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

Abstract

The present 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. The method first calculates the Gaussian kernel and Laplace kernel similarity of drugs and diseases, and then fuses them using nonlinear fusion technology. The method takes 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. The method mainly focuses on the neighboring nodes of drugs and diseases, filtering out potential noise from more distant nodes. In addition, the method adopts top-down and bottom-up strategies based on the drug-disease heterogeneous network to predict drug-disease associations. The synergistic effect 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.

Description

Technical Field

[0001] The present 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, significant resources are often wasted on drugs that ultimately prove ineffective. Therefore, new strategies are urgently needed to reduce the time and cost of drug development. One such approach is drug repositioning, which involves finding new therapeutic uses for existing drugs. This strategy has gained significant 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, enabling faster clinical translation and significantly reducing development costs compared to developing drugs from scratch. Identifying drug-disease associations (DDAs) is crucial 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 therapeutic options. However, traditional biological assay-based drug-disease association prediction is often labor-intensive and time-consuming, significantly limiting the efficiency of the prediction process. Therefore, developing efficient computational methods is crucial to accelerating progress in this prediction process.

[0005] Graph reasoning technology is widely used in association prediction due to its high efficiency and interpretability. However, existing methods often cannot 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 uses rich biological information to construct a heterogeneous network 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 typically rely on local network reasoning or one-way 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 one-way reasoning paths 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 for drugs is crucial for advancing drug research and development. Graph reasoning techniques have shown great promise in predicting drug-disease associations, offering high convergence accuracy and efficiency. However, most existing methods cannot adequately address the large amount of missing information in drug-disease association networks. Furthermore, 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 existing technology that a large amount of missing information in the drug-disease association network is not 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 as follows:

[0010] The drug-disease association prediction method based on matrix completion and dual-strategy graph reasoning includes the following steps:

[0011] S1. Calculate the Gaussian kernel and Laplace kernel similarity of drugs and diseases, and fuse them using nonlinear fusion technology to obtain integrated drug similarity and disease similarity;

[0012] 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:

[0013] S21. Integrate the drug-disease association network with the similarity network to construct a drug-disease heterogeneous network;

[0014] S22. Using the adjacency matrix of the heterogeneous network as the target matrix for minimizing the truncated inverse tangent rank;

[0015] S23, then using the alternating direction multiplier method to solve the corresponding objective function;

[0016] S3. Design a dual-strategy neighborhood constraint graph reasoning to complete the prediction;

[0017] Step S3 specifically includes the following contents:

[0018] S31, calculating the neighborhood similarity of drugs and diseases based on adjacent nodes;

[0019] S32. Integrate the established drug and disease neighborhood similarity networks and the refined drug-disease association network into a comprehensive heterogeneous network;

[0020] S33, uses top-down and bottom-up methods to perform reasoning on this network, effectively capturing key associations.

[0021] Optionally, in step S1, the Gaussian kernel similarity between drugs and diseases is calculated as follows:

[0022] The vector stores the drug vector in 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:

[0023] ;

[0024] ;

[0025] Among them, the variable Indicates drug Gaussian kernel similarity, variable Indicates disease and Gaussian kernel similarity, To store the disease vector in 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:

[0026] ;

[0027] .

[0028] Optionally, in step S1, the Laplace kernel similarity between drugs and diseases is calculated as follows:

[0029] ;

[0030] ;

[0031] 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.

[0032] 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:

[0033] The first step is to normalize the drug similarity matrix one by one, as shown below:

[0034] ;

[0035] in, represents the h-th drug similarity matrix, is the h-th normalized drug similarity matrix;

[0036] The second step is to introduce the k-nearest neighbor method;

[0037] ;

[0038] in, represents the neighborhood constraint matrix, Indicates drug The neighbor set of the k most similar drugs;

[0039] The third step is to normalize the similarity matrix and the neighbor constraint matrix Merge as follows:

[0040] ;

[0041] in, Indicates the The hth 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 normalization matrices, represents the transpose of the h-th neighborhood constraint matrix, The final matrix after iterations is as follows:

[0042] ;

[0043] The fourth step is to embed the weighted matrix into the nonlinear fusion. The weighted matrix embeds additional neighbor information. The weighted matrix is:

[0044] ;

[0045] Step 5: Get the final drug similarity matrix As shown below:

[0046] ;

[0047] Similarly, the final disease similarity matrix can be obtained .

[0048] Optionally, in step S21, the drug-disease heterogeneous network is constructed as follows:

[0049] 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, and 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. The weights on these edges are expressed as 、 and Represented as, corresponding to drug-drug, disease-disease and drug-disease networks respectively, the drug-disease heterogeneous network can be expressed as ;

[0050] The adjacency matrix of the heterogeneous network The construction form is as follows;

[0051] ;

[0052] Where 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.

[0053] Optionally, in step S22, the method of constructing the truncated inverse tangent rank minimization target matrix is ​​as follows:

[0054] The underlying model of matrix completion is summarized as follows:

[0055] ;

[0056] 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;

[0057] ;

[0058] 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:

[0059] ;

[0060] , represents the nuclear norm of matrix X;

[0061] Use the inverse tangent function instead of the rank function;

[0062] ;

[0063] in, is the i-th singular value of matrix X, It is differentiable, concave, monotonically increasing, and unitarily invariant on [0,1];

[0064] ;

[0065] 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;

[0066] ;

[0067] Among them, if is a balance parameter, and This means that all elements in X are in the range [0,1].

[0068] Optionally, in step S23, the alternating direction multiplier method is used to efficiently solve the truncated inverse tangent rank minimization as follows:

[0069] The updated directions are alternating in each iteration as follows:

[0070] ;

[0071] The augmented Lagrangian form can be expressed as:

[0072] ;

[0073] 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 Lagrange parameter term, Represents the penalty term, all matrices Initialized as L matrix, during k iterations, calculate .

[0074] Optionally, in step S31, the neighborhood similarity between drugs and diseases is calculated as follows:

[0075] Assumed disease and medications The likelihood 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:

[0076] ;

[0077] disease The nearest neighbors of , expressed as , disease neighborhood similarity matrix Calculated in a similar way;

[0078] .

[0079] Optionally, in step S32 and step S33, the method of performing dual-strategy neighborhood constraint graph reasoning based on the heterogeneous network is as follows:

[0080] Top-down graph reasoning strategy:

[0081] ;

[0082] Bottom-up graph reasoning strategy:

[0083] ;

[0084] 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;

[0085] ;

[0086] ;

[0087] The final prediction score matrix :

[0088] ;

[0089] and Represent the prediction results of top-down and bottom-up graph reasoning strategies respectively.

[0090] After adopting the above technical solution, the beneficial effects of the present invention are:

[0091] This paper proposes a novel approach combining truncated inverse tangent rank minimization and dual-strategy neighborhood-constrained graph inference (TARMDNGI) to predict drug-disease associations. First, the Gaussian and Laplacian kernel similarities of drugs and diseases are calculated and then integrated using a nonlinear fusion technique. This paper introduces a new matrix completion technique, called truncated inverse tangent rank minimization (TARM). TARM uses the adjacency matrix of a heterogeneous drug-disease network as the target matrix and enhances the robustness and formability of edges in the drug-disease association network through truncated inverse tangent rank minimization. Furthermore, this paper proposes a dual-strategy neighborhood-constrained graph inference approach to predict drug-disease associations. This technique focuses on nodes adjacent to drugs and diseases, filtering out potential noise from more distant nodes. Furthermore, the dual-strategy neighborhood-constrained graph inference (DNGI) approach employs both top-down and bottom-up strategies to infer associations across the entire heterogeneous drug-disease network. The synergistic effect of these two strategies enhances the ability to comprehensively process complex structures and cross-domain associations within heterogeneous graphs, ensuring that the rich information within the network is fully utilized. BRIEF DESCRIPTION OF THE DRAWINGS

[0092] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. 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 any creative work.

[0093] Figure 1 It is an overall framework based on matrix completion and dual-strategy graph reasoning. DETAILED DESCRIPTION

[0094] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. 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 making creative efforts are within the scope of protection of the present invention.

[0095] The embodiments of the present application disclose a drug-disease association prediction method based on matrix completion and dual-strategy graph reasoning.

[0096] 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.

[0097] 1. Related Work

[0098] 1.1 Matrix Completion

[0099] Matrix completion techniques have been widely used in association prediction tasks due to their effectiveness in predicting missing values ​​in the matrix. 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 score through heterogeneous graph reasoning. Similarly, the AMCSMMA algorithm integrates three types of biological data to construct a heterogeneous network and recovers 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 uses truncated schatten p-norm minimization on the adjacency matrix to obtain the prediction score. However, these methods have limited ability to approximate the rank function, resulting in suboptimal solutions.

[0100] This paper introduces a new matrix completion technique, called TRAM. Unlike previous methods that struggled to accurately approximate 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 preserving a certain prior. This approach significantly reduces noise without distorting the underlying structure of the matrix. As a result, TRAM more closely approximates the rank function and can effectively fill in missing values ​​in a matrix.

[0101] 2.2 Graph Reasoning

[0102] Graph reasoning is an effective method for predicting the associations 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 perform 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 utilize global network information and capture complex information. In addition, they are easily affected by remote nodes during the reasoning process, which reduces their robustness.

[0103] This paper develops a novel graph reasoning technique, called DNGI, which focuses on leveraging nearby nodes of drugs and diseases in a network while ignoring potential noise from distant nodes. DNGI integrates top-down and bottom-up strategies to reason across the entire heterogeneous drug-disease network. The synergy of these two strategies enhances the ability to comprehensively process the complex structures and cross-domain connections within heterogeneous graphs, ensuring that the rich information in the network is fully utilized.

[0104] 2. Method Introduction

[0105] 2.1 Matrix Completion and Dual-Strategy Graph Reasoning Method (TARMDNGI)

[0106] Figure 1 The overall framework of the TARMDNGI method is presented. First, Gaussian and Laplacian kernel similarities between drugs and diseases are calculated and then integrated using nonlinear fusion techniques. Second, a novel 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 inference method is proposed to predict drug-disease associations.

[0107] 2.2 Dataset

[0108] 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 ​​represented as , where m corresponds to the number of drugs and n represents the number of diseases.

[0109] 2.3 Similarity Measurement

[0110] 2.3.1 Gaussian kernel similarity

[0111] The Gaussian kernel function is widely used to calculate biosimilarity due to its powerful performance and generalizability to various types of biological data. In the present invention, based on the known drug-disease association, the Gaussian kernel is applied to calculate the similarity between drugs and diseases. The vector stores the drug vector in row i of the association matrix, Represents the disease vector in the jth column of the storage association matrix. The calculation formula is as follows:

[0112] ; (1)

[0113] ; (2)

[0114] Among them, the variable Indicates drug Gaussian kernel similarity, variable Indicates disease and Gaussian kernel similarity, To store the disease vector in 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:

[0115] ; (3)

[0116] ; (4)

[0117] 2.3.2 Laplace kernel similarity

[0118] 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 between drugs and diseases is calculated using the following formula:

[0119] ; (5)

[0120] ; (6)

[0121] 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.

[0122] 2.4 Similarity Matrix Fusion

[0123] 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.

[0124] The first step is to normalize the drug similarity matrix one by one, as shown below:

[0125] ; (7)

[0126] in, represents the h-th drug similarity matrix, is the h-th normalized drug similarity matrix.

[0127] The second step is to introduce the weighted k-nearest neighbor (KNN) method. KNN assigns different weights to each neighbor based on their distance, with closer neighbors receiving larger weights. This method allows KNN to more accurately reflect local patterns and trends, making it more robust to noisy data and outliers.

[0128] ; (8)

[0129] in, represents the neighborhood constraint matrix, Indicates drug The neighbor set of the k most similar drugs.

[0130] The third step is to merge the normalized similarity matrix Ph and the neighbor constraint matrix Sh as follows:

[0131] ; (9)

[0132] in, Indicates the The hth 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 normalization matrices, represents the transpose of the h-th neighborhood constraint matrix.

[0133] The final matrix after iterations is as follows:

[0134] ; (10)

[0135] The fourth step is to embed the weighted matrix into the nonlinear fusion. The weighted matrix embeds additional neighbor information. The weighted matrix is:

[0136] ; (11)

[0137] Step 5: Get the final drug similarity matrix As shown below:

[0138] ; (12)

[0139] Similarly, the final disease similarity matrix can be obtained .

[0140] 2.5 Truncated Arctangent Rank Minimization

[0141] 2.5.1 Building a Heterogeneous Network

[0142] 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 expressed as 、 and They correspond to drug-drug, disease-disease and drug-disease networks respectively. Therefore, the drug-disease heterogeneous network can be expressed as .

[0143] The adjacency matrix of the heterogeneous network The construction form is as follows:

[0144] ; (13)

[0145] Where 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.

[0146] 2.5.2. Building TARM

[0147] Matrix completion (MC) is an effective data recovery technique for drug-disease association prediction methods based on matrix completion and dual-strategy graph reasoning. It reconstructs a complete matrix by filling in missing values. This paper applies matrix completion to address the extreme sparsity of drug-disease association matrices. The underlying model of matrix completion is summarized as follows:

[0148] ; (14)

[0149] 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.

[0150] ; (15)

[0151] 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 address this challenge. The formula is as follows:

[0152] ; (16)

[0153] , represents the nuclear norm of matrix X.

[0154] 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.

[0155] 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):

[0156] ; (17)

[0157] in, is the i-th singular value of matrix X, It is differentiable, concave, monotonically increasing, and unitarily invariant on [0,1]. This invention develops an effective matrix completion technique for drug-disease association prediction based on matrix completion and dual-strategy graph reasoning. Based on formula (17), it is further transformed.

[0158] ; (18)

[0159] 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.

[0160] The present invention introduces a regularization term to accommodate potential noise in the block matrix. All values ​​of the matrix are constrained to the interval [0, 1] to ensure their actual correlation. In summary, the present invention constructs the following model:

[0161] ; (19)

[0162] Among them, if is a balance parameter, and This means that all elements in X are in the range [0,1].

[0163] 2.5.3. Solving TARM

[0164] The present invention develops a framework for solving the model using ADMM, which simplifies the calculation by introducing new variables and alternating the update direction in each iteration.

[0165] ; (20)

[0166] The augmented Lagrangian form of formula (20) can be expressed as:

[0167] ;(twenty one)

[0168] 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 Lagrange parameter term, Represents the penalty term, all matrices Initialized to L matrix. During k iterations, calculate .

[0169] 2.6 Dual-Strategy Neighborhood Constrained Graph Reasoning

[0170] 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 utilizes top-down and bottom-up strategies for more comprehensive graph reasoning. The synergy between these two strategies enhances the ability to handle complex structures and cross-domain associations in heterogeneous graphs, ensuring full utilization of the network's rich information. The process first calculates the neighborhood similarity of drugs and diseases based on adjacent nodes. Then, the established drug-disease neighborhood similarity network and the refined 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.

[0171] 2.6.1. Calculating Neighborhood Similarity of Drugs / Diseases

[0172] Based on the assumption that similar drugs are more likely to be associated with similar diseases, the present invention further assumes that diseases and medications The likelihood of association between and Adjacent association scores are closely corresponding. The neighborhood similarity of drugs is calculated by analyzing the 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:

[0173] ;(twenty two)

[0174] Similarly, disease The nearest neighbors of , expressed as Disease neighborhood similarity matrix Calculated in a similar way.

[0175] ;(twenty three)

[0176] 2.6.2. Dual-Strategy Graph Reasoning

[0177] The present invention combines the improved DDA network with the drug and disease neighborhood similarity network to construct a comprehensive drug-disease heterogeneous network. It then uses top-down and bottom-up graph reasoning strategies for prediction. The graph reasoning model combines these dual strategies as shown below:

[0178] Top-down graph reasoning strategy:

[0179] ;(twenty four)

[0180] Bottom-up graph reasoning strategy:

[0181] ; (25)

[0182] in, and Represent the prediction results of top-down and bottom-up graph reasoning strategies respectively. and Corresponding to the weights of the top-down and bottom-up strategies respectively. Before starting the inference process, the neighborhood similarity matrix must be and , and normalize it.

[0183] ; (26)

[0184] ; (27)

[0185] (15) and (16) are in the iteration stop condition and Converges downward.

[0186] Next, the present invention combines the correlation matrix calculated by the top-down and bottom-up strategies to obtain the final prediction score matrix :

[0187] ; (28)

[0188] and Represent the prediction results of top-down and bottom-up graph reasoning strategies respectively.

[0189] This paper introduces a novel matrix completion technique, called TRAM, to enhance the robustness and formativeness of edges in drug-disease association networks. Unlike previous methods that struggle to accurately approximate 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 significant singular values ​​while minimizing unimportant singular values ​​and preserving a certain prior. This approach significantly reduces noise without distorting the underlying matrix structure.

[0190] This paper develops a novel graph reasoning technique, called DNGI, which focuses on leveraging nearby nodes of drugs and diseases in the network while ignoring potential noise from more distant nodes. DNGI integrates top-down and bottom-up strategies to reason across the heterogeneous drug-disease network. The synergistic effect of these two strategies enhances the ability to comprehensively process the complex structures and cross-domain connections within the heterogeneous graph, ensuring that the rich information in the network is fully utilized.

[0191] Experimental results demonstrate that TARMDNGI consistently outperforms state-of-the-art models on two drug-disease datasets, one lncRNA-disease dataset, and one microbiome-disease dataset. The outstanding performance observed in the two case studies further highlights the effectiveness of TARMDNGI in real-world applications.

[0192] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A drug-disease association prediction method based on matrix completion and dual-strategy graph reasoning, characterized by: The following steps are involved: S1. Calculate the Gaussian kernel and Laplace kernel similarity of 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: S21. Integrate the drug-disease association network with the similarity network to construct a drug-disease heterogeneous network; S22. Using the adjacency matrix of the heterogeneous network as the target matrix for minimizing the truncated inverse tangent rank; S23, then using the alternating direction multiplier method to solve the corresponding objective function; 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. Integrate the established drug-disease neighborhood similarity network and the refined drug-disease association network into a comprehensive heterogeneous network; S33, using top-down and bottom-up methods to perform reasoning on this network, effectively capturing key associations; In step S21, the method of constructing the 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, and 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. The weights on these edges are expressed as 、 and Represented as, 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 disease similarity matrix, represents the drug-disease association matrix, represents the transpose of the drug-disease association matrix; 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 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 Indicates that all elements of X are in the range [0,1]; In step S23, the alternating direction multiplier method is used to efficiently solve the truncated inverse tangent rank minimization method as follows: The updated directions are alternating 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 Lagrange parameter term, Represents the penalty term, all matrices Initialized as L matrix, during k iterations, calculate ; In step S31, the neighborhood similarity between drugs and diseases is calculated as follows: Assumed disease and medications The likelihood 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 constitute the neighbor set , expressed as , disease neighborhood similarity matrix Calculated in a similar way; ； 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.

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 in 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 in 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 nonlinear fusion technology is used to fuse the integrated drug similarity and disease similarity as follows: The first step is to normalize the drug similarity matrix 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 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 The hth matrix after iterations, is the initial value, is the weight parameter, Represents the initial normalized matrix of the network to be fused, represents the hth neighborhood constraint matrix, Represents the fusion of different drug normalization 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 .

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