A collaborative drug prediction method based on multi-source similarity matrix kernel fusion

Abstract

This invention belongs to the field of collaborative drug prediction technology and relates to a collaborative drug prediction method based on kernel fusion of multi-source similarity matrices. Firstly, this invention overcomes the limitation of single-source information provided by drug structure, ATC encoding, and target features by introducing two types of information describing drug ADMET features: enzyme and pathway. Secondly, it uses a restarted random walk algorithm to process the similarity matrix and calculates the topological similarity between nodes under different similarity matrices using Spearman's rank correlation coefficient, overcoming the shortcomings of existing methods that do not consider the interaction information between different drug similarity networks, enabling the model to more comprehensively capture the multi-dimensional features of drug similarity. Finally, it uses a kernel fusion network to fuse the five topological similarity matrices, effectively nonlinearly integrating the topological similarity matrices of drugs under different conditions, overcoming the problem of existing methods simply merging all similarity matrices by averaging, which masks the differences in the importance of different drug features.

Description

Technical Field

[0001] This invention belongs to the field of collaborative drug prediction technology, and in particular relates to a collaborative drug prediction method based on multi-source similarity matrix kernel fusion. Background Technology

[0002] Both traditional and modern medicine fully utilize the combined use of multiple active substances to treat diseases. Compared to monotherapy, drug combinations can generally improve efficacy, reduce side effects, and overcome drug resistance. Drug combinations are increasingly used to treat various complex diseases, such as hypertension, infectious diseases, and cancer. For example, triple-negative breast cancer is a malignant tumor with strong invasiveness, high metastasis rate, and poor prognosis. Lapatinib or rapamycin alone have little efficacy, but their combination therapy significantly increases the apoptosis rate of triple-negative breast cancer cells. However, some drug combinations may produce antagonistic effects or even worsen the disease. Therefore, accurately identifying synergistic drug combinations for specific diseases is crucial. Traditional synergistic drug combination discovery is mainly based on clinical trials and is limited to a few drugs, far from meeting the urgent need for anticancer drugs. Due to the vast number of possible drug combinations, traditional methods are costly and impractical. In recent years, with the continuous development of machine learning and deep learning, their application in drug development has become increasingly widespread, and a large number of machine learning and deep learning algorithms for predicting synergistic drug combinations have emerged. The current processing steps of collaborative drug prediction algorithms are generally as follows: ① Extract drug features, including drug structural features, ATC coding features, and target features; ② Construct multiple drug similarity matrices based on different drug features; ③ Fuse the multiple drug similarity matrices by averaging; ④ Input the fused drug similarity matrix into a neural network for collaborative drug prediction.

[0003] Existing methods only consider drug features such as structure, ATC encoding, and target sites. While these features are crucial for predicting synergistic drugs, they only provide partial information about the drug. ADMET (Absorption, Distribution, Metabolism, Excretion, and Toxicity) features provide information on the extent of drug absorption in the human body, the way it is distributed to tissues, its metabolic rate, excretion pathway, and potential toxicity. These features are essential for determining the bioavailability, safety, and efficacy of drugs. By incorporating ADMET features such as enzymes and pathways, we can more accurately predict drug performance in the human body, thereby improving the accuracy of synergistic drug prediction.

[0004] Existing methods, after constructing multiple drug similarity matrices based on different drug features, simply fuse these matrices by averaging, without considering that different drug features may have different contributions and importance in describing drug similarity. This may mask these differences in importance, thereby reducing the discriminative power of drug similarity and the predictive performance of the model.

[0005] Existing methods only consider the fusion of multiple drug similarity matrices, but do not take into account the interaction information between different drug similarity networks. Since different drug similarity networks are built based on different types of drug features, such as structure, ATC encoding, and targets, these networks represent the similarity of drugs at different levels, such as structural similarity, functional similarity, and mechanistic similarity. There are often potential correlations and interactions between these networks because multiple features of a drug are often not independent of each other. By considering the interaction information between different drug similarity networks, the model can more comprehensively capture the multi-dimensional features of drug similarity. Summary of the Invention

[0006] To address the aforementioned problems, this invention proposes a synergistic drug prediction method based on multi-source similarity matrix kernel fusion. First, the structural features of drugs are extracted using a multi-hop subgraph weighted random walk algorithm and a weighted MPNN algorithm. Second, five pieces of information are introduced: drug structure information, drug ATC encoding information, drug-target association information, drug-enzyme association information, and drug-pathway association information, describing drug similarity from multiple perspectives, including chemical properties, chemical structure, drug function, mechanism of action, and metabolic mechanism. Third, a restarted random walk algorithm and Spearman's rank correlation coefficient are used to capture the network structure information of the drug network to construct a topological similarity matrix. Then, a similarity matrix kernel fusion method is employed to effectively fuse different topological similarity matrices in a highly nonlinear and learnable manner, forming a final fused similarity matrix. Finally, the final fused similarity matrix is ​​input into a deep neural network to predict synergistic drug combinations.

[0007] The technical solution of this invention is as follows:

[0008] A collaborative drug prediction method based on multi-source similarity matrix kernel fusion, such as Figure 1 As shown, it includes the following steps:

[0009] S1. Based on the SMILES of drug molecules, use the RDKit tool to generate a two-dimensional undirected graph G = (V, E) corresponding to the drug molecules, where V is the set of nodes and E is the set of edges. Define N = |V| to represent the total number of nodes.

[0010] S2. Detecting drug community clusters using multi-hop subgraph random walks: Specifically, by seeding, the transition probability vector is calculated consistently starting from the nodes in each seed. The transition probability vector of each node in graph G is considered as a point in a vector space, and spectral clustering algorithms are used to cluster these vectors into different community clusters, thus obtaining the expanded drug community clusters for each seed. The calculation method for the transition probability vector is as follows:

[0011] First, calculate the transition probability vector of the k-hop neighbor subgraph of the starting node u after expanding by m(k) drug communities using the following formula:

[0012]

[0013] Among them, I u Let α be a vector whose u-th element is 1 and all other elements are 0. k ∈(0,1) is the attenuation parameter. For the k-hop neighbor subgraph of node u The above describes the random walk dynamic transition matrix, starting with u and extending to the m(k)th drug community cluster:

[0014]

[0015] in, k-hop neighbor subgraph of node u The adjacency matrix, Adjacency matrix The degree matrix, The weighted matrix extended to the m(k)th drug community group:

[0016]

[0017] Among them, μ1>0, 0<μ2<μ3<1, n(v i ) represents the i-th node v i The number of affiliated drug community groups Subgraph The jump weight between the i-th node and the j-th node:

[0018]

[0019] Among them, link k (i,j) represents a subgraph N is the number of links connecting the i-th node and the j-th node in the original graph G through k-1 nodes. k (i) represents a subgraph The set of neighboring nodes of the i-th node;

[0020] Finally, the transition probability vector of the starting node u is obtained as follows:

[0021]

[0022] Among them, ω i is the probability fusion weight, satisfying ω1 > ω2 >... > ω k > 0 and ω1 + ω2 +... + ω k = 1, i = 1, 2,..., k;

[0023] Fuse two drug community clusters with similarity greater than the threshold in the obtained drug community clusters to obtain n drug community clusters C = {c1, c2,..., c n}, where 0 < n ≤ π, and π is the set number of seeds; sort the obtained n drug community clusters in ascending order of conductivity, only retain the first a community clusters, dissolve all the remaining community clusters, and perform a new round of multi-hop subgraph random walk guided by the retained a community clusters. After iterating t times, the final drug community clusters C = {c1, c2,..., c s} are obtained, where s is the number of final drug community clusters; the conductivity is the fitness function of the drug community cluster:

[0024]

[0025]

[0026] Among them, L(c) represents the total number of external links of the nodes in the community cluster, M represents the number of edges in the graph G, d(u) represents the degree of the node u, and the lower the conductivity Ψ(c) of the community cluster c, the higher the cohesion of the community cluster;

[0027] S步骤3、利用第一个MPNN模块提取药物社区团局部特征:

[0028] Use the transition probability vector p(u) of each node u to weighted optimize the message passing function:

[0029]

[0030] Among them, is the information vector transferred from node v to node u, is the feature vector of node u on the (l - 1)th layer, is the feature vector of node v on the (l - 1)th layer, e vu is the attribute value indicating whether there is an edge between node v and node u. If there is an edge, then e vu = 1, otherwise e vu = 0, p(u) v represents the probability of node u transferring to node v;

[0031] Weighted optimization of the aggregation function using probabilistic fusion weights:

[0032]

[0033] in, ω is the sum of features passed to node u by its l-hop neighbors, N(u) is the set of neighboring nodes of node u, and ω is the sum of features passed to node u by its l-hop neighbors. l The fusion weight, representing the transition probability of the l-th hop subgraph, is weighted when aggregating the features passed by all l-hop nodes, where l = 1, 2, ..., k;

[0034] For each community group c i The resulting two-dimensional graph is processed by an MPNN with optimized message passing and message aggregation functions to extract graph features through message passing, message aggregation, and node representation updates in the following manner:

[0035]

[0036]

[0037]

[0038]

[0039] The MPNN module takes as input the initial features of each node in the graph. Initial features Initialized by graph G embedding, `Massage(·)` is the message passing function used to pass feature information of the neighboring nodes of node u; `Aggregation(·)` is the aggregation function used to aggregate the feature information passed by all the neighboring nodes of node u; `Update(·)` is the update function used to update the feature information of node u; and `Read(·)` is the read function used to extract the feature vector of the entire drug community subgraph, finally obtaining the drug community c. i eigenvectors i = 1, 2, ..., s, where the feature corresponds to the local community features of the drug, and T represents the transpose operation;

[0040] S4. Extract global drug features using the second MPNN module:

[0041] Each community group is treated as a node, and the characteristics of the node are the characteristics of the community group. Based on the original link relationships between the community groups, a community group subgraph G is constructed. com Then, using the same method as in S3, MPNN is employed for message passing, message aggregation, and node representation updates to extract the community cluster graph G. comFeatures h glob This feature corresponds to the global characteristics of the drug;

[0042] Ultimately, the feature matrix of a drug consists of local and global features, represented as follows:

[0043]

[0044] in, For drug community group c i The feature vectors of , where i takes values ​​from 1 to s, h glob H is the feature vector of the community subgraph. struct ∈R (s+1)×q q is the feature dimension;

[0045] S5. Construct a drug similarity matrix:

[0046] Drug multi-source information is defined to include drug structure information, drug-target association information, drug-enzyme association information, drug-pathway association information, and drug ATC code information. Target information, enzyme information, and pathway information related to the drug are extracted from relevant databases respectively. For the i-th drug d... i Target characteristics, pathway characteristics, and enzyme characteristics are defined as follows:

[0047]

[0048]

[0049]

[0050] Where x, y, and z represent the number of extracted target sites, pathways, and enzymes, respectively, and element t il p il e il The value can be 1 or 0, where 1 indicates that the l-th corresponding feature is related to drug d. i Related; a value of 0 indicates no relatedness.

[0051] The Jaccard similarity coefficient is used to calculate the similarity between the i-th drug and the j-th drug:

[0052]

[0053] in, This represents the calculation of the Jaccard similarity between drug i and drug j under the *feature*, where * represents target, path, or enzyme; thus, drug similarity matrices are obtained under the three feature conditions: target, pathway, and enzyme. and M represents the total number of drugs;

[0054] An ATC code represented by a vector consists of B entries, each representing a sub-code at a corresponding level in the ATC hierarchy. Assuming the first A entries of two vectors are identical, the ATC similarity between the two drugs is defined as follows: Obtain the drug similarity matrix under ATC feature conditions

[0055] Structural similarity among different drugs was calculated using the Hilbert-Schmidt independence criterion:

[0056]

[0057] Where HSIC(×) represents the HSIC function, and These represent the structural features of the i-th drug and the j-th drug, respectively. H is the centered kernel matrix, defined by H = I - (1 / q)ee T The calculation yields the drug similarity matrix under the given drug structure conditions, where I is the identity matrix, e is a q-dimensional vector of all 1s, Tr(·) represents the trace of the matrix (the sum of the diagonal elements), and T represents the transpose operation.

[0058] S6. Construct the topological similarity matrix:

[0059] The drug similarity matrix obtained from S5 is processed using a restart-based random walk algorithm:

[0060] p t =αp t-1 W+(1-α)p 0

[0061] Among them, P t Let be the state transition matrix at time step t, where the i-th element represents drug d. i Confidence score at time step t; P 0 Let be the initial state transition matrix, where the i-th element is 1 and the rest are 0; α∈(0,1) is the restart probability controlling the relative influence of local and global topological information; W is the normalized similarity matrix, denoted as . S represents the similarity score between the i-th drug and the j-th drug under the given condition. * Represents the similarity matrix, where * represents struct, atc, target, path, or enzyme; when Δp = p t -p t-1 The L1 norm is less than the positive number ε = 10 -9At this point, a stationary distribution vector p is obtained, which represents the diffusion state of a drug node;

[0062] definition In the similarity matrix S * The diffusion state of the i-th drug node is obtained to get all p i The constructed diffusion state matrix Where i = 1, ..., M, and M is the total number of drugs;

[0063] The Spearman rank correlation coefficient was used to calculate the topological similarity between nodes in the similarity matrices of different drugs.

[0064]

[0065] in, Represented by the i-th drug diffusion state matrix P in the information source* * And the j-th drug diffusion state matrix P in information source # # The Spearman rank correlation coefficient was calculated based on the given conditions. Represents the diffusion state matrix P * The element corresponding to the i-th row and k-th column;

[0066] Each drug similarity matrix is ​​combined with the other four drug similarity matrices. Based on the diffusion state of drug nodes in the current information source and the diffusion states of drug nodes in other information sources, the Spearman rank correlation coefficient between each drug in the current information source and each drug in other information sources is calculated. There are four Spearman rank correlation coefficient values ​​between each drug and the other drugs. These four values ​​are averaged and fused to construct the topological similarity matrix. The topological similarity matrix N is obtained by capturing and fusing the topological information of each drug node from other information sources from the perspective of drug structure. struct From the perspective of drug ATC encoding, the topological information of each drug node is captured and fused from other information sources to obtain the topological similarity matrix N. atc From the perspective of drug targets, the topological information of each drug node is captured and fused from other information sources to obtain the topological similarity matrix N. target From the perspective of drug pathways, topological information of each drug node is captured and fused from other information sources to obtain the topological similarity matrix N. path From an enzyme perspective, topological information of each drug node is captured and fused from other information sources to obtain a topological similarity matrix N. enmyze ;

[0067] S7. Perform kernel fusion on the topological similarity matrix:

[0068] The five similarity matrices obtained from S6 form the kernel tensor of the first layer, denoted as N. (1) ∈R M×M×5 :

[0069]

[0070] Each basic core express The topological similarity scores between the i-th and j-th elements are obtained by convolution operations, resulting in a kernel tensor N with 5 different basic kernels. (1) This will be transformed into a new tensor N with 5 basic kernels. (2) :

[0071]

[0072] in, It is a filter bank, each It is a learnable filter parameter vector, l = 1,...,5, where σ(·) is a differential nonlinear scalar activation function; the convolution operator uses the kernel tensor N. (1) and five filters W (1) As input, and for each filter Generate a basic kernel

[0073]

[0074] in, This represents the k-th element in the l-th filter of layer 1; each filter Convolution operation Output M×M kernel Through W (1) The five convolution operations in N (1) Transform a tensor of size M×M×5 into a new tensor of size M×M×5.

[0075] From the first-layer kernel tensor Initially, the kernel fusion network with L layers processes the tensor through a chain of nonlinear filter chains:

[0076]

[0077] These filters gradually transform low-level kernel tensors into highly nonlinear combinations of basic kernels:

[0078] N (L) =FusionNet (L-1) (N (1) ;Θ)

[0079] Where, Θ=[W(1) W (2) ,...,W (L-1) [] represents the trainable parameters involved in the filter bank; FusionNet (L -1) (·) represents the output of the (L-1)th layer of the kernel fusion network, where filter parameters are learned through supervised learning;

[0080] S8. Construct deep neural networks to predict whether drug pairs are synergistic:

[0081]

[0082] Z out =Sigmoid(Z) k W k +b k )

[0083] Where, N (L) ∈R M×M To merge the similarity matrices, This is the drug synergistic prediction label matrix; Pr(·) represents the entire prediction model, and θ is the set of all parameters involved in the model; Z out and Z k These are hidden neurons, k = 1, ..., l, with corresponding weight matrix W. out and W k b out and b k It is the bias vector; Sigmoid(·) is the Sigmoid activation function; f(·) is the Softmax activation function, used in the last layer to convert the output layer values ​​into probabilities. Elements with a value greater than 0.5 are set to 1, and elements with a value less than or equal to 0.5 are set to 0.

[0084] Furthermore, the seed in S2 is initialized using the following rules:

[0085] Sort all nodes in descending order of degree, and select nodes with higher degree as seeds.

[0086] If a seed contains more than 1 node, then the nodes within the seed must satisfy the following:

[0087] Jaccard(N(i),N(j))>Φ

[0088] Where N(i) represents the set of neighboring nodes of the i-th node in graph G, Jaccard(N(i),N(j)) is a function to calculate the Jaccard similarity between two sets N(i) and N(j), and Φ is the similarity threshold.

[0089] Initialize π seeds according to the initialization rules to form an initial seed set S = {s1, s2, ..., s...} π}

[0090] Furthermore, the spectral clustering algorithm described in S2 treats data points as vectors, performs spectral decomposition on these vectors, and finally clusters these vectors. The input to the spectral clustering algorithm is:

[0091] P = [p(u1), p(u2), ..., p(u...] N )] T

[0092] Where P represents the matrix consisting of the transition probability vectors of all nodes in graph G, and each row of the matrix represents the transition probability vector of a node; u1, u2, ..., u N Let N be the nodes in graph G; N is the total number of nodes in graph G; and T represents the transpose operation.

[0093] Furthermore, the method in S2 for fusing two drug communities with a similarity greater than a threshold is as follows:

[0094] c i =c i ∪c j stJaccard(c i ,c j )>θ

[0095] Among them, c i Let θ represent the node set of the i-th community group, and θ be the similarity threshold.

[0096] Furthermore, if L is set to 4 in S7, the specific calculation process is as follows:

[0097] Through filter bank W (1) ∈R 5×5 Perform convolution operations to obtain five secondary intermediate kernels N of size M×M. (2) Then, by using three filters N (2) Transformed into a three-level intermediate core N (3) ∈R M×M×3 Finally, through a filter N (3) Transform into an integral similarity kernel N (4) ∈R M×M×1 ;

[0098] Each element N of the final integrator kernel (4) (i,j) is calculated using the following formula:

[0099]

[0100] in, also, and Represented using a lower-level kernel:

[0101]

[0102] The beneficial effects of this invention are as follows:

[0103] Compared with existing technologies, this invention proposes to introduce two pieces of information describing the characteristics of the drug ADMET: enzymes and pathways. This enriches the characteristics of the drug and describes the similarity of the drugs from multiple perspectives, such as chemical properties, chemical structure, drug function, mechanism of action, and metabolic mechanism.

[0104] Furthermore, this invention uses a restarted random walk algorithm combined with Spearman's rank correlation coefficient to calculate the topological similarity between nodes under different similarity matrices, taking into account the interaction information between different drug similarity networks, so that the model can more comprehensively capture the multi-dimensional features of drug similarity.

[0105] Finally, this invention employs a kernel fusion network to fuse the five topological similarity matrices, effectively integrating the topological similarity matrices of drugs under different conditions in a nonlinear manner, taking into account the fundamental fact that different drug features may have different contributions and importance in describing drug similarity. Attached Figure Description

[0106] Figure 1 This is the overall flowchart of the present invention.

[0107] Figure 2 This is a schematic diagram of the overall network structure of matrix-core fusion.

[0108] Figure 3 This is a schematic diagram illustrating the conversion of the first-layer kernel tensor of the similarity matrix into the second-layer kernel tensor. Detailed Implementation

[0109] The present invention will now be described in detail with reference to the accompanying drawings.

[0110] The synergistic drug prediction method proposed in this invention can be summarized as consisting of four main modules: ① drug structural feature extraction module; ② similarity matrix construction module; ③ drug similarity matrix fusion module; ④ synergistic drug prediction module. Specifically:

[0111] Module 1: Drug Structure Feature Extraction Module

[0112] Step 1: Convert drug molecules into two-dimensional diagrams based on drug SMILES.

[0113] Based on the SMILES of drug molecules, the RDKit tool is used to generate a two-dimensional undirected graph G = (V, E) corresponding to the drug molecules, where V is the set of nodes, E is the set of edges, and N = |V| represents the total number of nodes.

[0114] Step 2: Detecting drugs in community groups using multi-hop subgraph weighted random walks

[0115] The multi-hop subgraph weighted random walk mainly consists of four parts: seeding, expansion rule definition, seed expansion, and iterative update. Its core idea is to use the information of the expanded drug community to guide the subsequent expansion of the drug community.

[0116] (1) Seeding. The initial seed is a key component of drug community detection. A seed can contain only a single node or multiple nodes simultaneously. For seeds containing multiple nodes, the nodes should have high node degree and nearest neighbor similarity to ensure that the nodes in the seed belong to the same community. Initialize π seeds according to the following rules (π should be large enough to ensure that it is greater than the number of possible communities), forming the initial seed set S = {s1, s2, ..., s...} π}:

[0117] ① Sort all nodes in descending order of degree, and select nodes with higher degree as seeds first;

[0118] ② If a seed contains more than 1 node, then the nodes within the seed should satisfy:

[0119]

[0120] Where N(i) represents the set of neighboring nodes of the i-th node in graph G, and Jaccard(A,B) is a function for calculating the Jaccard similarity between sets A and B. This is the similarity threshold.

[0121] (2) Extended rule definition (multi-hop subgraph weighted random walk dynamic transition matrix). The elements in the adjacency matrix A of the two-dimensional undirected graph G corresponding to the drug molecule are represented as follows:

[0122]

[0123] Among them, v i Let represent the i-th node. Then, embedding operations are performed on the nodes in graph G to obtain the initial features of each node in graph G, which are used as the input to the subsequent Message Passing Neural Network (MPNN).

[0124] Given an original undirected graph G that has been expanded to include m drug communities, a random walk dynamic transition matrix P is constructed based on the adjacency matrix A after expanding to the m-th drug community. m,1 :

[0125]

[0126] Where D is the degree matrix of adjacency matrix A; Q m,1 This is the weighted matrix extended in the original undirected graph G to the m-th drug community. This represents the Hadamarda complex. Q m The elements in can be represented as:

[0127]

[0128] Among them, μ1>0, 0<μ2<μ3<1, n(v i ) represents the i-th node v i Number of affiliated drug community groups. Weighted matrix Q m,1 The significance is as follows: Maintain the probability that the walker continues to explore new nodes (nodes not yet visited), increase the probability that the walker leaves the current drug community to explore new nodes by μ1, decrease the probability that the walker returns to an already explored drug community from a newly explored node by μ2, and decrease the probability that the walker enters another already explored drug community by μ3. The weighted matrix's role is to use the expanded drug community information to guide the subsequent expansion of drug communities.

[0129] In the original undirected graph G, relative to the starting node u, its transition probability vector after expanding by m drug communities is:

[0130]

[0131] Among them, I u Let be a vector whose u-th element is 1 and all other elements are 0, and α1∈(0,1) be the decay parameter; This represents the dynamic transition matrix of a random walk in the original undirected graph G, starting with node u and expanded with m drug communities.

[0132] For each node u (u∈V) in graph G, based on the one-hop neighbor subgraph starting with u. (i.e., the initial undirected graph G), construct a two-hop neighbor subgraph with node u as the starting node according to the following rules.

[0133] ①If nodes u, v and w are in In an undirected graph G (i.e., initially undirected graph), if u is adjacent to v and v is adjacent to w, then in the two-hop neighbor subgraph starting with u... In the diagram, u and w are directly adjacent, and the intermediate node is deleted by v;

[0134] ② Apart from the above modifications, all adjacency relationships remain unchanged.

[0135] In subgraph Following the same rules, a random walk is performed to obtain the transition probability vector after expanding the two-hop neighbor subgraph of node u by m drug communities:

[0136]

[0137] Where α2∈(0,1) is the attenuation parameter. For the two-hop neighbor subgraph of node u The dynamic transition matrix of the random walk after extending to the m-th drug community, with u as the starting node, can be expressed as:

[0138]

[0139] in, The two-hop neighbor subgraph of node u The adjacency matrix, Adjacency matrix The degree matrix, This is the weighted matrix extended to the m-th drug community group. The elements in It can be represented as:

[0140]

[0141] in, Subgraph The jump weight between the i-th node and the j-th node can be expressed as:

[0142]

[0143] Where link2(i,j) represents a subgraph The number of links connecting the i-th node and the j-th node in the original undirected graph G, where N2(i) represents the subgraph. The set of neighboring nodes of the i-th node.

[0144] Similarly, by analogy, using the same rules, we can calculate the k-1 hop neighbor subgraph based on node u (u∈V). Obtain the k-hop neighbor subgraph for each node u (u∈V). The transition probability vector is extended to include m drug community groups:

[0145]

[0146] Among them, I u Let α be a vector whose u-th element is 1 and all other elements are 0. k ∈(0,1) is the attenuation parameter. For the k-hop neighbor subgraph of node u The dynamic transition matrix of the random walk after extending to the m-th drug community, with u as the starting node, can be expressed as:

[0147]

[0148] in, k-hop neighbor subgraph of node u The adjacency matrix, Adjacency matrix The degree matrix, This is the weighted matrix extended to the m-th drug community group. The elements in It can be represented as:

[0149]

[0150] in, Subgraph The jump weight between the i-th node and the j-th node can be expressed as:

[0151]

[0152] Among them, link k (i,j) represents a subgraph N is the number of links connecting the i-th node and the j-th node in the original undirected graph G, which are linked by k-1 nodes. k (i) represents a subgraph The set of neighboring nodes of the i-th node.

[0153] Finally, the transition probability vector of the starting node u (u∈V) is:

[0154]

[0155] Where, ω i (i = 1, 2, ..., k) are the probability fusion weights, satisfying ω1 > ω2 > ... > ω k >0 and ω1+ω2+...+ω k =1.

[0156] (3) Seed expansion. The conductivity Ψ(c) of community c in graph G is defined as follows:

[0157]

[0158]

[0159] Where L(c) represents the total number of external links of nodes within a community c, Edge represents the number of edges in graph G, and d(u) represents the degree of node u. The lower the conductivity Ψ(c) of community c, the higher the cohesion of the community c, indicating a better community c structure.

[0160] Using conductivity as the fitness function of the drug community, for each seed s in the initial seed set S... i First, from s i The nodes in graph G uniformly begin calculating the transition probability vector. Then, the transition probability vector of each node in graph G is treated as a point in a vector space, and these vectors are clustered into different community groups using a spectral clustering algorithm (the spectral clustering algorithm treats data points as vectors, performs spectral decomposition on these vectors, and finally clusters them). The input to the spectral clustering algorithm is:

[0161] P = [p(u1), p(u2), ..., p(u...] N )] T

[0162] Where P represents the matrix consisting of the transition probability vectors of all nodes in graph G, and each row of the matrix represents the transition probability vector of a node; u1, u2, ..., u N Each node in graph G; N is the total number of nodes in graph G; T represents the transpose operation. Extract the nodes containing the seed s. i Community group c i Mark community group c i All nodes in the set indicate that they belong to at least one existing community group. Each drug community group is obtained through various sub-expansions, resulting in π drug communities C = {c1, c2, ..., c...} generated from all π seeds. π Then, communities with high similarity are merged:

[0163]

[0164] Among them, c i This represents the node set of the i-th community group. The similarity threshold is used. Through fusion processing, n drug community groups C = {c1, c2, ..., c...} are obtained. n}, where 0 <n≤π。

[0165] (4) Iterative update. After the multi-hop subgraph weighted random walk first completes the extraction of drug community cliques, all community cliques are sorted in ascending order of conductivity, and only the first a (0 < a ≤ n) community cliques are retained. The remaining community cliques are all dissolved, and a new round of multi-hop subgraph random walk is carried out guided by the retained a community cliques. After iterating t times in this way, the final drug community cliques C = {c1, c2,..., c s}, where s is the number of final drug community cliques.

[0166] Step 3: Use the weighted MPNN to extract drug local structure features

[0167] First, the message passing function of the MPNN is optimized by weighting. Specifically, the message passing function of the original MPNN can be expressed as:

[0168]

[0169] where, is the information vector passed from node v to node u, is the feature vector of node u on the l-th layer; e vu is the attribute value indicating whether there is an edge between node v and node u. If there is an edge, then e vu = 1, otherwise e vu = 0.

[0170] In step 2, the transition probability vector p(u) of each node u (u ∈ V) has been calculated. This vector indicates the transition probability of node u to all other nodes in the graph. The higher the transition probability of a certain node v (v ∈ V), the higher the possibility that node u and node v belong to the same drug community clique, which also indicates that node v is more important to node u than other nodes. Therefore, in this invention, the transition probability vector p(u) of each node u (u ∈ V) is used to optimize the message passing function by weighting:

[0171]

[0172] where, (p(u)) v is the v-th element in the p(u) vector, representing the probability of node u transitioning to node v. In this way, the features passed from node v to node u will be weighted by the transition probability to distinguish the importance differences of different nodes at the same hop count.

[0173] Secondly, the message aggregation function of the MPNN is optimized by weighting. Specifically, the message aggregation function of the original MPNN can be expressed as:

[0174]

[0175] Where N(u) is the set of neighboring nodes of node u; The sum of features passed to node u by its l-hop neighbors represents the total features that node u receives. Node u collects information from its neighbors to update its own features. Since the importance of messages passed by nodes varies with different hop counts (the higher the hop count, the lower the importance), the probability fusion weight ω from step two is considered. i (i=1,2,...,k, satisfying ω1>ω2>...>ω k >0 and ω1+ω2+...+ω k =1) to perform weighted optimization on the aggregate function:

[0176]

[0177] Where, ω l The fusion weight, representing the transition probability of the l-th hop subgraph, is weighted when aggregating the features passed by all l-hop nodes, in order to distinguish the differences in the importance of nodes under different hop numbers.

[0178] For each community group c i The two-dimensional graph (i = 1, 2, ..., s) is used by an MPNN with optimized message passing and message aggregation functions to perform message passing, message aggregation, and node representation updates in the following manner to extract graph features:

[0179]

[0180]

[0181]

[0182]

[0183] in, Initialization is performed by embedding graph G in step one; h u This section describes the feature information of node u after aggregating the feature information of its multi-hop neighbors; T represents the transpose operation. `Massage(·)` is the message passing function used to pass the feature information of node u's neighbors; `Aggregation(·)` is the aggregation function used to aggregate the feature information passed by all of node u's neighbors; `Update(·)` is the update function used to update the feature information of node u; `Read(·)` is the read function used to extract the feature vector of the entire drug community subgraph. Finally, the feature vector of the drug community c is obtained. i eigenvectors This feature corresponds to the local features of the drug's community cluster.

[0184] Step 4: Extract global structural features of the drug using MPNN

[0185] In step three, feature vectors for each community cluster in a drug have been extracted. Now, each community cluster is considered a node, and the features of the node are the features of the community cluster. Based on the original link relationships between the communities, a community cluster subgraph G is constructed. com Then, similar to the method in step three, MPNN is used for message passing, message aggregation, and node representation updates to extract the community cluster graph G. com Features h glob This feature corresponds to the global characteristics of the drug.

[0186] Ultimately, the structural feature matrix of a drug, composed of local and global features, can be represented as:

[0187]

[0188] in, For drug community group c i eigenvectors, h glob H is the feature vector of the community subgraph. struct ∈R (s+1)×q s represents the number of community groups for the current drug (variable), and q represents the feature dimension.

[0189] Module 2: Similarity Matrix Construction Module

[0190] In this section, five drug similarity matrices are first constructed based on multi-source drug information, and then a topological similarity matrix is ​​constructed based on the topological similarity between each drug similarity matrix and the other four drug similarity matrices.

[0191] Step 5: Construct a drug similarity matrix

[0192] Drug multi-source information includes drug structure information, drug-target association information, drug-enzyme association information, drug-pathway association information, and drug ATC encoding information, each corresponding to a set of feature descriptors. Drug-related target information was extracted from the DrugBank database, yielding 1162 drug-related targets. Therefore, for the i-th drug d... i Its target features can be defined as Where x = 1162, t il =1 indicates that the l-th target and drug d i Related, otherwise t il =0. Similarly, drug-related pathway information was extracted from the DrugBank database, yielding 957 drug-associated pathways. Pathway characteristics can be defined as... Where y = 957, p il =1 indicates that the l-th pathway is related to drug di Related, otherwise p il =0. Enzyme information related to drugs was extracted from the DrugBank database, resulting in 202 drug-associated enzymes. Enzyme characteristics can be defined as... Where z = 202, e il =1 indicates that the l-th enzyme and drug d i Related, otherwise e il =0.

[0193] The Jaccard similarity coefficient is used to calculate the similarity between the i-th drug and the j-th drug, as shown below:

[0194]

[0195] in, This represents calculating the Jaccard similarity between drug i and drug j under the feature * (where * can be target, path, or enzyme); ∩ and ∪ represent intersection and union operations, respectively. Drug similarity matrices are calculated under the three feature conditions: target, pathway, and enzyme. and M represents the total number of drugs. Since ATC encoding provides hierarchical semantic codes for drugs (e.g., ATC code B01AC06), the ATC similarity between two drugs is calculated by examining the common sub-codes from top to bottom in the hierarchical structure. If the ATC code represented by a vector consists of B entries, each representing a sub-code at the corresponding level in the ATC hierarchy, and if the first A entries of two vectors are identical, then the ATC similarity between the two drugs is... Obtain the drug similarity matrix under ATC feature conditions Regarding the structural characteristics of the drug H struct ∈R (s+1)×q Although the number of community groups *s* for each drug is not uniform, the dimension *q* of the community group features and the global features of each drug is the same. Therefore, the Hilbert-Schmidt Independence Criterion (HSIC) is used to calculate the structural similarity between different drugs, as shown below:

[0196]

[0197] Where HSIC(,) represents the HSIC function; and These represent the structural features of the i-th drug and the structural features of the j-th drug, respectively. H is the centered kernel matrix, defined by H = I - (1 / q)ee TThe calculation yields a matrix where I is the identity matrix and e is a q-dimensional vector of all ones; Tr(·) represents the trace of the matrix, i.e., the sum of the elements on the diagonal; T represents the transpose operation. This provides the drug similarity matrix under the given drug structure conditions.

[0198] Step 6: Construct the topological similarity matrix

[0199] Unlike approaches that directly fuse multiple features, this invention uses a Random Walk with Restart (RWR) algorithm to process the similarity matrix. The RWR algorithm captures the network's topology through random walks and features few hyperparameters and low computational cost, thus finding wide application in complex network analysis and feature representation learning. Applying the RWR algorithm to the similarity matrix (network) can be formulated as follows:

[0200] p t =αp t-1 W+(1-α)p 0

[0201] Among them, P t Let be the state transition matrix at time step t, where the i-th element represents drug d. i Confidence score at time step t; P 0 Let be the initial state transition matrix, where the i-th element is 1 and the rest are 0; α∈(0,1) is the restart probability controlling the relative influence of local and global topological information; W is the normalized similarity matrix, which can be represented as... S represents the similarity score between the i-th drug and the j-th drug under the given condition. * Represents the similarity matrix (* represents struct, atc, target, path, or enzyme). When Δp = p t -p t-1 The L1 norm is less than a small positive number ε = 10 -9 At this point, a stationary distribution vector p can be obtained, which represents the diffusion state of a drug node. To facilitate the differentiation of the diffusion states of different drug nodes under different similarity matrices (networks), let... In the similarity matrix S * (* represents the diffusion state of the i-th drug node under struct, atc, target, path, or enzyme) then all p can be obtained. i The diffusion state matrix consisting of (i = 1, ..., M) Where M represents the total number of drugs, and * represents struct, atc, target, path, or enzyme.

[0202] Then, the Spearman rank correlation coefficient was used to calculate the topological similarity between nodes in the different drug similarity matrices. The Spearman rank correlation coefficient was calculated as follows:

[0203]

[0204] in, Represented by the i-th drug diffusion state matrix P in the information source* * (* represents struct, atc, target, path, or enzyme,) and the j-th drug diffusion state matrix P in the information source #. # The Spearman rank correlation coefficient is calculated based on the given conditions; M is the total number of drugs. Represents the diffusion state matrix P * The element corresponding to the i-th row and k-th column. Each drug similarity matrix is ​​combined with the other four drug similarity matrices. Based on the diffusion state of drug nodes under the current information source and the diffusion state of other drug nodes under other information sources, the Spearman rank correlation coefficient between each drug under the current information source and each drug under other information sources is calculated. This value is obtained from the perspective of a certain drug under the current information source, capturing and fusing the topological information of each drug node from other information sources. There are four Spearman rank correlation coefficient values ​​between each drug and other drugs. These four values ​​are averaged and fused to construct the topological similarity matrix. Through the processing in step six, from the perspective of drug structure, the topological information of each drug node is captured and fused from other information sources to obtain the topological similarity matrix N. struct From the perspective of drug ATC encoding, the topological information of each drug node is captured and fused from other information sources to obtain the topological similarity matrix N. atc From the perspective of drug targets, the topological information of each drug node is captured and fused from other information sources to obtain the topological similarity matrix N. target From the perspective of drug pathways, topological information of each drug node is captured and fused from other information sources to obtain the topological similarity matrix N. path From an enzyme perspective, topological information of each drug node is captured and fused from other information sources to obtain a topological similarity matrix N. enmyze .

[0205] Module 3: Topological similarity matrix fusion module, the matrix fusion model is as follows: Figure 2 As shown.

[0206] Step 7: Perform kernel fusion on the topological similarity matrix

[0207] To effectively integrate the topological similarity matrices of drugs under different conditions nonlinearly, a kernel fusion network is used to fuse five topological similarity matrices. The motivation for fusing five similarity matrices into three, and then further fusing these three into a single similarity matrix, is as follows: ① Fusion of the structural similarity matrix and the ATC-encoded similarity matrix: The structural similarity matrix considers the molecular structural similarity between drugs, while the ATC-encoded similarity matrix reflects the similarity of therapeutic pathways and action categories. Fusion of these two matrices comprehensively considers the similarity of drugs in molecular structure and therapeutic pathways, thereby increasing the accuracy and comprehensiveness of similarity calculation; ② Fusion of the enzyme similarity matrix and the pathway similarity matrix: The enzyme similarity matrix reflects the similarity of drugs in metabolic pathways, i.e., they are metabolized by similar enzymes, while the pathway similarity matrix considers the similarity of the effects of biological pathways on drugs. Fusion of these two matrices comprehensively considers the similarity of drugs at the molecular level and in biological pathways, which is particularly important when studying complex diseases; ③ The target similarity matrix represents the similarity of the targets of drug action. By combining the information obtained from the first two steps with target similarity information, a more comprehensive and integrated topological similarity matrix can be obtained by considering the similarity of drugs in molecular structure, therapeutic pathway, mechanism of action, and target level. To further explain, during the transformation from the second-layer tensor to the third-layer tensor, each similarity matrix captures some feature information from the other four similarity matrices. This is to avoid completely isolating feature information from different sources. However, in this feature extraction and fusion process, the feature fusion weight between the structural similarity matrix and the ATC coding similarity matrix, and between the enzyme similarity matrix and the pathway similarity matrix, is greater, while the target similarity matrix treats the features of the other four similarity matrices equally. Next, we will describe the details of the transformation from the lower-layer kernel tensor to the higher-layer kernel tensor.

[0208] The kernel tensor of the first layer is represented as N. (1) ∈R M×M×5 It consists of five basic kernels (similarity matrices), namely Each basic core (* represents struct, atc, target, path, or enzyme). (i = 1, ..., M, j = 1, ..., M) represents The topological similarity score between the i-th and j-th elements. Through convolution operations, a kernel tensor N with 5 different basic kernels is generated. (1) This will be transformed into a new tensor N with five basic kernels. (2) The convolution operation is as follows:

[0209]

[0210] in, It is a filter bank, each It is a learnable filter parameter vector, where σ(·) is a differential nonlinear scalar activation function, such as the rectified linear unit (ReLU) or hyperbolic tangent (Tanh). The convolution operator uses the kernel tensor N. (1) and five filters W (1) As input, and for each filter Generate a basic kernel The calculation formula is as follows:

[0211]

[0212] in, This represents the k-th element in the l-th filter of layer 1. Therefore, each filter... Convolution operation Output M×M kernel Through W (1) The five convolution operations in N (1) Transform a tensor of size M×M×5 into a new tensor of size M×M×5. like Figure 3 As shown.

[0213] From the first-layer kernel tensor Beginning, each of them (* represents struct, atc, target, path, or enzyme) is the basic kernel of the first layer. A kernel fusion network with L layers processes tensors through a nonlinear filter chain, i.e.:

[0214]

[0215] These filters gradually transform low-level kernel tensors into highly nonlinear combinations of fundamental kernels. The transformation can be expressed as:

[0216] N (L) =FusionNet (L-1) (N (1) ;Θ)

[0217] Where, Θ=[W (1) W (2) ,...,W (L-1) [] represents the trainable parameters involved in the filter bank; FusionNet (L -1) (·) represents the output of layer (L-1) of the kernel fusion network. Furthermore, similar to the basic idea of ​​CNNs, filter parameters can be learned through supervised learning. Therefore, the final integral kernel of the output can non-linearly fuse the basic kernels in a desired manner.

[0218] This invention sets L to 4. First, the first level is the kernel tensor N, which consists of five basic kernels. (1) ∈R M×M×5 Then, through filter bank W (1) ∈R 5×5 Perform convolution operations to obtain five secondary intermediate kernels N of size M×M. (2) , such as equation The above is mentioned. Then, by using three filters... N (2) Transformed into a three-level intermediate core N (3) ∈R M×M×3 Finally, it is filtered. N (3) Transform into an integral similarity kernel N (4) ∈R M×M×1 .

[0219] Each element N of the final integrator kernel (4) (i,j) is calculated using the following formula:

[0220]

[0221] in, also, and This can be represented using a lower-level kernel:

[0222]

[0223] Module 4: Collaborative Drug Prediction Module

[0224] Step 8: Predicting Synergistic Drugs

[0225] Construct the following deep neural network to predict whether drug pairs are synergistic:

[0226]

[0227] Z out =Sigmoid(Z) k W k +b k )

[0228] Where, N (4) ∈R M×M To merge the similarity matrices, This is the drug synergistic prediction label matrix; Pr(·) represents the entire prediction model, and θ is the set of all parameters involved in the model; Z out and Z k(k = 1, ..., l) are hidden neurons, and their corresponding weight matrix W out and W k b out and b k `f` is the bias vector; `Sigmoid(·)` is the Sigmoid activation function; `f(·)` is the Softmax activation function, used in the last layer to convert the output layer values ​​into probabilities. Elements with a value greater than 0.5 are set to 1, and elements with a value less than or equal to 0.5 are set to 0.

[0229] This invention first overcomes the limitation of single-source information provided by drug structure, ATC encoding, and target features by introducing two types of information describing drug ADMET characteristics: enzyme and pathway. Second, it employs a restarted random walk algorithm to process the similarity matrix and uses Spearman's rank correlation coefficient to calculate the topological similarity between nodes under different similarity matrices. This overcomes the shortcomings of existing methods that do not consider the interaction information between different drug similarity networks, enabling the model to more comprehensively capture the multi-dimensional features of drug similarity. Finally, it uses a kernel fusion network to fuse the five topological similarity matrices, effectively nonlinearly integrating the topological similarity matrices of drugs under different conditions. This overcomes the shortcomings of existing methods that simply fuse all similarity matrices by averaging, which masks the differences in the importance of different drug features and reduces the discriminative power of drug similarity and the predictive performance of the model.

Claims

1. A collaborative drug prediction method based on multi-source similarity matrix kernel fusion, characterized in that, Includes the following steps: S1. Based on the SMILES of drug molecules, use the RDKit tool to generate a two-dimensional undirected graph G = (V,E) corresponding to the drug molecules, where V is the set of nodes and E is the set of edges. Define N = |V| to represent the total number of nodes. S2. Detecting drug community clusters using multi-hop subgraph random walks: Specifically, by seeding, the transition probability vector is calculated consistently starting from the nodes in each seed. The transition probability vector of each node in graph G is considered as a point in a vector space, and spectral clustering algorithms are used to cluster these vectors into different community clusters, thus obtaining the expanded drug community clusters for each seed. The calculation method for the transition probability vector is as follows: First, calculate the transition probability vector of the k-hop neighbor subgraph of the starting node u after expanding by m(k) drug communities using the following formula: ， Among them, I u Let α be a vector whose u-th element is 1 and all other elements are 0. k ∈(0, 1) is the attenuation parameter. For the k-hop neighbor subgraph of node u The above describes the random walk dynamic transition matrix, starting with u and extending to the m(k)th drug community cluster: ， in, k-hop neighbor subgraph of node u The adjacency matrix, Adjacency matrix The degree matrix, The weighted matrix extended to the m(k)th drug community group: ， Among them, μ1> 0, 0< μ2< μ3< 1, n(v i ) represents the i-th node v i The number of subordinate drug community groups, λu,k ij represents the subgraph. The jump weight between the i-th node and the j-th node: ， Among them, link k (i, j) represents a subgraph N is the number of links connecting the i-th node and the j-th node in the original graph G through k-1 nodes. k (i) represents a subgraph The set of neighboring nodes of the i-th node; The final transition probability vector of the starting node u is: ， Where, ω i The probabilistic fusion weights satisfy ω1> ω2> ...> ω k > 0 and ω1 + ω2 + ... + ω k =1, i = 1, 2, ..., k; Two drug communities with similarity greater than a threshold are merged to obtain n drug communities C={c1, c2, ..., c n }, where 0 < n ≤ π, and π is the set number of seeds; sort the obtained n drug communities in ascending order of conductivity, keep only the first a communities, and disband all the remaining communities. Use the retained a communities as a guide to perform a new round of multi-hop subgraph random walk. After iterating t times, the final drug community C = {c1, c2, ..., c} is obtained. s }, where s is the final number of drug communities; the conductivity is the fitness function of the drug community: ， ， Where L(c) represents the total number of external links of nodes within a community group, M represents the number of edges in graph G, d(u) represents the degree of node u, and the lower the conductivity Ψ(c) of community group c, the higher the cohesion of the community group. S3. Extract local features of drug community clusters using the first MPNN module: The message passing function is then weighted and optimized using the transition probability vector p(u) of each node u: ， in, This is the information vector passed from node v to node u. Let u be the feature vector of node u in the (l-1)th layer. Let v be the feature vector of node v in the (l-1)th layer. This is an attribute value indicating whether an edge exists between node v and node u. If an edge exists, then... ,otherwise , p(u) v This represents the probability of node u transitioning to node v; Weighted optimization of the aggregation function using probabilistic fusion weights: ， in, It is the sum of features passed to node u by its l-hop neighbors. It is the set of neighboring nodes of node u. The fusion weight, representing the transition probability of the l-th hop subgraph, is weighted when aggregating the features passed through all l-hop nodes, where l = 1, 2, ..., k; For each community group c i The resulting two-dimensional graph is processed by an MPNN with optimized message passing and message aggregation functions to extract graph features through message passing, message aggregation, and node representation updates in the following manner: ， ， ， ， The MPNN module takes as input the initial features of each node in the graph. initial features Initialized by graph G embedding, `Massage(∙)` is the message passing function used to pass feature information of the neighboring nodes of node u; `Aggregation(∙)` is the aggregation function used to aggregate the feature information passed by all the neighboring nodes of node u; `Update(∙)` is the update function used to update the feature information of node u; and `Read(∙)` is the read function used to extract the feature vector of the entire drug community subgraph, finally obtaining the drug community c. i eigenvectors , i = 1, 2, ..., s, this feature corresponds to the local community features of the drug, and T represents the transpose operation; S4. Extract global drug features using the second MPNN module: Each community group is treated as a node, and the characteristics of the node are the characteristics of the community group. Based on the original link relationships between the community groups, a community group subgraph G is constructed. com Then, using the same method as in S3, MPNN is employed for message passing, message aggregation, and node representation updates to extract the community cluster graph G. com Features This feature corresponds to the global characteristics of the drug; Ultimately, the feature matrix of a drug consists of local and global features, represented as follows: ， in, For drug community group c i The feature vector, where i takes values ​​from 1 to s, The feature vector of the community subgraph. q is the feature dimension; S5. Construct a drug similarity matrix: Drug multi-source information is defined to include drug structure information, drug-target association information, drug-enzyme association information, drug-pathway association information, and drug ATC code information. Target information, enzyme information, and pathway information related to the drug are extracted from relevant databases respectively. For the i-th drug d... i Target characteristics, pathway characteristics, and enzyme characteristics are defined as follows: ， ， ， Where x, y, and z represent the number of extracted target sites, pathways, and enzymes, respectively, and element t il p il e il The value can be 1 or 0, where 1 indicates that the l-th corresponding feature is related to drug d. i Related; a value of 0 indicates no relatedness. The Jaccard similarity coefficient is used to calculate the similarity between the i-th drug and the j-th drug: ， in, This represents the calculation of the Jaccard similarity between drug i and drug j under the *feature*, where * represents target, path, or enzyme; thus, drug similarity matrices are obtained under the three feature conditions: target, pathway, and enzyme. , and M represents the total number of drugs; An ATC code represented by a vector consists of B entries, each representing a sub-code at a corresponding level in the ATC hierarchy. Assuming the first A entries of two vectors are identical, the ATC similarity between the two drugs is defined as follows: The drug similarity matrix under ATC feature conditions is obtained. ; Structural similarity among different drugs was calculated using the Hilbert-Schmidt independence criterion: ， in, Represents the HSIC function. and These represent the structural features of the i-th drug and the j-th drug, respectively. , H is the centered kernel matrix, derived from... The calculation yields the drug similarity matrix under the given drug structure conditions, where I is the identity matrix, e is a q-dimensional vector of all 1s, Tr(·) represents the trace of the matrix (the sum of the diagonal elements), and T represents the transpose operation. ; S6. Construct the topological similarity matrix: The drug similarity matrix obtained from S5 is processed using a restart-based random walk algorithm: ， Among them, P t Let be the state transition matrix at time step t, where the i-th element represents drug d. i Confidence score at time step t; P 0 Let be the initial state transition matrix, where the i-th element is 1 and the rest are 0; It represents the restart probability, which controls the relative influence of local and global topological information; W is the normalized similarity matrix, expressed as... , The similarity score between the i-th drug and the j-th drug under the given condition is represented by *. Represents the similarity matrix, where * represents struct, atc, target, path, or enzyme; when Δp = p t - p t−1 The L1 norm is less than the positive number ε = 10 −9 At this point, a stationary distribution vector p is obtained, which represents the diffusion state of a drug node; definition In the similarity matrix The diffusion state of the i-th drug node is obtained to get all p i The constructed diffusion state matrix , where i = 1, ..., M, and M is the total number of drugs; The Spearman rank correlation coefficient was used to calculate the topological similarity between nodes in the similarity matrices of different drugs. ， in, Represents the i-th drug diffusion state matrix in the information source* And the j-th drug diffusion state matrix in information source # The Spearman rank correlation coefficient was calculated based on the given conditions. Represents the diffusion state matrix The element corresponding to the i-th row and k-th column; Each drug similarity matrix is ​​combined with the other four drug similarity matrices. Based on the diffusion state of drug nodes in the current information source and the diffusion states of drug nodes in other information sources, the Spearman rank correlation coefficient between each drug in the current information source and each drug in other information sources is calculated. There are four Spearman rank correlation coefficient values ​​between each drug and the other drugs. These four values ​​are averaged and fused to construct the topological similarity matrix. The topological similarity matrix N is obtained by capturing and fusing the topological information of each drug node from other information sources from the perspective of drug structure. struct From the perspective of drug ATC encoding, the topological information of each drug node is captured and fused from other information sources to obtain the topological similarity matrix N. atc From the perspective of drug targets, the topological information of each drug node is captured and fused from other information sources to obtain the topological similarity matrix N. target From the perspective of drug pathways, topological information of each drug node is captured and fused from other information sources to obtain the topological similarity matrix N. path From an enzyme perspective, topological information of each drug node is captured and fused from other information sources to obtain a topological similarity matrix N. enmyze ; S7. Perform kernel fusion on the topological similarity matrix: The five similarity matrices obtained from S6 form the kernel tensor of the first layer, denoted as: : ， Each basic core express The topological similarity score between the i-th and j-th elements is obtained by convolution operation, resulting in a kernel tensor with 5 different basic kernels. It will be converted into a new tensor with 5 basic kernels. : ， in, It is a filter bank, each It is a learnable filter parameter vector, l = 1, ..., 5. It is a differential nonlinear scalar activation function; the convolution operator uses the kernel tensor and five filters As input, and for each filter Generate a basic kernel : ， in, This represents the k-th element in the l-th filter of layer 1; each filter Convolution operation Output M×M kernel ,pass The five convolution operations in the text will Transform a tensor of size M×M×5 into a new tensor of size M×M×5. ; From the first-layer kernel tensor Initially, the kernel fusion network with L layers processes the tensor through a chain of nonlinear filter chains: ， These filters gradually transform low-level kernel tensors into highly nonlinear combinations of basic kernels: ， in, This represents the trainable parameters involved in the filter bank; This represents the output of the (L-1)th layer of the kernel fusion network, through supervised learning to learn the filter parameters; S8. Construct deep neural networks to predict whether drug pairs are synergistic: ， ， in, To merge the similarity matrices, It is a drug synergistic prediction tag matrix; Represents the entire prediction model, Z is the set of all parameters involved in the model. out and Z k These are hidden neurons, k=1,...,l, with corresponding weight matrices W. out and W k b out and b k It is the bias vector; It is the Sigmoid activation function; It's the Softmax activation function, used in the last layer, to convert the output layer values ​​into probabilities. Elements with a value greater than 0.5 are set to 1, and elements with a value less than or equal to 0.5 are set to 0.

2. The collaborative drug prediction method based on multi-source similarity matrix kernel fusion according to claim 1, characterized in that, The seed in S2 is initialized using the following rules: Sort all nodes in descending order of degree, and select nodes with higher degree as seeds. If a seed contains more than 1 node, then the nodes within the seed must satisfy the following: ， Where N(i) represents the set of neighboring nodes of the i-th node in graph G. Φ is a function for calculating the Jaccard similarity between two sets N(i) and N(j), where Φ is the similarity threshold. Initialize π seeds according to the initialization rules to form an initial seed set S = {s1, s2, ..., s}. π } 3. The collaborative drug prediction method based on multi-source similarity matrix kernel fusion according to claim 1, characterized in that, The spectral clustering algorithm described in S2 treats data points as vectors, performs spectral decomposition on these vectors, and finally clusters them. The input to the spectral clustering algorithm is: ， Where P represents the matrix consisting of the transition probability vectors of all nodes in graph G, and each row of the matrix represents the transition probability vector of a node. Let N be the nodes in graph G; N is the total number of nodes in graph G; and T represents the transpose operation.

4. The collaborative drug prediction method based on multi-source similarity matrix kernel fusion according to claim 1, characterized in that, The method for fusing two drug communities with a similarity greater than a threshold in S2 is as follows: ， Among them, c i Let θ represent the node set of the i-th community group, and θ be the similarity threshold.

5. The collaborative drug prediction method based on multi-source similarity matrix kernel fusion according to claim 1, characterized in that, If L is set to 4 in S7, the specific calculation process is as follows: Through filter bank Perform convolution operations to obtain five secondary intermediate kernels of size M×M. Then, by using three filters Will Transformed into a three-level intermediate core Finally, through a filter Will Transform into an integral similarity kernel ; Each element of the final integrator kernel Calculated using the following formula: ， in, , , ;also, , and Represented using a lower-level kernel: 。

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