Disease-miRNA Relationship Prediction Method, Model and Application Based on Multi-Scale Hypergraph Convolution

Abstract

The present invention relates to a method and application for predicting disease - miRNA relationships based on multi - scale hypergraph convolution. miRNA similarity is calculated on the ncRNA - miRNA - mRNA transcriptional regulatory network. The Jaccard method is used to obtain the similarity matrix of miRNAs, and the obtained targeting relationship information is more comprehensive than the miRNA - target relationship network data currently used for predicting disease - related miRNAs and can better represent the characteristics of miRNAs at the transcriptional level. Using a similar method, we obtain a disease similarity matrix based on the disease - signature directed acyclic graph, and the miRNA - disease matrix in the training set supplements the sparse matrix to a certain extent. Multiple top - selections of different pairs of similarities are performed on the matrix to obtain multiple uniform hypergraphs, which are then spliced to obtain the final multi - scale uniform hypergraph. End - to - end training is then carried out on it using cross - entropy loss. We comprehensively consider similarity - based methods and simple - graph - based methods, creatively propose a model based on multi - scale hypergraph learning, and finally obtain good experimental results.

Description

Technical Field

[0001] The present invention belongs to the research in the cross - field of computer and medicine, and relates to a method and application for predicting disease - miRNA relationships based on multi - scale hypergraph convolution. Background Art

[0002] MicroRNA (miRNA) is a small non - coding RNA molecule that plays a crucial role in gene expression regulation. They bind to target sites, promoting their degradation or inhibiting their translation into proteins. Research shows that miRNAs are involved in a wide range of physiological and pathological processes, including the occurrence and development of various diseases. The prediction research of miRNA - disease is a new bioinformatics research field, which aims to predict the occurrence of a certain disease by using the expression level of miRNAs or other information. At the same time, miRNAs are often regarded as an important indicator for cancer diagnosis and prognosis. By detecting the expression level of specific miRNAs, potential lesions and diseases can be detected in advance. Through the combined analysis of corresponding miRNAs, the specific phenotypes and pathological types of diseases can be further obtained, so as to more accurately predict the development trend of the disease, provide a reference basis for personalized treatment, take treatment measures earlier, reduce the patient's condition, and thus improve the patient's quality of life.

[0003] Traditional experimental methods for predicting disease - miRNA relationships mainly include reverse transcription polymerase chain reaction (PCR), Northern blotting, microarray analysis, etc. Generally speaking, experimental methods are often inefficient and require a large investment of time and money. However, due to the reliability of these experimental methods, many authoritative bioinformatics databases have been established to store experimentally verified disease - related miRNAs, such as the database of differentially expressed miRNAs in human cancers (dbDEMC), the human miRNA disease database (HMDD), and human diseases (miR2Disease).

[0004] In the past decade, many methods for predicting disease-related miRNAs based on traditional machine learning or deep learning have been proposed. Based on the hypothesis that miRNAs with similar functions tend to be associated with diseases with similar phenotypes, the correlation of disease-related miRNAs is ranked, and the role of the similarity matrix is particularly important in these methods. For example, Jiang et al. first developed a computational method to examine the relationship between functionally related miRNAs and phenotypically similar diseases based on the human phenotype-miRNA network. Due to the high false positive and false negative rates in miRNA-target associations, the prediction performance of this method is limited. In addition, Chen et al. proposed the concepts of internal score and external score for miRNA-disease pairs in 2016. The internal score (WS), that is, the functional similarity between miRNA and disease, is calculated based on the miRNA-disease network, and the external score (BS), that is, the functional similarity between miRNA and the neighbor nodes of the disease, is calculated. According to WS and BS, the comprehensive score (WBS) of each miRNA-disease pair is calculated to predict potential disease-related miRNAs. Che et al. designed a computational method for calculating miRNA functional similarity based on latent feature extraction, used the Levenshtein distance to calculate the distance between miRNA sequences, and proposed the LFEMDA method for predicting potential associations. In addition, Zhang et al. proposed a network link inference method based on fast linear neighborhood similarity, abbreviated as FLNSNLI. This method first constructs the known miRNA-disease association data as a bipartite network, and miRNAs (or diseases) are represented as association vectors; then the miRNA-miRNA similarity and disease-disease similarity are calculated using the association vectors, and combined with the linear neighborhood similarity formula to obtain the potential link score between miRNA and disease; finally, the disease-related miRNAs are ranked and predicted according to the link score. Based on multiple integrated data sources, including disease gene information, miRNA target gene information, and gene similarity information, Ma et al. constructed a new miRNA and disease similarity matrix and applied the kernel similarity algorithm to calculate the kernel neighbor similarity between miRNA and disease. Finally, they obtained the prediction score using the bidirectional propagation algorithm.

[0005] To further predict different types of miRNA-disease associations, rather than simply operating on the similarity matrix, Chen et al. used a restricted Boltzmann machine as a classifier and proposed the RBMMDA method. Then, Chen et al. proposed the RFMDA method, which combines a filter-based feature selection strategy and a random forest classifier to enhance the prediction performance. Subsequently, inspired by RFMDA, Yao et al. further designed the IRFMDA method. This model utilized the functional similarity, topological similarity, and co-expression similarity between miRNAs and diseases, as well as the known association information between miRNAs and diseases to construct a multi-dimensional feature space. Then, the model adopted a sample space dimensionality reduction method based on density peak clustering to reduce the computational complexity and improve the prediction accuracy. Finally, the model trained a random forest regression model on the dimensionality-reduced sample space for scoring. In addition, Yan et al. proposed the DNRLMF-MDA method, which uses logistic matrix factorization and dynamic neighborhood regularization to calculate the miRNA-disease association probability. Peng et al. proposed the MDA-CNN method, which uses a three-layer network and an autoencoder to capture significant miRNA-disease feature combinations and a convolutional neural network to obtain the final prediction score. Zheng et al. developed MLMDA by integrating heterogeneous information sources, training a random forest classifier by fully utilizing miRNA sequence information based on the k-mer sparse matrix. Zhou et al. proposed a new miRNA-disease correlation prediction method called GBDT-LR. This method first screens negative samples by using k-means clustering for unknown miRNA-disease associations, then applies gradient boosting decision trees to mine more differential features, and uses a logistic regression model to obtain the final prediction score. Meanwhile, by integrating the interactions between miRNAs, diseases, lncRNAs, drugs, and proteins into a heterogeneous network, Ji et al. used the global structure information (GraRep) method to learn the graph representation to obtain the comprehensive features of miRNAs and diseases, and adopted a random forest as the classifier for prediction. Influenced by the great progress made by graph neural networks in graph-structured data, a large number of graph neural network-based methods are being applied to biological networks to solve the prediction of potential miRNA-disease associations. For example, Li et al. proposed the HGCNMDA method to infer disease-related miRNAs, using the node2vec algorithm and graph convolutional networks on the PPI network to obtain the cross features of miRNAs and diseases, and designed a potential edge feature extraction component for association prediction. To obtain more valuable features of miRNAs and diseases, Li et al. performed graph convolutional networks on the miRNA similarity network and the disease similarity network and proposed a method based on neural inductive matrix completion to generate miRNA-disease associations.By integrating miRNA similarity and disease similarity into a complete network, Li et al. proposed an algorithm based on graph convolutional network for potential miRNA-disease association prediction.

[0006] The existing common methods for predicting disease-miRNA relationships have the following defects and deficiencies:

[0007] (1) Methods based on experimental verification (including Northern blotting, qPCR, RNAseq, miRNA microarray, etc.) can provide direct experimental data to verify disease-miRNA relationships. However, these experiments are costly, time-consuming, and resource-intensive, and there are certain technical limitations.

[0008] (2) Similarity-based methods infer the relationships between diseases or miRNAs by calculating the similarities between them. Although this method can provide useful information in some cases, similarity-based prediction methods rely on the assumption that similar diseases or miRNAs have similar biological characteristics or functions, and this assumption does not always hold, especially when dealing with complex disease or miRNA networks.

[0009] (2) Methods based on simple graphs have achieved some success in predicting disease-miRNA relationships, but their ability to model complex relationships between biological entities is still limited. Graphs essentially simulate the relationships between entity pairs, but the relationships between entities in biological systems are complex and diverse, and simple graphs cannot reflect complex relationships. Summary of the Invention

[0010] Technical Problem to be Solved

[0011] To avoid the deficiencies of the prior art, the present invention proposes a method and application for predicting disease-miRNA relationships based on multi-scale hypergraph convolution.

[0012] Technical Solution

[0013] A method for predicting disease-miRNA relationships based on multi-scale hypergraph convolution, characterized by the following steps:

[0014] Step 1: Construct a disease-disease similarity matrix DM and a miRNA-miRNA similarity matrix IM:

[0015] Step a1: Calculate the similarity between miRNAs MSSM(i,j) and the similarity between diseases DSSM(i,j):

[0016] Calculate the MSSM similarity MSSM(i,j) between any two miRNAs:

[0017]

[0018] Where: J(i, j) represents the Jaccard similarity between miRNA i and miRNA j, and M i and M j represent the target sets of miRNA i and miRNA j respectively, that is, the set of nodes connected to the miRNA node;

[0019] Calculate the DSSM similarity DSSM(i, j) between any two diseases

[0020]

[0021] Where DSSM1(i, j) represents the DSSM1 similarity between disease i and disease j, and DSSM2(i, j) represents the DSSM2 similarity between disease i and disease j;

[0022] Step a2: Calculate the Gaussian similarity MGSM(i, j) between miRNAs and the Gaussian similarity DGSM(i, j) between diseases using the miRNA-disease association matrix

[0023] Calculate the Gaussian similarity MGSM(i, j) between any two miRNAs:

[0024] MGSM(i, j) = exp(-r m ||IP(i) - IP(j)|| 2 )

[0025] Where:

[0026]

[0027] IP(i) and IP(j) in the Gaussian similarity MGSM(i, j) represent the column sums of the i-th row and the j-th row in the miRNA-disease association matrix respectively, and r' m is set to 1;

[0028] Calculate the Gaussian similarity DGSM(i, j) between any two diseases:

[0029] DGSM(i, j) = exp(-r d ||IP(i) - IP(j)|| 2 )

[0030] Where:

[0031]

[0032] In the Gaussian similarity DGSM(i,j), IP(i) and IP(j) represent the row sums of the i-th and j-th columns in the miRNA-disease association matrix, respectively, and r' d is set to 1;

[0033] Step a3: Obtain the miRNA-miRNA similarity matrix IM through MSSM(i,j) and MGSM(i,j):

[0034]

[0035] For each position (i, j) in the matrix IM, if there is an MSSM(i,j) between miRNA i and miRNA j, then the value at this position is equal to MSSM(i,j); if not, then the value is equal to MGSM(i,j);

[0036] Obtain the disease-disease similarity matrix DM through DSSM(i,j) and DGSM(i,j):

[0037]

[0038] For each position (i, j) in the matrix DM, if there is a DSSM(i,j) between disease i and disease j, then the value at this position is equal to DSSM(i,j); if not, then the value is equal to DGSM(i,j);

[0039] Step 2: Obtain the multi-scale hypergraph according to the similarity matrix;

[0040] The k-uniform hypergraph of miRNAs: Consider the set of all miRNAs as the vertex set V of the miRNA k-uniform hypergraph m ; For each miRNA, regard its top k most similar miRNAs as connected to it, regarded as a hyperedge, to obtain the hyperedge set Because each hyperedge will be assigned a weight, there is a weight matrix W, and use to represent the k-uniform hypergraph of miRNAs; Starting from the miRNA similarity matrix IM, by setting k = 2 to 8, obtain the hypergraphs of miRNAs at different scales

[0041] Among them: V in the hypergraphs of miRNAs at different scales m is the same; One hyperedge contains k + 1 miRNAs: This miRNA and its k most similar miRNAs; W in the hypergraphs of miRNAs at different scales is the same;

[0042] The k-uniform hypergraph of diseases: Consider the set of all diseases as the vertex set V of the disease k-uniform hypergraph d; For each disease, consider the top k diseases most similar to it as connected to it, regarded as a hyperedge, and obtain the hyperedge set Since each hyperedge will be assigned a weight, there is a weight matrix W, and use to represent the k-uniform hypergraph of diseases; starting from the disease similarity matrix DM, by setting k = 2 to 8, obtain hypergraphs of different scales of diseases

[0043] Among them: In the hypergraphs of different scales of diseases, V d is the same; a hyperedge contains three diseases: this disease and the two diseases most similar to it; in the hypergraphs of different scales of diseases, W is the same;

[0044] Step 3: Use hypergraph convolution to learn the multi-scale hypergraph:

[0045] Adopt the hypergraph convolutional neural network HGNN to learn the hypergraphs of different scales obtained in Step 2 to obtain the node representations in the hypergraphs of different scales:

[0046] The formula for updating the node features of the multi-scale hypergraph of miRNA-miRNA:

[0047]

[0048] Among them: k represents the operation on the k-uniform hypergraph of miRNAs; represents the features of m miRNAs from the (l + 1)-th layer of hypergraph convolution, represents the features of m miRNAs from the l-th layer of hypergraph convolution; σ(·) is a non-linear activation function; D v [k] represents the diagonal matrix of the hyperedge degree matrix of the k-uniform hypergraph of miRNAs, D e [k] represents the diagonal matrix of the vertex degree matrix of the k-uniform hypergraph of miRNAs; H m [k] represents the adjacency matrix corresponding to the k-uniform hypergraph of miRNA-miRNA; W represents the weight matrix; Θ represents the filter. Since it is a parallel operation, the filters are not shared, represents the filter on the l-th hypergraph convolution layer on the k-uniform hypergraph of miRNAs;

[0049] The formula for updating the node features of the multi-scale hypergraph of disease-disease:

[0050]

[0051] Among them: k represents the operation on the k-uniform hypergraph of diseases; represents the features of d diseases from the (l + 1)-th layer of hypergraph convolution, Represent the features of d diseases from the l-th layer of hypergraph convolution; σ(·) is a non-linear activation function; D v [k] represents the diagonal matrix of the hyperedge degree matrix of the k-uniform hypergraph of diseases, D e [k] represents the diagonal matrix of the vertex degree matrix of the k-uniform hypergraph of diseases; H d [k] represents the adjacency matrix corresponding to the k-uniform hypergraph of disease-disease, W represents the weight matrix; hypergraphs of different scales are treated equally, so W is unchanged in hypergraphs of different scales; Θ represents the filter, and since it is a parallel operation, the filters are not shared, Denote the filter on the l-th hypergraph convolution layer on the k-uniform hypergraph of diseases;

[0052] Step 4, Design the objective function and concatenate the trained node representations on hypergraphs of different scales:

[0053] For the multi-scale hypergraph of miRNA-miRNA, use the formula:

[0054]

[0055] where represents the final representation of m miRNAs, represents the representations of m miRNAs on the 2-hypergraph to 8-hypergraph, and concat(·) represents the concat operation;

[0056] For the multi-scale hypergraph of disease-disease, use the formula:

[0057]

[0058] where represents the final representation of d diseases, represents the representations of d diseases on the 2-hypergraph to 8-hypergraph, and concat(·) represents the concat operation;

[0059] Then, use the cross-entropy loss function to train and optimize the model:

[0060]

[0061] where, y ij represents the true label of the miRNA-disease pair, represents the predicted score of the miRNA-disease pair, y∪y - represents the set of positive and negative samples used in training, that is, the entire training set; through the backpropagation of the neural network, the training data is trained so that LOSS continuously decreases as the number of training iterations increases, and finally the model is trained on the training data to obtain the model based on multi-scale hypergraph learning;

[0062] Step 5: Input the test data into the trained model, and the output test data is the prediction result.

[0063] The miRNA-disease association matrix is an m*n matrix, which is constructed according to the miRNA-disease relationship: if there is an association between miRNAi and disease j, then (xi,yj) in the matrix is equal to 1, otherwise it is 0.

[0064] The data in Step 1 is from the data related to diseases in the MESH database.

[0065] An application of the disease-miRNA relationship prediction method based on multi-scale hypergraph convolution, characterized in that: the creation process of the model based on multi-scale hypergraph learning in Steps 1 to 4 is used for the creation of a miRNA-disease prediction model for a certain type of disease.

[0066] A model established by using the above application, characterized in that: the model has three modules: a similarity matrix construction module, a hypergraph convolution module, and a prediction module; the miRNA-miRNA similarity matrix IM is obtained through MSSM and MGSM, and the disease-disease similarity matrix DM is obtained through DSSM and DGSM; in the hypergraph convolution module, a k-uniform hypergraph of miRNAs and a k-uniform hypergraph of diseases are respectively constructed through the similarity matrices IM and DM. and the k-uniform hypergraph of diseases Then and are respectively input into the hypergraph convolutional neural network to obtain the node representations on different-scale hypergraphs, and the final vector representations of miRNAs and the final vector representations of diseases are obtained by splicing the node representations on different-scale hypergraphs; through the prediction module, the final vector representations of miRNAs and the final vector representations of diseases are dot-multiplied to obtain the prediction result of any pair of <miRNA-disease>, and the larger the dot-multiplication result, the greater the possibility of an association between the two.

[0067] The sources of the above MSSM, MGSM, DSSM, and DGSM are: the miRNA-miRNA similarity MSSM and the disease-disease similarity DSSM are respectively obtained from the lncRNA-miRNA-mRNA transcriptional regulatory network and the MESH database, and then the Gaussian kernel similarity MGSM between miRNAs and the Gaussian kernel similarity DGSM between diseases are obtained through the miRNA-disease association matrix.

[0068] The miRNA-disease prediction model of the disease is used for predicting the correlation between miRNAs and diseases of this type.

[0069] Beneficial effects

[0070] A method and application for predicting disease - miRNA relationships based on multi - scale hypergraph convolution proposed by the present invention first adopts a model based on multi - scale hypergraph learning for the miRNA - disease prediction problem. Since most of the previous similarity - based methods use functional data or disease data, it will cause the problem of data leakage for the miRNA - disease prediction problem. Therefore, this solution calculates miRNA similarity on the ncRNA - miRNA - mRNA transcriptional regulatory network and uses the Jaccard method to obtain the similarity matrix of miRNAs. The obtained target relationship information is more complete than the miRNA - target relationship network data currently used for predicting disease - related miRNAs and can better represent the characteristics of miRNAs at the transcriptional level. Using a similar method, we can obtain the disease similarity matrix based on the disease - marker directed acyclic graph, and then use the miRNA - disease matrix in the training set to supplement the sparse matrix to a certain extent. Multiple top - selections are performed on the matrix for different pairs of similarities to obtain multiple uniform hypergraphs, which are then spliced to obtain the final multi - scale uniform hypergraph, and then end - to - end training is performed on it using cross - entropy loss. We comprehensively consider similarity - based methods and simple - graph - based methods, creatively propose a model based on multi - scale hypergraph learning, and finally obtain good experimental results. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 : Model diagram of the method of the present invention

[0072] Figure 2 : Graph of the results of the comparative experiment

[0073] Figure 3 : Multi - scale hypergraph splicing experiment DETAILED DESCRIPTION OF THE EMBODIMENTS

[0074] The technical solution of the present invention mainly consists of two parts, namely: (1) Similarity measurement; (2) Prediction based on multi - scale hypergraphs. The following is a detailed introduction to the technical solutions of the three parts:

[0075] The technical solution of the present invention mainly consists of two parts, namely: (1) Similarity measurement; (2) Prediction based on multi - scale hypergraphs. The following is a detailed introduction to the technical solutions of the three parts:

[0076] (1) Similarity measurement

[0077] In this part of similarity measurement, we further divide it into four steps: miRNA similarity measurement, disease similarity measurement, similarity matrix filling, and similarity matrix fusion.

[0078] First, we need to measure miRNA similarity. Measuring miRNA functional similarity to predict disease-miRNA relationships is a current research hotspot. Our method also involves constructing a miRNA similarity network. Currently, miRNA similarity measurement methods can be divided into three types: those based on sequence data, those based on gene expression data, and those based on relationship graph data.

[0079] As endogenous small RNA molecules, miRNAs can exert regulatory effects by binding to mRNAs. Since they have binding targets in their sequences, sequence-based methods can measure miRNA functional similarity through sequence similarity. Furthermore, miRNA regulatory effects can lead to upregulation or downregulation of mRNA expression, and the expression of the miRNA itself can also change. Therefore, methods based on gene expression data can be used to perform correlation analysis. If miRNAs are co-expressed and have strong correlations in expression trends, they may play similar roles. Graph-based methods generally use miRNA-disease, miRNA-mRNA, or miRNA function data, using this relationship data to uncover commonalities between miRNA nodes in the graph structure.

[0080] By constructing the lncRNA-miRNA-mRNA transcriptional regulatory network, we can easily derive the targeted relationship network of miRNA containing lncRNA and mRNA information. Then we use the Jaccard similarity method to measure the similarity between miRNAs, and regard lncRNA-miRNA-mRNA as belonging to M i The target set. Jaccard similarity is often used to measure the similarity of a finite number of sets and has been applied in similar biological computing problems. The specific formula is:

[0081]

[0082] ② Similar to finding miRNA similarity, disease similarity can also be determined by mining graph relationships. We establish a hierarchical structure by constructing a disease-disease directed acyclic graph. The root node is a basic or general disease, such as tumors, labeled C04 in the undirected graph. Internal nodes are tumors classified by site, labeled C04.588 in MeSH. Meanwhile, in another branch, the root node is skin and connective tissue diseases, labeled C17 in MeSH. The internal node is skin diseases, labeled C17.800 in MeSH. There is also an internal node, breast diseases, labeled C17.800.090 in MeSH, which is a child node of skin diseases. The leaf node where the two branches intersect is breast cancer, labeled C04.588.180 and C17.800.090.500 in MeSH. As can be seen, a disease may be represented by multiple labels in the database, and such nodes are often leaf nodes. Therefore, calculating the similarity between two diseases requires a relatively complex process of considering multiple subgraphs.

[0083] This approach uses the term "hierarchical distance" to evaluate the similarity between two diseases in a subgraph. The greater the hierarchical distance, the greater the similarity. Based on existing research results, we believe that within a subgraph, the hierarchical distance between diseases increases as the distance between them increases. The hierarchical distance between disease i and disease j can be expressed as:

[0084]

[0085] We use α to control the decay rate of the hierarchical distance. We can see that only two diseases that belong to the same subgraph, that is, that have the same root node in the DAG, have a hierarchical distance. To better measure the similarity between two diseases, we provide a metric for the relationship between a disease and its subgraph. The more layers from the root node, the more internal nodes in the DAG are needed to express the specific semantics of the disease. This can be expressed in the formula combined with D1:

[0086] DS1(i)=∑ j∈T(i) D1(i,j)(

[0087] In this formula, T(i) is the node set consisting of node i and its previous ancestor nodes.

[0088] Inspired by previous research results, we believe that two diseases that share more common ancestral nodes i with d j has a more similar relationship, so the formula can be listed:

[0089]

[0090] Since DSSM1 is based on D1, and D1 is based on the condition that two diseases i and j must belong to the same subgraph; otherwise, there is no so-called hierarchical distance. Therefore, the calculated DSSM1 has certain deficiencies. Thus, we adopted a new distance formula for supplementation based on existing research results:

[0091]

[0092] Similar to DS1, a measurement criterion for the relationship between a disease and its containing subgraph needs to be given:

[0093] DS2(i) = ∑ j∈T(i) D2(i, j))

[0094] Diseases with higher occurrence frequencies may be more common, and their semantic contribution degrees at the same layer in the DAG should be smaller. That is to say, two diseases d i and d j with more shared rare ancestor nodes have a more similar relationship. DSSM1 is insufficient to fully describe these relationships. Therefore, we also adopted another disease similarity calculation method:

[0095]

[0096] Considering the similarities between two diseases by combining the above two similarity calculation methods, the formula is:

[0097]

[0098] ③ Since both the miRNA-disease similarity matrices are very sparse, we introduced Gaussian kernel similarity and filled them according to the miRNA-disease matrix. Given the existing research results, we believe that if two miRNAs are similar, they are very likely to play roles in the same disease. Therefore, we can calculate the Gaussian kernel similarity based on the existing miRNA-disease relationships. Finally, we constructed a vector IP(i) to represent the association between miRNA and each disease, and used r m to limit the ratio. The Gaussian kernel similarity between two miRNAs i and j can be calculated according to the following formula:

[0099] MGSM(i, j) = exp(-r m ‖IP(i) - IP(j)‖ 2 )

[0100]

[0101] We used the same method to calculate the Gaussian kernel similarity between two diseases i and j:

[0102] DGSM(i,j) = exp(-r d ‖IP(i) - IP(j)‖ 2 )

[0103]

[0104] Among us, IP(i) is represented as the column sum of the i-th row of the association matrix, such as or the row sum of the i-th column, such as Referring to the previous research result r' d and r' m are both set to 1.

[0105] ④Finally, we fuse the two similarity matrices according to the following formula:

[0106]

[0107]

[0108] (2) Prediction based on multi-scale hypergraph

[0109] Based on the miRNA and disease similarity matrices obtained above, we propose a model based on multi-scale hypergraph learning to predict miRNA-disease. The main idea is to mine it through multi-scale hypergraph convolution and finally make predictions through matrix completion. The algorithm framework diagram is as Figure 1 shown. The technical solution will be described in detail below through three parts: the hypergraph convolution layer, multi-scale hypergraph construction, and objective function design.

[0110] ①First, different from a simple graph where there are only two vertices on a fixed edge, a hyperedge in a hypergraph can connect two or more vertices. Compared with a simple graph, a hypergraph has its own unique advantages for heterogeneous networks. Combining the previous research results, we decide to use a hypergraph convolution hypergraph to perform the miRNA-disease prediction task and fully extract the information from the miRNA and disease similarity matrices. The miRNA and disease similarity matrices can be regarded as two weighted networks. A hypergraph is defined as G = (V, E, W), which contains a vertex set V and a hyperedge set E. The weight assigned to each hyperedge is W. The hypergraph G can be represented by a |V|×|E| incidence matrix H, and the formula definition is:

[0111]

[0112] For any vertex v i , its degree can be expressed by the formula as Similarly, for any hyperedge e i , its degree can be expressed by the formula as δi =∑ v∈V h(v,e i ). From this, we can calculate the diagonal matrix D of the hyperedge degree matrix and vertex degree matrix respectively e and D v .

[0113] We join the hyperedge groups to generate the hypergraph adjacency matrix H. The hypergraph feature matrix H and the node features are fed into the HGNN layer to obtain the node labels. We establish the hyperedge convolution layer f(X,W,Θ) using the following formula.

[0114] For the node dimension c1, the initial feature x (1) , we use the filter Θ (1) To extract, we get the node high-order features of dimension c2. Then we get the hyperedge features by node aggregation. This step is done by multiplying the feature from R E×N The matrix H of the space T Then, by aggregating the relevant hyperedge features of the nodes and multiplying them by the matrix H, we can get the node embedding x (2) .

[0115] The rigorous description is as follows:

[0116]

[0117] Among them, X (l) Represents the features from the hypergraph convolution layer l, and the feature space dimension is R N×C , X (0) Initialized as node feature X, σ(·) is a nonlinear activation function.

[0118] ② Then, to exploit features at different scales, we train in parallel on multiple uniform hypergraphs with different numbers of hyperedges, and fuse the node representations obtained on them into the final node representation. For multi-scale uniform hypergraphs, it can be seen as combining multiple uniform hypergraphs of different scales, giving corresponding inputs, and merging their outputs as the final node representation for the prediction task. The operation process on each uniform hypergraph can be expressed as:

[0119]

[0120] Among them, k represents the degree diagonal matrix of vertices and hyperedges on the k-uniform hypergraph. For uniform hypergraphs of different scales, the degree diagonal matrix of vertices and hyperedges will change, so D e [k] and D v [k] represents. Since it is a parallel operation, the filters are not shared and are represented by Θ (l) [k]. In this scheme, all hyperedges are given the same attention, so the weight matrix W remains unchanged.

[0121] As shown in the algorithm framework diagram, our hypergraph is built on two similarity matrices of miRNA and disease. In this regard, when building a k-uniform hypergraph, actually for each miRNA and disease, the top k miRNAs and diseases with the highest similarity are selected, and the corresponding positions in the adjacency matrix are set to 1, while the rest are filled with 0.

[0122] Thus, formulas can be established respectively to express that for miRNA:

[0123]

[0124] There is G m =(V m , E m , W). For the above formula, v ∈ V m , e ∈ E m .

[0125] For diseases:

[0126]

[0127] There is G d =(V d , E d , W). For the above formula, v ∈ V d , e ∈ E d .

[0128] ③Finally, we need to design an objective function to train the model. In this scheme, we use dot product for miRNA-disease prediction. First, the trained node representations on the multi-scale hypergraph need to be concatenated. For miRNA, it is:

[0129]

[0130] For diseases, it is:

[0131]

[0132] The prediction result can be written in the following form. The prediction score for miRNA i and disease j is:

[0133]

[0134] This scheme uses the cross-entropy loss function to train and optimize the model we proposed. The formula is:

[0135]

[0136] Among them, yij is the sample label, y and y - represent whether the corresponding places in the adjacency matrix are 1 or 0, that is, positive and negative samples.

[0137] Based on the completed algorithm model, comparative experiments and multi-scale hypergraph splicing experiments were also carried out to verify the feasibility and superiority of our model. The specific implementation methods, related parameters and experimental results are introduced in detail as follows:

[0138] (1) Data sources and related experimental settings

[0139] ① Data sources:

[0140] We selected 50,956 medical-related entries from the MeSH database, and after screening, we obtained a directed acyclic graph containing 4,407 diseases;

[0141] We selected a total of 35,548 experimentally verified miRNA-disease pairs from the HMDD database;

[0142] We extracted experimentally verified miRNA-lncRNA interaction data from the lncRNASNP2 database and downloaded experimentally verified miRNA-mRNA interaction data from miRTarBase. After fusion and screening, we obtained the lncRNA-miRNA-mRNA transcriptional regulatory network we needed. Through this network, we can easily obtain the targeting relationship network of miRNA containing lncRNA and mRNA. These targeting relationships are more comprehensive than the miRNA-target relationship network data currently used and can better represent the characteristics of miRNA at the transcriptional level.

[0143] ② The implementation steps and methods of the related technical solutions are as follows:

[0144] First is the similarity measurement: We use the Jaccard similarity to measure the similarity between miRNAs to obtain J(i,j); by establishing a hierarchical structure to calculate the similarity DSSM1 between diseases, and averaging it with DSSM2, we obtain the final similarity DSSM(i,j) of the two diseases; introducing Gaussian kernel similarity, according to the miRNA-disease matrix, filling two sparse similarity matrices; finally, fusing the similarity matrices according to the relevant formula.

[0145] Then is the construction of the prediction framework based on multi-scale hypergraphs: We use hypergraph convolution to perform miRNA-disease prediction tasks, fully extracting information from the miRNA and disease similarity matrices; at the same time, training in parallel on uniform hypergraphs with different numbers of hyperedges, and fusing the node representations obtained on them into the final representation of the nodes.

[0146] Finally, it is the training of the predictor: We splice the trained node representations on the multi-scale hypergraph, use the dot product result as the prediction score, and adopt the cross-entropy loss function to train and optimize the model.

[0147] ③ Related experimental settings:

[0148] This model uses 2-layer hypergraph convolution, performs uniform hypergraph splicing at 6 scales, and conducts experiments using the 5-fold cross-validation method. The miRNA and disease dimensions are kept consistent, fixed at 256 dimensions. When performing 5-fold cross-validation, the Gaussian kernel similarity based on the training set is used to complete the miRNA and disease similarity matrices to avoid label leakage.

[0149] (2) Comparative experiments

[0150] As Figure 2 shown, for the miRNA-disease prediction task, it is not difficult to see that the method we proposed has the highest performance in all metrics. Especially compared with the traditional graph machine learning methods LINE, SDNE, and GAE, it has achieved great improvements. In the AUROC prediction metric, it has increased by at least 25.79% (from 0.694 to 0.9519), in the AUPR prediction metric, it has increased by at least 43.29% (from 0.5133 to 0.9462), and in the F1-score prediction metric, it has increased by 35.83% (from 0.4789 to 0.8372). Compared with the graph representation learning methods based on random walks such as deepwalk, node2vec, and struc2vec, it has increased by at least 24.99% (from 0.702 to 0.9519) in the AUROC prediction metric, at least 42.22% (from 0.524 to 0.9462) in the AUPR prediction metric, and 30.51% (from 0.5321 to 0.8372) in the F1-score prediction metric. This shows that our method has made significant progress compared with the graph representation learning methods based on random walks. Compared with the graph representation learning methods based on matrix factorization such as Laplacian, GF, SVD, HOPE, and GraRep, it has increased by at least 22.43% (from 0.7276 to 0.9519) in the AUROC prediction metric, at least 38.93% (from 0.5569 to 0.9462) in the AUPR prediction metric, and 28.52% (from 0.552 to 0.8372) in the F1-score prediction metric. For the newly proposed NIMCGCN in 2020 specifically for the miRNA-disease prediction task, we have also made breakthroughs in the three performance metrics, especially in the metrics regarding the imbalance between positive and negative samples. The specific metrics of each method are shown in Table 1.

[0151] Table 1 Comparison test results

[0152]

[0153] (3) Multi-scale hypergraph stitching experiment

[0154] The algorithm proposed in this patent is based on multi-scale hypergraphs. To prove that the stitched hypergraphs of different scales are beneficial for the

[0155] prediction task, we demonstrated the effectiveness of multi-scale hypergraph stitching through experiments in two aspects. First, we conducted experiments on hypergraphs of each scale, and second, we performed stitching experiments on multiple hypergraphs of different scales, proving that the idea of parallel training of multi-scale hypergraphs we proposed is effective.

[0156] As Figure 3 shown, for the miRNA-disease prediction task, single hypergraph convolution is also effective and better than traditional graph representation learning methods. However, not all uniformly scaled hypergraphs can completely outperform ordinary graphs. There are hypergraphs at some scales, such as 2-uniform hypergraphs that have degenerated into ordinary graphs, and some model performance metrics are even worse and cannot completely outperform. This also shows the Figure 1 rationality of using 2-uniform hypergraphs as part of the multi-scale hypergraph. For the AUROC prediction metric, the multi-scale model varies in the range of 0.9147 to 0.9266. For the AUPR prediction metric, the multi-scale model varies in the range of 0.9106 to 0.9241. For the F1-score performance metric, the variation range is between 0.7474 and 0.7656. The specific metrics are shown in Table 2 below.

[0157] Table 2 Experimental results of single-scale hypergraphs

[0158]

[0159] As shown in the figure, for the miRNA-disease prediction task, the method of parallel training of multi-scale hypergraphs finally stitches the node representations for prediction, showing obvious superiority. The model performance has generally been greatly improved compared to single-scale hypergraphs.

[0160] For the AUROC prediction metric, the multi-scale model varies in the range of 0.9189 to 0.9519. For the AUPR prediction metric, the multi-scale model varies in the range of 0.9183 to 0.9462. For the F1-score performance metric, the variation range is between 0.7415 and 0.8372. The specific metrics are shown in Table 3 below.

[0161] Table 3 Experimental results of multi-scale hypergraph stitching

[0162]

Claims

1. A method for predicting disease-miRNA relationships based on multi-scale hypergraph convolution, characterized in that The steps are as follows: Step 1. Construct a disease-disease similarity matrix DM and a miRNA-miRNA similarity matrix IM: Step a1. Calculate the similarity MSSM(i,j) between miRNAs and the similarity DSSM(i,j) between diseases: Calculate the similarity MSSM(i,j) between any two miRNAs: Where: (i, j) represents the Jaccard similarity between miRNAi and miRNAj, M i 、M j Represent the target sets of miRNA i and miRNAj, respectively, that is, the set of nodes connected to the miRNA node; Calculate the similarity DSSM(i,j) between any two diseases where: DSSM1(i,j) represents the DSSM1 similarity between disease i and disease j, and DSSM2(i,j) represents the DSSM2 similarity between disease i and disease j; The calculation process of the similarity DSSM(i,j) between any two diseases is: The similarity between disease i and disease j in the same subgraph is evaluated using the term "hierarchical distance", and α is used to control the attenuation rate of the hierarchical distance. The hierarchical distance between two diseases i and j with the same root node is: The semantic value of a disease is measured by the number of layers from the root node. The formula is the sum of the hierarchical distances between node i and all its ancestor nodes: T(i) is the set of nodes composed of node i and its previous ancestor nodes; Two diseases d that share more identical ancestor nodes i and d j have a more similar relationship, thus obtaining: In the same layer of nodes in the subgraph, different diseases j and j′ have different semantic contributions to disease i. The overall commonness of the diseases is used as a supplementary measure for the hierarchical distance, and the following distance formula is used for supplementation: Similarly, the disease semantic value is given, with the rarity of diseases in the subgraph as the measurement standard: DS2(i) = ∑ j∈T(i) D2(i, j) Obtain the disease similarity calculation method: Comprehensively consider the similarity between two diseases through two similarity calculation methods. The formula is: Step a2. Calculate the Gaussian similarity MGSM(i,j) between miRNAs and the Gaussian similarity DGSM(i,j) between diseases using the miRNA-disease association matrix Calculate the Gaussian similarity MGSM(i,j) between any two miRNAs: MGSM(i,j) = exp(-r m ||IP(i) - IP(j)|| 2 ) where: In the Gaussian similarity MGSM(i,j), IP(i) and IP(j) represent the column sums of the i-th row and the j-th row in the miRNA-disease association matrix, respectively, and r' m is set to 1; Calculate the Gaussian similarity DGSM(i,j) between any two diseases: DGSM(i,j) = exp(-r d ||IP(i) - IP(j)|| 2 ) where: In the Gaussian similarity DGSM(i,j), IP(i) and IP(j) respectively represent the row sums of the i-th column and the j-th column in the miRNA-disease association matrix, and r′ d is set to 1; Step a3. Obtain the miRNA-miRNA similarity matrix IM through MSSM(i,j) and MGSM(i,j): For each position (i, j) in matrix IM, if there is MSSM(i,j) between miRNA i and miRNA j, then the value of this position is equal to MSSM(i,j); if not, then the value is equal to MGSM(i,j); Obtain the disease-disease similarity matrix DM through DSSM(i,j) and DGSM(i,j): For each position (i, j) in matrix DM, if there is DSSM(i,j) between disease i and disease j, then the value of this position is equal to DSSM(i,j); if not, then the value is equal to DGSM(i,j); Step 2. Obtain a multi-scale hypergraph based on the similarity matrix; k-uniform hypergraph of miRNAs: Consider the set of all miRNAs as the vertex set V of the miRNA k-uniform hypergraph m ; For each miRNA, regard its top k most similar miRNAs as those connected to it, regarded as a hyperedge, to obtain the hyperedge set Since each hyperedge will be assigned a weight, with the weight matrix W, use to represent the k-uniform hypergraph of miRNAs; Starting from the miRNA similarity matrix IM, by setting k = 2 to 8, obtain hypergraphs of different scales of miRNAs Among them: V in the hypergraphs of miRNAs at different scales is the same; one hyperedge contains k + 1 miRNAs: this miRNA and the k miRNAs most similar to it; W in the hypergraphs of miRNAs at different scales is the same; m the same; one hyperedge contains k + 1 miRNAs: this miRNA and the k miRNAs most similar to it; W in the hypergraphs of miRNAs at different scales is the same; k-uniform hypergraph of diseases: The set of all diseases is regarded as the vertex set V of the disease k-uniform hypergraph d ; For each disease, its top k most similar diseases are regarded as connected to it and regarded as a hyperedge, obtaining the hyperedge set Since each hyperedge will be assigned a weight, there is a weight matrix W, denoted by to represent the k-uniform hypergraph of diseases; Starting from the disease similarity matrix DM, by setting k = 2 to 8, hypergraphs of different scales of diseases are obtained Among them: V in the hypergraphs of diseases at different scales is the same; a hyperedge contains three diseases: this disease and the two diseases most similar to it; W in the hypergraphs of diseases at different scales is the same; d the same; a hyperedge contains three diseases: this disease and the two diseases most similar to it; W in the hypergraphs of diseases at different scales is the same; Step 3. Use hypergraph convolution to learn the multi-scale hypergraph: Use the hypergraph convolutional neural network HGNN to learn the different-scale hypergraphs obtained in Step 2 to obtain the node representations in the different-scale hypergraphs: The formula for updating the node features of the miRNA-miRNA multi-scale hypergraph: Where: k represents the operation on the k-uniform hypergraph of miRNA; represents the features of m miRNAs from the (l + 1)-th layer of hypergraph convolution, represents the features of m miRNAs from the l-th layer of hypergraph convolution; σ(·) is a non-linear activation function; D v [k] represents the diagonal matrix of the hyperedge degree matrix of the k-uniform hypergraph of miRNA, D e [k] represents the diagonal matrix of the vertex degree matrix of the k-uniform hypergraph of miRNA; H m [k] represents the adjacency matrix corresponding to the k-uniform hypergraph of miRNA-miRNA; W represents the weight matrix; Θ represents the filter. Since it is a parallel operation, the filters are not shared, represents the filter on the l-th hypergraph convolution layer on the k-uniform hypergraph of miRNA; The multi-scale hypergraph node feature update formula for disease-disease: where: k represents the operation on the k-uniform hypergraph of the disease; represents the features of d diseases from the (l + 1)-th layer of hypergraph convolution, represents the features of d diseases from the l-th layer of hypergraph convolution; σ(·) is a non-linear activation function; D v [k] represents the diagonal matrix of the hyperedge degree matrix of the k-uniform hypergraph of the disease, D e [k] represents the diagonal matrix of the vertex degree matrix of the k-uniform hypergraph of the disease; H d [k] represents the adjacency matrix corresponding to the disease-disease k-uniform hypergraph, W represents the weight matrix; hypergraphs of different scales are treated equally, so W is invariant in hypergraphs of different scales; Θ represents the filter, and since it is a parallel operation, the filters are not shared, represents the filter on the l-th hypergraph convolution layer on the k-uniform hypergraph of the disease; Step 4: Design the objective function and concatenate the trained node representations on hypergraphs of different scales: For the multi-scale hypergraph of miRNA-miRNA, use the formula: Among them represents the final representation of m miRNAs represents the representation of m miRNAs on 2-hypergraph to 8-hypergraph, and concat(·) represents the concat operation; For the multi-scale hypergraph of disease-disease, use the formula: Among them represents the final representation of d diseases represents the representation of d diseases on 2-hypergraph to 8-hypergraph, and concat(·) represents the concat operation; Then, use the cross-entropy loss function to train and optimize the model: where y ij represents the true label of the miRNA-disease pair, represents the predicted score of the miRNA-disease pair, y ∪ y - represents the set of positive and negative samples used in training, that is, the entire training set; through the backpropagation of the neural network, the training data is trained to make the LOSS continuously decrease as the number of training iterations increases. Finally, the model is trained on the training data to obtain a model based on multi-scale hypergraph learning; Step 5: Input the test data into the trained model, and the output test data is the prediction result. The larger the dot product result, the greater the likelihood of an association between the two.

2. The method for predicting disease - miRNA relationships based on multi - scale hypergraph convolution according to claim 1, wherein: The miRNA-disease association matrix is an m*n matrix constructed based on the miRNA-disease relationship: If there is an association between miRNAi and disease j, then the value of (xi,yj) in the matrix is equal to 1; otherwise, it is 0.

3. The disease-miRNA relationship prediction method based on multi-scale hypergraph convolution according to claim 1, wherein: The data in Step 1 is sourced from data related to diseases in the MESH database.

4. Use of the method for predicting disease-miRNA relationships based on multi-scale hypergraph convolution according to claim 1 or 2 or 3, characterized in that: The creation process of the model based on multi-scale hypergraph learning in Steps 1 to 4 is used for the creation of a miRNA-disease prediction model for a certain type of disease.

5. A system established by using the application according to claim 4, characterized in that: The system consists of three modules: a similarity matrix construction module, a hypergraph convolution module, and a prediction module. The miRNA-miRNA similarity matrix IM is obtained through MSSM and MGSM, and the disease-disease similarity matrix DM is obtained through DSSM and DGSM. In the hypergraph convolution module, the k-uniform hypergraph of miRNAs and the k-uniform hypergraph of diseases are constructed respectively through the similarity matrices IM and DM. and the k-uniform hypergraph of diseases Then and are respectively input into the hypergraph convolutional neural network to obtain the node representations on hypergraphs of different scales. The final vector representations of miRNAs and diseases are obtained by concatenating the node representations on hypergraphs of different scales. Through the prediction module, the final vector representations of miRNAs and diseases are dot-multiplied to obtain the prediction results for any pair of <miRNA-disease>. The larger the dot-multiplication result, the greater the likelihood of an association between the two.

6. The system according to claim 5, characterized in that: The sources of MSSM, MGSM, DSSM, and DGSM are as follows: The miRNA-miRNA similarity MSSM and the disease-disease similarity DSSM are obtained from the lncRNA-miRNA-mRNA transcriptional regulatory network and the MESH database respectively, and then the Gaussian kernel similarity MGSM between miRNAs and the Gaussian kernel similarity DGSM between diseases are obtained through the miRNA-disease association matrix.

7. Use of the system according to claim 5, characterized in that: The miRNA-disease prediction model for the disease is used to predict the correlation between miRNA and disease of this type.

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