabilities of complex structures and cross-domain associations in heterogeneous graphs, ensuring that the rich information in the network is fully utilized. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0020] Figure 1 It is an overall framework based on matrix completion and dual-strategy graph reasoning. DETAILED DESCRIPTION

[0021] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0022] The embodiments of the present application disclose a drug-disease association prediction method based on matrix completion and dual-strategy graph reasoning.

[0023] Embodiment, according to Figure 1 As shown in the figure, a drug-disease association prediction method based on matrix completion and dual-strategy graph reasoning is named TARMDNGI.

[0024] 1. Related Work 1.1 Matrix completion Matrix completion techniques have been widely used in association prediction tasks due to their effectiveness in predicting missing values ​​in matrices. For example, the SLHGISMMA algorithm uses a sparse learning method based on the kernel norm to fill in the missing values ​​in the correlation matrix, and then obtains the prediction scores through heterogeneous graph reasoning. Similarly, the AMCSMMA algorithm integrates three types of biological data to construct a heterogeneous network and restores the missing values ​​by minimizing the truncated kernel norm in the network adjacency matrix. The TSPN algorithm also integrates three types of biological information to construct a heterogeneous network and obtains the prediction scores using truncated schatten p-norm minimization on the adjacency matrix. However, these methods have limited ability to approximate the rank function, resulting in suboptimal solutions.

[0025] This paper introduces a new matrix completion technique called TRAM. Unlike previous methods that have difficulty accurately approximating the rank function, TRAM enhances this approximation by using a well-defined mathematical expression to rationalize the relationship between singular values ​​and rank. Structurally, TRAM truncates and retains the most important singular values ​​while minimizing unimportant singular values ​​and retaining certain prior values. This method significantly reduces noise without distorting the underlying structure of the matrix. Therefore, TRAM is closer to the rank function and can effectively fill in the missing values ​​in the matrix.

[0026] 2.2 Graph Reasoning Graph reasoning is an effective method for predicting the association of unknown molecules in complex bioinformatics networks. For example, the NetPro algorithm first preprocesses the similarity and association matrices and then uses label propagation to predict DDAs. Similarly, the DR-IBRWb algorithm uses double random walks to make such predictions. The MDHGI algorithm enhances the association matrix through matrix factorization and then performs heterogeneous graph reasoning based on the bioinformatics network to generate prediction scores. However, these methods have certain limitations. They are limited to local or unidirectional reasoning in heterogeneous networks, which makes them unable to exploit global network information and capture complex information. In addition, they are easily affected by remote nodes during reasoning, which reduces their robustness.

[0027] The present invention develops a new graph reasoning technique, called DNGI, which focuses on utilizing neighboring nodes of drugs and diseases in the network while ignoring potential noise from distant nodes. DNGI integrates top-down and bottom-up strategies to reason throughout the heterogeneous drug-disease network. The synergy of the two strategies can enhance the comprehensive processing capabilities of complex structures and cross-domain associations in heterogeneous graphs, ensuring that the rich information in the network is fully utilized.

[0028] 2. Method introduction 2.1 Based on matrix completion and dual strategy graph reasoning method (TARMDNGI) Figure 1 The overall framework of the TARMDNGI method is presented. First, the Gaussian and Laplacian kernel similarities of drugs and diseases are calculated and then integrated using nonlinear fusion techniques. Second, a new matrix completion technique, TRAM, is introduced to enhance the robustness and structural integrity of the edges of the drug-disease association network. Finally, a dual-strategy neighborhood-constrained graph reasoning method is proposed to predict drug-disease associations.

[0029] 2.2 Dataset To evaluate the performance of TARMDNGI, we conducted a series of experiments on four datasets, including different association prediction tasks in different fields. Specifically, the method was tested on three different types of datasets: drug-disease, lncRNA-disease, and microbial disease. For the drug-disease dataset, we deliberately selected two datasets of different sizes to verify the scalability of the model, containing 269 drugs and 598 diseases, respectively. The larger dataset contains 18,416 known drug-disease associations from the Comparative Toxicogenomics Database (CTD). In addition, a smaller therapeutic dataset containing 6,244 annotated therapeutic drug-disease associations from CTD was used for performance comparison. For the lncRNA-disease dataset, we collected 605 associations involving 82 lncRNAs and 157 diseases. For the microbial-disease dataset, 450 microbial-disease associations were collected from HMDAD, involving 292 microorganisms and 39 diseases. In this case, the drug-disease association matrix is ​​expressed as , where m corresponds to the number of drugs and n represents the number of diseases.

[0030] 2.3 Similarity Measurement 2.3.1 Gaussian Kernel Similarity Gaussian kernel function is widely used to calculate biological similarity due to its powerful performance and generalizability to various types of biological data. In the present invention, based on the known drug-disease association, Gaussian kernel is applied to calculate the similarity between drugs and diseases. The vector stores the drug vector of row i of the association matrix, Represents the disease vector of the jth column of the storage association matrix. The calculation formula is as follows: ; (1) ; (2) Among them, the variable Indicates drug Gaussian kernel similarity, variable Indicates disease and Gaussian kernel similarity, To store the disease vector of column i of the association matrix, To store the drug vector of row j of the association matrix, the adjustable parameter and Control the bandwidth of the kernel function. The specific calculation formula is as follows: ; (3) ; (4) 2.3.2 Laplace kernel similarity Compared with the Gaussian kernel function, the Laplace kernel function shows stronger robustness in processing noise or abnormal data. In the present invention, the Laplace similarity of drugs and diseases is calculated, and the calculation formula is as follows: ; (5) ; (6) Among them, the variable Represents the Laplace kernel similarity of drugs, variable Represents the Laplace kernel similarity of the disease. In the present invention, represents the bandwidth of the control function, using the parameter To control the bandwidth of the function.

[0031] 2.4 Similarity Matrix Fusion In order to reduce the deviation caused by relying on a single similarity metric, the present invention adopts a nonlinear fusion method to fuse the similarities of two drugs and diseases respectively.

[0032] In the first step, the drug similarity matrix is ​​normalized one by one, as shown below: ; (7) in, represents the h-th drug similarity matrix, is the h-th normalized drug similarity matrix.

[0033] The second step is to introduce the weighted k-nearest neighbor (KNN) method. KNN assigns different weights to each neighbor based on the distance, and the closer the neighbor, the greater the weight. This method allows KNN to more accurately reflect local patterns and trends, making it more robust to noisy data and outliers; ; (8) in, represents the neighborhood constraint matrix, Indicates drug The neighbor set consisting of the k most similar drugs.

[0034] The third step is to merge the normalized similarity matrix Ph and the neighbor constraint matrix Sh as follows: ; (9) in, Indicates The h-th matrix after iterations, is the initial value, is the weight parameter, α represents the initial normalized matrix of the network to be fused, represents the hth neighborhood constraint matrix, represents the fusion of different drug normalized matrices, represents the transpose of the h-th neighborhood constraint matrix.

[0035] The final matrix after iterations is as follows: ; (10) The fourth step is to embed the weighted matrix into the nonlinear fusion. The weighted matrix embeds additional neighbor information. The weighted matrix is: ; (11) Step 5: Get the final drug similarity matrix As shown below: ; (12) Similarly, the final disease similarity matrix can be obtained .

[0036] 2.5 Truncated Inverse Tangent Rank Minimization 2.5.1 Building a Heterogeneous Network The present invention integrates similarity matrix and association matrix to construct a drug-disease heterogeneous network rich in biological information. The network includes two types of nodes: drug nodes and disease nodes. , represents m drug nodes and represents n disease nodes. The similarity scores between drugs and between diseases are used as edge weights in the drug and disease similarity networks, respectively. In addition, when there is a drug-disease association in the dataset, an edge is established between the corresponding drug and disease nodes, with the association score as the weight of the edge. , and are defined as the edge sets representing drug-drug, disease-disease, and drug-disease relationships, respectively. The weights on these edges are denoted by , and They correspond to drug-drug, disease-disease and drug-disease networks respectively. Therefore, the drug-disease heterogeneous network can be expressed as .

[0037] The adjacency matrix of the heterogeneous network The construction form is as follows: ; (13) Among them, RR represents the integrated drug similarity matrix, DD represents the integrated basic similarity matrix, represents the drug-disease association matrix, Represents the transpose of the drug-disease association matrix.

[0038] 2.5.2. Building TARM Matrix completion (MC) is an effective data recovery technique for drug-disease association prediction methods based on matrix completion and dual-strategy graph reasoning, which reconstructs the complete matrix by filling in missing values. The present invention applies matrix completion to solve the extreme sparsity problem of drug-disease association matrix. The underlying model of matrix completion is summarized as follows: ; (14) in, represents the rank function, Ω represents the coordinate index set of the elements in L, and the operator represents the orthogonal projection operator applied to Ω.

[0039] ; (15) Minimizing the rank function is an NP-hard problem, and there is currently no effective optimization algorithm that can directly solve it. Approximating the rank function based on the nuclear norm can solve this challenge. The formula is as follows: ; (16) , represents the nuclear norm of matrix X.

[0040] A large number of studies have shown that the nuclear norm can approximately replace the rank function. However, it is not an optimal substitute and practical applications can only produce suboptimal solutions. In recent years, several rank relaxation paradigms have been proposed to replace the nuclear norm, including the truncated nuclear norm, the schatten p-norm, the truncated schatten p-norm, and the However, all these rank relaxation paradigms have certain limitations and cannot fully consider the mathematical properties and physical structure of matrix rank.

[0041] In order to restore the target matrix more accurately and effectively, the present invention uses the inverse tangent function instead of the rank function, as shown in formula (17): ; (17) in, is the i-th singular value of the matrix X, It is differentiable, concave, monotonically increasing, and unitarily invariant on [0,1]. The present invention develops an effective matrix completion technology for drug-disease association prediction method based on matrix completion and dual-strategy graph reasoning. Based on formula (17), it is further transformed.

[0042] ; (18) here, , and represents the identity matrix, represents the projection matrix of matrix X applied to Ω, represents the projection matrix of matrix L applied to Ω, Indicates the truncation property. , indicating that the matrix A is an orthogonal matrix, Indicates that the matrix B is an orthogonal matrix.

[0043] The present invention introduces a regularization term to adapt to the potential noise in the block matrix. All values ​​of the matrix are restricted to the interval [0,1] to ensure their actual correlation. In summary, the present invention constructs the following model: ; (19) Among them, if is a balance parameter, and This means that all elements in X are in the range [0,1].

[0044] 2.5.3. Solving TARM The present invention develops a framework for solving the model using ADMM, which simplifies the calculation by introducing new variables and alternately updates the direction in each iteration.

[0045] ; (20) The augmented Lagrangian form of formula (20) can be expressed as: ;(twenty one) Among them, Z represents the Lagrange multiplier, β represents the penalty parameter, represents the objective function to be minimized, Indicates the truncation property. represents the Lagrangian parameter term, Represents the penalty term, all matrices Initialized to L matrix. During k iterations, calculate .

[0046] 2.6 Dual-Strategy Neighborhood Constraint Graph Reasoning This paper proposes a dual-strategy neighborhood-constrained graph reasoning method DNGI for predicting unknown DDAs based on matrix completion and dual-strategy graph reasoning. Compared with previous graph reasoning techniques, DNGI introduces several key improvements: (1) It emphasizes that similar drugs are more likely to be associated with similar diseases, focusing on the neighboring nodes of drugs and diseases to minimize the noise from distant, less relevant nodes. (2) DNGI operates in a drug-disease heterogeneous network and uses top-down and bottom-up strategies for more comprehensive graph reasoning. The synergy between these two strategies enhances the processing capabilities of complex structures and cross-domain associations in heterogeneous graphs and ensures full utilization of the rich information of the network. The process first calculates the neighborhood similarity of drugs and diseases based on adjacent nodes. Then, the established network with drug-disease neighborhood similarity and the perfect DDA network are integrated into a comprehensive heterogeneous network. Finally, reasoning is performed on this network using top-down and bottom-up methods to effectively capture key associations.

[0047] 2.6.1. Calculating Neighborhood Similarity of Drugs / Diseases Based on the assumption that similar drugs are more likely to be associated with similar diseases, the present invention further assumes that the disease and medications The possibility of association between and Adjacent association scores correspond closely. The neighborhood similarity of drugs is calculated by analyzing adjacent nodes in the drug similarity network. For a given drug ,choose (Number of neighbors of the most similar drug) Based on the most similar drugs, the comprehensive drug similarity indicates that this neighbor set Then define the neighborhood similarity matrix , whose elements are calculated as follows: ;(twenty two) Similarly, disease The nearest neighbors of , expressed as Disease Neighborhood Similarity Matrix Calculated in a similar manner.

[0048] ;(twenty three) 2.6.2. Dual-Strategy Graph Reasoning The present invention combines the improved DDA network with the drug and disease neighborhood similarity network to construct a comprehensive drug-disease heterogeneous network. Then, top-down and bottom-up graph reasoning strategies are used for prediction. The graph reasoning model combines these dual strategies as shown below Top-down graph reasoning strategy: ;(twenty four) Bottom-up graph reasoning strategy: ; (25) in, and Represent the prediction results of top-down and bottom-up graph reasoning strategies respectively. and The weights of the top-down and bottom-up strategies are respectively. Before starting the reasoning process, the neighborhood similarity matrix and , normalized.

[0049] ; (26) ; (27) (15) and (16) are in the iteration stop condition and Converge down.

[0050] Next, the present invention combines the association matrix calculated by the top-down and bottom-up strategies to obtain the final prediction score matrix : ; (28) and Represent the prediction results of top-down and bottom-up graph reasoning strategies respectively.

[0051] This paper introduces a new matrix completion technique, called TRAM, to enhance the robustness and formativeness of drug-disease association network edges. Unlike previous methods that have difficulty accurately approximating the rank function, TRAM enhances this approximation by using a well-defined mathematical expression to rationalize the relationship between singular values ​​and rank. Structurally, TRAM truncates and retains the most important singular values ​​while minimizing unimportant singular values ​​and retaining certain priors. This approach significantly reduces noise without distorting the underlying structure of the matrix.

[0052] The present invention develops a new graph reasoning technology called DNGI, which focuses on utilizing the neighboring nodes of drugs and diseases in the network, while ignoring the potential noise from distant nodes. DNGI integrates top-down and bottom-up strategies to reason throughout the heterogeneous drug-disease network. The synergy of the two strategies can enhance the comprehensive processing capabilities of complex structures and cross-domain associations in heterogeneous graphs, ensuring that the rich information in the network is fully utilized.

[0053] Experimental results show that TARMDNGI consistently outperforms state-of-the-art models on two drug-disease datasets, one lncRNA-disease dataset, and one microbe-disease dataset. The outstanding performance observed in two case studies further highlights the effectiveness of TARMDNGI in real-world applications.

[0054] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A drug-disease association prediction method based on matrix completion and dual-strategy graph reasoning, characterized in that: The following steps are involved: S1. Calculate the Gaussian kernel and Laplace kernel similarities between drugs and diseases, and fuse them using nonlinear fusion technology to obtain integrated drug similarity and disease similarity; S2. Use the truncated inverse tangent rank minimization method to enhance the robustness and structural integrity of the drug-disease network edge; Step S2 specifically includes the following contents: S21, integrating the drug-disease association network with the similarity network to construct a drug-disease heterogeneous network; S22, taking the adjacency matrix of the heterogeneous network as the target matrix for minimizing the truncated inverse tangent rank; S23, then solving the corresponding objective function using the alternating direction multiplier method; S3, design a dual-strategy neighborhood constraint graph reasoning to complete the prediction; Step S3 specifically includes the following contents: S31, calculating the neighborhood similarity of drugs and diseases based on adjacent nodes; S32, integrating the established drug and disease neighborhood similarity networks and the well-established drug-disease association network into a comprehensive heterogeneous network; S33, uses top-down and bottom-up methods to perform reasoning on this network, effectively capturing key associations.

2. The drug-disease association prediction method based on matrix completion and dual-strategy graph reasoning according to claim 1, characterized in that: In step S1, the Gaussian kernel similarity between drugs and diseases is calculated as follows: The vector stores the drug vector of row i of the association matrix, Represents the disease vector of the jth column of the storage association matrix, and the calculation formula is as follows: ； ； Among them, the variable Indicates drug Gaussian kernel similarity, variable Indicates disease and Gaussian kernel similarity, To store the disease vector of column i of the association matrix, To store the drug vector of row j of the association matrix, the adjustable parameter and Control the bandwidth of the kernel function. The specific calculation formula is as follows: ； 。 3. The drug-disease association prediction method based on matrix completion and dual-strategy graph reasoning according to claim 2, characterized in that: In step S1, the Laplace kernel similarity between drugs and diseases is calculated as follows: ； ； Among them, the variable Represents the Laplace kernel similarity of drugs, variable represents the Laplace kernel similarity of the disease, Represents the bandwidth of the control function.

4. The drug-disease association prediction method based on matrix completion and dual-strategy graph reasoning according to claim 3, characterized in that: In step S1, the method of using nonlinear fusion technology to fuse them to obtain integrated drug similarity and disease similarity is as follows: In the first step, the drug similarity matrix is ​​normalized one by one, as shown below: ； in, represents the h-th drug similarity matrix, is the h-th normalized drug similarity matrix; The second step is to introduce the k nearest neighbor method; ； in, represents the neighborhood constraint matrix, Indicates drug The neighbor set consisting of the k most similar drugs; The third step is to normalize the similarity matrix and the neighbor constraint matrix Merge as follows: ； in, Indicates The h-th matrix after iterations, is the initial value, is the weight parameter, α represents the initial normalized matrix of the network to be fused, represents the hth neighborhood constraint matrix, represents the fusion of different drug normalized matrices, represents the transpose of the h-th neighborhood constraint matrix, The final matrix after iterations is as follows: ； The fourth step is to embed the weighted matrix into the nonlinear fusion. The weighted matrix embeds additional neighbor information. The weighted matrix is: ； Step 5: Get the final drug similarity matrix As shown below: ； Similarly, the final disease similarity matrix can be obtained .

5. The drug-disease association prediction method based on matrix completion and dual-strategy graph reasoning according to claim 4, characterized in that: In step S21, the method of constructing a drug-disease heterogeneous network is as follows: Integrate the similarity matrix and the association matrix to construct a drug-disease heterogeneous network rich in biological information. The network includes two types of nodes: drug nodes and disease nodes. , represents m drug nodes, Represents n disease nodes. The similarity scores between drugs and between diseases are used as edge weights in the drug and disease similarity networks, respectively. When there is a drug-disease association in the dataset, an edge is established between the corresponding drug and disease nodes, and the association score is used as the weight of the edge. They are defined as the edge sets representing drug-drug, disease-disease, and drug-disease relationships, respectively, and the weights on these edges are expressed as , and Represented by, corresponding to drug-drug, disease-disease and drug-disease networks respectively, the drug-disease heterogeneous network can be expressed as ; The adjacency matrix of the heterogeneous network The construction form is as follows; ； Among them, RR represents the integrated drug similarity matrix, DD represents the integrated basic similarity matrix, represents the drug-disease association matrix, Represents the transpose of the drug-disease association matrix.

6. The drug-disease association prediction method based on matrix completion and dual-strategy graph reasoning according to claim 5, characterized in that: In step S22, the method of constructing the truncated inverse tangent rank minimization target matrix is ​​as follows: The underlying model of matrix completion is summarized as follows: ； in, represents the rank function, Ω represents the coordinate index set of the elements in L, and the operator represents the orthogonal projection operator applied to Ω; ； Minimizing the rank function is an NP-hard problem. Approximate rank function based on nuclear norm can solve this problem. The formula is as follows: ； , represents the nuclear norm of matrix X; Use the inverse tangent function instead of the rank function; ； in, is the i-th singular value of the matrix X, It is differentiable, concave, monotonically increasing, and unitarily invariant on [0,1]; ； in, , and represents the identity matrix, represents the projection matrix of matrix X applied to Ω, represents the projection matrix of matrix L applied to Ω, Indicates the truncation property. , indicating that the matrix A is an orthogonal matrix, Indicates that the matrix B is an orthogonal matrix; ； Among them, if is a balance parameter, and This means that all elements in X are in the range [0,1].

7. The drug-disease association prediction method based on matrix completion and dual-strategy graph reasoning according to claim 6, characterized in that: In step S23, the method of efficiently solving the truncated inverse tangent rank minimization using the alternating direction multiplier method is as follows: The directions are updated alternately in each iteration as follows: ； The augmented Lagrangian form can be expressed as: ； Among them, Z represents the Lagrange multiplier, β represents the penalty parameter, represents the objective function to be minimized, Indicates the truncation property. represents the Lagrangian parameter term, Represents the penalty term, all matrices Initialized as L matrix, during k iterations, calculate .

8. The drug-disease association prediction method based on matrix completion and dual-strategy graph reasoning according to claim 7, characterized in that: In step S31, the neighborhood similarity between drugs and diseases is calculated as follows: Assumed disease and medications The possibility of association between and Adjacent association scores correspond closely, and for a given drug ,choose Based on the most similar drugs, the comprehensive drug similarity indicates that this neighbor set , define the neighborhood similarity matrix , which is calculated as follows: ； disease The nearest neighbors of , expressed as , disease neighborhood similarity matrix Calculated in a similar manner; 。 9. The drug-disease association prediction method based on matrix completion and dual-strategy graph reasoning according to claim 8, characterized in that: In step S32 and step S33, the method of performing dual-strategy neighborhood constraint graph reasoning based on heterogeneous networks is as follows: Top-down graph reasoning strategy: ； Bottom-up graph reasoning strategy: ； in, and Represent the prediction results of top-down and bottom-up graph reasoning strategies respectively, where and Corresponding to the weights of the top-down and bottom-up strategies, respectively, before starting the reasoning process, the neighborhood similarity matrix must be and Perform normalization; ； ； The final prediction score matrix : ； and Represent the prediction results of top-down and bottom-up graph reasoning strategies respectively.

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