CircRNA-disease association prediction method based on attention fusion graph-hypergraph convolutional network

Abstract

The invention belongs to the field of bioinformatics, and relates to a circRNA-disease association prediction method based on an attention fusion graph-hypergraph convolutional network. The method comprises the following steps: firstly, constructing a circRNA-disease incidence matrix and a plurality of similarity matrixes based on a database; secondly, respectively constructing a graph adjacent matrix and a hypergraph adjacent matrix based on the similarity matrix, extracting circRNA and disease low-order local features by using a graph convolutional network, and extracting circRNA and disease high-order global features by using a hypergraph convolutional network; then, dynamically fusing circRNA and disease low-order local features obtained from the graph convolutional network and circRNA and disease high-order global features obtained from the hypergraph convolutional network through an attention aggregation mechanism, and enhancing feature interaction by means of comparative learning; then, using a variational auto-encoder to extract circRNA and disease nonlinear characteristics from the incidence matrix; and finally, integrating a plurality of circRNAs and disease characteristics, and predicting a circRNA-disease association score. According to the method, multi-level features can be effectively fused, and the prediction accuracy and robustness are improved.

Description

Technical Field

[0001] This invention belongs to the fields of bioinformatics and computational biology, specifically relating to a circRNA-disease association prediction method based on attention fusion graph-hypergraph convolutional networks. Background Technology

[0002] Recent studies have shown that while circular RNAs (circRNAs) do not directly encode proteins, they play crucial regulatory roles in life processes. Specifically, as a novel type of non-coding RNA, circRNAs possess a unique covalently closed circular structure, lacking the 5' cap and 3' poly-A tail of traditional linear RNAs, and are generated via transcription by RNA polymerase II. With the development of high-throughput sequencing technology, it has been discovered that circRNAs participate in multiple key physiological processes through complex molecular mechanisms. This indicates that circRNAs play an important role in disease regulation. Therefore, in-depth analysis of the association between circRNAs and diseases can help reveal the mechanisms of disease development at the molecular level, thus having significant scientific implications for the treatment of complex diseases.

[0003] Although researchers have established circRNA-disease association databases based on traditional biomedical experiments, such as the circRNADisease database (https: / / cgga.org.cn / circRNADisease) and the circad database (https: / / clingen.igib.res.in / circad), their construction requires significant human and material resources. The revolutionary development of computational algorithms in the field of bioinformatics has opened up a completely new paradigm for studying the mechanisms of circRNA-disease association. These methods can be broadly categorized into two types: those based on traditional machine learning and those based on deep learning.

[0004] In the field of traditional machine learning, Yan et al. innovatively integrated the weighted k-nearest neighbor algorithm with Kronecker kernel-regularized least squares regression to construct an association matrix optimization prediction model. Ding et al. extracted network topology features by restarting the random walk algorithm and combined it with logistic regression to achieve association prediction. Lei et al. integrated multi-source omics data to construct a gradient boosting decision tree ensemble learning model. Xiao et al. proposed to mine the potential association between circRNAs and diseases through graph multi-label learning based on the local invariance assumption. Wei et al. used matrix factorization technology to extract low-dimensional features from the association matrix, successfully solving the link prediction problem in complex networks. Wang et al. innovatively introduced a personalized ranking algorithm into this field, achieving accurate ranking and prediction of disease-related circRNAs.

[0005] Deep learning algorithms possess powerful learning capabilities and the ability to automatically extract new features, demonstrating versatility across multiple fields. Therefore, numerous deep learning models have been applied in bioinformatics. For example, Li et al. proposed a novel deep learning model based on a graph autoencoder (GAE) constructed using a graph attention network (GAT) and restarted random walk (RWR) to predict circRNA-disease associations. Gao et al. proposed a novel method based on graph random propagation networks and multi-head dynamic graph attention networks to predict potential associations between circRNAs and diseases. Wang et al. proposed a unique method based on resistive distance and graph attention networks (RDGAN) to predict circRNA-disease associations. Dai et al. proposed a hybrid graph embedding model combining graph convolutional networks and graph attention networks to predict potential circRNA-disease associations. Guo et al. proposed a method (THGNCDA) to predict circRNA-disease associations. This method employs a graph neural network with attention to learn the importance of each neighbor, and then uses a multi-layer convolutional neural network to explore the relationships between circRNA-disease pairs based on their attributes. Wang et al. used the graph-weighted nearest neighbor method to establish an overview of circRNA interactions related to diseases, in order to reduce the influence of spurious negative associations, and inferred the association between circRNAs and diseases through non-negative matrix factorization. Summary of the Invention

[0006] This paper proposes a method for predicting circRNA-disease associations based on attention-fusion graph-hypergraph convolutional networks. First, based on circRNA similarity data and disease similarity data (e.g., circRNA functional second-order similarity, disease semantic second-order similarity, disease association cosine similarity, and circRNA association cosine similarity), corresponding graph adjacency matrices and hypergraph adjacency matrices with circRNA and disease as nodes are constructed, respectively. Low-order feature representations of circRNA and disease are obtained through graph convolutional networks. High-order feature representations are mined using hypergraph convolutional networks. We designed an attention aggregation mechanism to dynamically weight features obtained from different graph convolutional networks, fusing the low-order features obtained from the graph convolutional networks and the high-order features obtained from the hypergraph convolutional networks. Meanwhile, contrastive learning is used to promote information interaction between features. Then, a variational autoencoder is used to capture the features of circRNA and disease. Finally, the obtained circRNA and disease features are integrated to obtain a circRNA-disease score matrix for predicting the association between circRNA and disease. Experimental results show that our method AGHCL significantly outperforms existing methods on benchmark datasets and can accurately predict circRNAs associated with diseases.

[0007] To achieve the aforementioned technical effects and objectives, this invention provides a circRNA-disease association prediction method based on attention fusion graph-hypergraph convolutional networks, comprising:

[0008] S1: Based on database information, construct the circRNA-disease association matrix (ACD), circRNA association cosine similarity matrix (SAC), disease association cosine similarity matrix (SAD), circRNA functional second-order similarity matrix (SCS), and disease semantic second-order similarity matrix (SDS).

[0009] S2: Based on four similarity matrices (SAC, SAD, CSC, SDS), corresponding graph adjacency matrices and hypergraph adjacency matrices are constructed respectively. Graph convolutional networks are used to extract low-order local feature representations of circRNAs and diseases in the graph, and hypergraph convolutional networks are used to extract high-order global feature representations of circRNAs and diseases in the hypergraph.

[0010] S3: Dynamically fuse low-order local features of circRNA and disease obtained from graph convolutional networks and high-order global features of circRNA and disease obtained from hypergraph convolutional networks through an attention aggregation mechanism, and use contrastive learning to promote information interaction between features;

[0011] S4: Extracting circRNA and nonlinear features of the disease from ACD using a variational autoencoder;

[0012] S5: Integrate multiple circRNAs and disease features to obtain a circRNA-disease association score matrix to predict key circRNAs associated with diseases.

[0013] Preferably, S1 includes:

[0014] S1.1: The method for constructing the circRNA-disease association matrix (ACD) is as follows:

[0015] We obtain m circRNAs, n diseases, and association information between circRNAs and diseases from known databases, and use this data to construct a circRNA-disease association matrix. For any element ACD(i,j) in ACD, if there is a correlation between circRNA i and disease j, then ACD(i,j) = 1, otherwise it is 0;

[0016] S1.2: Constructing the cosine similarity matrix of circRNA associations The calculation formula is:

[0017]

[0018] Where ACD is the association matrix between circRNA and disease, ACD(i,:) is the vector in the i-th row of ACD, ACD(j,:) is the vector in the j-th row of ACD, ||ACD(i,:)|| is the modulus of ACD(i,:), ||ACD(j,:)|| is the modulus of ACD(j,:), and SAC(i,j) represents the cosine similarity between the i-th and j-th circRNAs. According to the above formula, we calculate the cosine similarity between each circRNA to obtain the circRNA association cosine similarity matrix (SAC).

[0019] S1.3: Constructing a cosine similarity matrix of disease associations The calculation formula is:

[0020]

[0021] Where ACD is the association matrix of circRNA-disease, ACD(:,i) is the vector in the i-th column of ACD, ACD(:,j) is the vector in the j-th column of ACD, ||ACD(:,i)|| is the modulus of ACD(:,i), ||ACD(:,j)|| is the modulus of ACD(:,j), and SAD(i,j) represents the cosine similarity between the i-th and j-th diseases. According to the above formula, we calculate the cosine similarity between each disease to obtain the disease association cosine similarity matrix (SAD).

[0022] S1.4: Constructing a second-order semantic similarity matrix for diseases

[0023] We use the Bioconductor package in R to calculate the semantic similarity between diseases, which yields a disease semantic similarity matrix. We calculate the second-order semantic similarity SDS(i,j) of a disease based on its semantic similarity matrix, using the following formula:

[0024]

[0025] Where SD is the disease semantic similarity matrix, SD(i,:) is the vector in the i-th row of SD, SD(j,:) is the vector in the j-th row of SD, ||SD(i,:)|| is the modulus of SD(i,:), ||SD(j,:)|| is the modulus of SD(j,:), and SDS(i,j) represents the semantic second-order similarity between the i-th and j-th diseases. According to the above formula, we calculate the cosine similarity between each disease to obtain the disease semantic second-order similarity matrix.

[0026] S1.5: The method for constructing the second-order functional similarity matrix (SCS) of circRNAs is as follows:

[0027] Based on the property that two circRNAs with similar disease groups often have similar functions, a functional similarity matrix of circRNAs can be obtained. We calculate the second-order functional similarity (SCS(i,j)) of circRNAs based on the functional similarity matrix of circRNAs, using the following formula:

[0028]

[0029] Where SC is the circRNA functional similarity matrix, SC(i,:) is the vector in the i-th row of SC, SC(j,:) is the vector in the j-th row of SC, ||SC(i,:)|| is the modulus of SC(i,:), ||SCj,:)|| is the modulus of SC(j,:), and SCS(i,j) represents the functional second-order similarity between the i-th and j-th circRNAs. Based on the above formula, we calculate the functional second-order similarity between each circRNA, thus obtaining the circRNA functional second-order similarity matrix.

[0030] Preferably, S2 includes:

[0031] S2.1: Methods for constructing graph adjacency matrices using the four similarity matrices mentioned above:

[0032] In a simple graph, each edge connects only two nodes. We construct an adjacency matrix to reflect the relationship between any two nodes by finding the nodes most similar to each node. In this study, if the graph is constructed using a circRNA similarity matrix, the nodes represent each circRNA; if the graph is constructed using a disease similarity matrix, the nodes represent each disease. For example, in the adjacency matrix of the graph, if node i and node j are connected, then G(i,j) = 1, indicating that the i-th circRNA and the j-th circRNA are related or the i-th disease and the j-th disease are related; otherwise, it is 0.

[0033] Based on the second-order similarity matrix of circRNA function, the cosine similarity matrix of disease association, the second-order similarity matrix of disease semantics, and the cosine similarity matrix of circRNA association, their corresponding graph adjacency matrices are constructed, resulting in the graph adjacency matrix G. SCS G SAD G SDS G SAC ;

[0034] S2.2: Methods for constructing hypergraph adjacency matrices using the four similarity matrices mentioned above:

[0035] A hypergraph is a special form of graph where a hyperedge can connect any number of nodes, representing common associations between them. Therefore, a hypergraph can represent higher-order relationships between nodes. We construct hyperedges by collecting the nodes most similar to each node; the number of hyperedges corresponds to the number of nodes. In this study, a hypergraph constructed using a circRNA similarity matrix represents each circRNA, while a hypergraph constructed using a disease similarity matrix represents each disease. For example, in the hypergraph adjacency matrix, if node a is contained in hyperedge e, then H(a,e) = 1, indicating that hyperedge e contains either the a-th circRNA or the a-th disease; otherwise, it is 0.

[0036] Based on the second-order similarity matrix of circRNA function, the cosine similarity matrix of disease association, the second-order similarity matrix of disease semantics, and the cosine similarity matrix of circRNA association, their corresponding hypergraph adjacency matrices are constructed respectively, resulting in hypergraph adjacency matrices denoted as: H SCS H SAD H SDS H SAC ;

[0037] S2.3: The calculation formula for the graph convolutional network described in S2 is:

[0038]

[0039] Where G is the input graph adjacency matrix, D is the degree matrix corresponding to the input graph adjacency matrix, and X... G (l) It is a graph convolutional network X G The feature matrix of the l-th layer, where each row of the matrix represents the feature representation of a node (circRNA or disease) in the l-th layer. X is the weight matrix of the l-th layer in a graph convolutional network. G (l+1) is the feature matrix of the (l+1)th layer output by the graph convolutional network. Each row of the matrix represents the feature representation of a node (circRNA or disease) in the (l+1)th layer, and σ represents the non-linear activation function.

[0040] We will respectively view Figure G SCS Figure G SAD Figure G SAC And Figure G SDS Substituting these values ​​into the above graph convolutional network formula, we obtain the corresponding feature representation matrices.

[0041] S2.4: The calculation formula for the hypergraph convolutional network described in S2 is as follows:

[0042]

[0043] Where H is the input hypergraph adjacency matrix, X H (l) This represents the feature matrix of the l-th layer in a hypergraph convolutional network. D represents the weight matrix of the l-th layer in a hypergraph convolutional network. e This is the hyperedge degree matrix of the input hypergraph adjacency matrix. This matrix is ​​a diagonal matrix describing the degree of each hyperedge, i.e., the sum of the number of nodes (circRNAs or diseases) connected by that hyperedge. D v is a matrix of vertex degrees of the hypergraph adjacency matrix. This matrix is ​​a diagonal matrix that describes the degree of each vertex, i.e., the sum of the number of hyperedges to which the node (circRNA or disease) belongs. P is the weight matrix of the hyperedges. Specifically, during hypergraph convolution, nodes connected by common hyperedges propagate more widely. Hyperedges with larger weights should be regarded as more reliable feature propagation carriers and occupy a higher proportion in the information aggregation process.

[0044] We will respectively define the hypergraph H SCS Hypergraph H SAD Hypergraph H SAC He Chaotu H SDS Substituting these values ​​into the hypergraph convolutional network formula above, we obtain the corresponding feature representation matrices.

[0045] Preferably, S3 includes:

[0046] S3.1: We take the hypergraph H as an example. SAC And Figure G SAC After performing hypergraph convolution and graph convolution operations, the two feature matrices obtained are and Let's take an example to illustrate. and The i-th row represents the feature representation of the i-th circRNA, and the feature matrix... and The attention score is calculated by transforming the i-th row respectively:

[0047]

[0048] Among them, W i It is a weight matrix, and tanh is the activation function. This indicates that the graph convolutional network starts from the graph adjacency matrix G. SAC The low-order local features of the i-th circRNA extracted from it are represented as follows: This indicates that the hypergraph convolutional network starts from the hypergraph adjacency matrix H. SACThe high-order global feature representation of the i-th circRNA extracted, q i It is a trainable parameter vector. yes Attention score yes Attention score;

[0049] S3.2: To make attention scores comparable, we normalize them using the exp exponential function. and

[0050]

[0051] in, Indicates to Process the resulting new attention score, Indicates to The resulting new attention score is processed, where exp is an exponential function.

[0052] S3.3: Using the obtained attention score and Aggregate feature matrix and The feature representation of the i-th row yields C. SAC (i,:):

[0053]

[0054] Finally, we aggregate the feature matrix using the formula described above. and The feature representation of each row can be used to obtain the final feature representation matrix C. SAC Similarly, we consider the characteristic matrix and and and An attention aggregation mechanism is also used to obtain the feature representation matrix: C SCS D SAD D SDS ;

[0055] S3.4: Next, we will perform the feature matrix C of the two circRNAs obtained after attention fusion. SAC and C SCS Comparative learning is performed, and the calculation formula for comparative learning is as follows:

[0056]

[0057] Where τ is the temperature hyperparameter in contrastive learning, sim(,) is the function for calculating cosine similarity, and M is C SAC and C SCS The number of rows, C SAC (i,:) and C SCS (i,:) represent C SAC and C SCS The feature representation of the i-th row of the matrix, L c It yields the contrastive learning loss value, where log is a logarithmic function;

[0058] We will perform attention fusion to obtain the feature matrices D of the two diseases. SAD and D SDS Comparative learning is performed, and the calculation formula for comparative learning is as follows:

[0059]

[0060] Where τ is the temperature hyperparameter in contrastive learning, sim(,) is the function for calculating cosine similarity, and N is the D... SAD and D SDS The number of rows, D SAD (i,:) and D SDS (i,:) represent D respectively SAD and D SDS The feature representation of the i-th row of the matrix, L d It yields the contrastive learning loss value, where log is a logarithmic function;

[0061] S3.5: Therefore, the total learning loss value is compared as follows:

[0062] L c+d =L c +L d

[0063] During training, the model optimizes to obtain four feature matrices related to the final disease and circRNA by minimizing the loss value of contrastive learning: C SAC C SCS D SAD D SDS .

[0064] Preferably, S4 includes:

[0065] S4.1: Considering the importance of the known association between circRNA and disease, the model uses a variational autoencoder (VAE) to obtain nonlinear features of circRNA and disease. Here, we take obtaining the nonlinear features of circRNA as an example:

[0066]

[0067] Where ACD is the association matrix of circRNA-disease, W CD It is the weight matrix of ACD, b CD W is the deviation matrix of ACD. CD and b CD Given by a variational autoencoder, It is the feature matrix after activation processing, and tanh is an activation function;

[0068] S4.2: Next, we use two independent fully connected layers to obtain the mean M of the features. c Sum of variance U c The calculation is as follows:

[0069]

[0070] Among them, W Mc and W Uc yes The learnable weight matrix, b Mc and b Uc yes The deviation matrix, W Mc W Uc b Mc b Uc Given by the variational autoencoder, tanh is an activation function;

[0071] S4.3: Finally, the nonlinear characteristics of the circRNA obtained by VAE are calculated using the following formula:

[0072] C v =M c +U c ⊙ε

[0073] Where ε is a random vector sampled from the standard normal distribution, and ⊙ represents element-wise multiplication. Similarly, we can also use ACD. T The input is fed into a variational autoencoder to obtain the nonlinear features D of the disease. v .

[0074] Preferably, S5 includes:

[0075] S5.1: Integrating circRNAs and disease features obtained through attention fusion graph-hypergraph convolutional networks and contrastive learning:

[0076]

[0077] Here, sigmoid is an activation function because C SAC and D SADBoth are cosine similarity matrices calculated based on ACD, so here we use the product of these two feature matrices and activate them to obtain the circRNA-disease score matrix CD1,C. SCS and D SDS After multiplication and activation, the circRNA-disease score matrix CD2 is obtained.

[0078] The obtained CD1 and CD2 are smoothed as follows:

[0079] CD e =βCD1+(1-β)CD2

[0080] Where β is a parameter that balances the contributions of CD1 and CD2;

[0081] S5.2: Integrating circRNAs and disease features obtained through a variational autoencoder:

[0082]

[0083] Where sigmoid is an activation function, C v and D v The circRNA and disease feature matrix obtained through an autoencoder, CD v This indicates that by integrating C v and D v The resulting circRNA-disease score matrix;

[0084] S5.3: Finally, the final circRNA-disease score matrix CD is obtained:

[0085] CD = λCD e +(1-λ)CD v

[0086] Where λ is the equilibrium CD e and CD v The parameters of the contribution.

[0087] Compared with the prior art, the beneficial effects of the present invention are:

[0088] 1. Based on two circRNA similarity matrices and two disease similarity matrices, we constructed corresponding graph adjacency matrices and hypergraph adjacency matrices, respectively. Then, we used graph convolutional and hypergraph convolutional networks to obtain feature representations, which fully explored the multi-level features in the data.

[0089] 2. We used an attention aggregation mechanism to assign importance to features obtained from graph convolutional networks and hypergraph convolutional networks, which promoted the complementarity of low-order and high-order features during the fusion process.

[0090] 3. We use contrastive learning to achieve information exchange between features.

[0091] 4. Our method, AGHCL, significantly outperforms existing methods across all metrics on benchmark datasets. Attached Figure Description

[0092] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0093] In the attached diagram:

[0094] Figure 1 This describes the algorithm flow.

[0095] Figure 2 To predict the matching of the top 10 circRNAs associated with lung cancer with literature PMID numbers, and to create a chord diagram of the relationship between circRNAs and miRNAs.

[0096] Figure 3 This is a comparison of our method with other methods.

[0097] Figure 4 This is a flowchart of the method of the present invention. Detailed Implementation

[0098] The following is in conjunction with the appendix Figure 1-4 The preferred embodiments of the present invention will be described herein. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0099] A method for predicting circRNA-disease associations based on attention fusion graph-hypergraph convolutional networks includes:

[0100] S1: Construct the following matrices based on database information: circRNA-disease association matrix (ACD), circRNA association cosine similarity matrix (SAC), disease association cosine similarity matrix (SAD), circRNA functional second-order similarity matrix (SCS), and disease semantic second-order similarity matrix (SDS); including:

[0101] S1.1: Constructing the association matrix between circRNA and disease The method is as follows:

[0102] Obtain m circRNAs, n diseases, and association information between circRNAs and diseases from known databases. Use these data to construct a circRNA-disease association matrix (ACD). For any element ACD(i,j) in ACD, if there is an association between circRNA i and disease j, then ACD(i,j) = 1, otherwise it is 0.

[0103] S1.2: Constructing the cosine similarity matrix of circRNA associations The calculation formula is:

[0104]

[0105] Where ACD is the association matrix between circRNA and disease, ACD(i,:) is the vector in the i-th row of ACD, ACD(j,:) is the vector in the j-th row of ACD, ||ACD(i,:)|| is the modulus of ACD(i,:), ||ACD(j,:)|| is the modulus of ACD(j,:), and SAC(i,j) represents the cosine similarity between the i-th and j-th circRNAs. According to the above formula, we calculate the cosine similarity between each circRNA to obtain the circRNA association cosine similarity matrix.

[0106] S1.3: Constructing a cosine similarity matrix of disease associations The calculation formula is:

[0107]

[0108] Where ACD is the association matrix of circRNA-disease, ACD(:,i) is the vector in the i-th column of ACD, ACD(:,j) is the vector in the j-th column of ACD, ||ACD(:,i)|| is the modulus of ACD(:,i), ||ACD(:,j)|| is the modulus of ACD(:,j), and SAD(i,j) represents the cosine similarity between the i-th and j-th diseases. According to the above formula, we calculate the cosine similarity between each disease to obtain the disease association cosine similarity matrix.

[0109] S1.4: Constructing a second-order semantic similarity matrix for diseases

[0110] We use the Bioconductor package in R to calculate the semantic similarity between diseases, which yields a disease semantic similarity matrix. We calculate the second-order semantic similarity SDS(i,j) of a disease based on its semantic similarity matrix, using the following formula:

[0111]

[0112] Where SD is the disease semantic similarity matrix, SD(i,:) is the vector in the i-th row of SD, SD(j,:) is the vector in the j-th row of SD, ||SD(i,:)|| is the modulus of SD(i,:), ||SD(j,:)|| is the modulus of SD(j,:), and SDS(i,j) represents the semantic second-order similarity between the i-th disease and the j-th disease; according to the above formula, we calculate the cosine similarity between each disease to obtain the disease semantic second-order similarity matrix;

[0113] S1.5: Constructing a second-order functional similarity matrix for circRNAs The method is as follows:

[0114] Based on the property that two circRNAs with similar disease groups often have similar functions, a functional similarity matrix of circRNAs can be obtained. We calculate the second-order functional similarity (SCS(i,j)) of circRNAs based on the functional similarity matrix of circRNAs, using the following formula:

[0115]

[0116] Where SC is the circRNA functional similarity matrix, SC(i,:) is the vector in the i-th row of SC, SC(j,:) is the vector in the j-th row of SC, ||SC(i,:)|| is the modulus of SC(i,:), ||SCj,:)|| is the modulus of SC(j,:), and SCS(i,j) represents the functional second-order similarity between the i-th circRNA and the j-th circRNA. According to the above formula, we calculate the functional second-order similarity between each circRNA, and we can obtain the circRNA functional second-order similarity matrix.

[0117] S2: Based on four similarity matrices (SAC, SAD, CSC, SDS), corresponding graph adjacency matrices and hypergraph adjacency matrices are constructed respectively. Graph convolutional networks are used to extract low-order local feature representations of circRNAs and diseases in the graph, and hypergraph convolutional networks are used to extract high-order global feature representations of circRNAs and diseases in the hypergraph; including:

[0118] S2.1: Methods for constructing graph adjacency matrices using the four similarity matrices mentioned above:

[0119] In a simple graph where each edge connects only two nodes, we construct an adjacency matrix to reflect the relationships between any two nodes by finding the nodes most similar to each node. In this study, if the graph is constructed using a circRNA similarity matrix, the nodes represent each circRNA; if the graph is constructed using a disease similarity matrix, the nodes represent each disease. For example, in the adjacency matrix, if node i and node j are connected, then G(i,j) = 1, indicating that the i-th circRNA and the j-th circRNA are related, or the i-th disease and the j-th disease are related; otherwise, it is 0.

[0120] Based on the second-order similarity matrix of circRNA function, the cosine similarity matrix of disease association, the second-order similarity matrix of disease semantics, and the cosine similarity matrix of circRNA association, their corresponding graph adjacency matrices are constructed, resulting in the graph adjacency matrix G. SCS G SAD G SDS G SAC ;

[0121] S2.2: Methods for constructing hypergraph adjacency matrices using the four similarity matrices mentioned above:

[0122] A hypergraph is a special form of graph where a hyperedge can connect any number of nodes, representing the common associations between them. Therefore, a hypergraph can represent higher-order relationships between nodes. We construct hyperedges by collecting the nodes most similar to each node; the number of hyperedges corresponds to the number of nodes. In this study, a hypergraph constructed using a circRNA similarity matrix represents each circRNA, while a hypergraph constructed using a disease similarity matrix represents each disease. For example, in the hypergraph adjacency matrix, if node a is contained in hyperedge e, then H(a,e) = 1, indicating that hyperedge e contains either the a-th circRNA or the a-th disease; otherwise, it is 0.

[0123] Based on the second-order similarity matrix of circRNA function, the cosine similarity matrix of disease association, the second-order similarity matrix of disease semantics, and the cosine similarity matrix of circRNA association, their corresponding hypergraph adjacency matrices are constructed respectively, resulting in hypergraph adjacency matrices denoted as: H SCS H SAD H SDS H SAC ;

[0124] S2.3: The calculation formula for the graph convolutional network described in S2 is:

[0125]

[0126] Where G is the input graph adjacency matrix, and D is the degree matrix corresponding to the input graph adjacency matrix. G (l) It is a graph convolutional network X G The feature matrix of the l-th layer, where each row of the matrix represents the feature representation of a node (circRNA or disease) in the l-th layer. X is the weight matrix of the l-th layer in a graph convolutional network. G (l+1) is the feature matrix of the (l+1)th layer output by the graph convolutional network. Each row of the matrix represents the feature representation of a node (circRNA or disease) in the (l+1)th layer, and σ represents the non-linear activation function.

[0127] We will respectively view Figure G SCS Figure G SAD Figure G SAC And Figure G SDS Substituting these values ​​into the above graph convolutional network formula, we obtain the corresponding feature representation matrices.

[0128] S2.4: The calculation formula for the hypergraph convolutional network described in S2 is as follows:

[0129]

[0130] Where H is the input hypergraph adjacency matrix, X H (l) This represents the feature matrix of the l-th layer in a hypergraph convolutional network. D represents the weight matrix of the l-th layer in a hypergraph convolutional network; e This is the hyperedge degree matrix of the input hypergraph adjacency matrix. This matrix is ​​a diagonal matrix describing the degree of each hyperedge, i.e., the sum of the number of nodes (circRNAs or diseases) connected by that hyperedge; D v is a matrix of vertex degrees from the input hypergraph adjacency matrix. This matrix is ​​a diagonal matrix that describes the degree of each vertex, i.e., the sum of the number of hyperedges to which the node (circRNA or disease) belongs. P is the weight matrix of the hyperedges. Specifically, during hypergraph convolution, nodes connected by common hyperedges propagate more widely. Hyperedges with larger weights should be considered more reliable feature propagation carriers and occupy a higher proportion in the information aggregation process.

[0131] We will respectively define the hypergraph H SCS Hypergraph H SAD Hypergraph H SAC He Chaotu H SDS Substituting these values ​​into the hypergraph convolutional network formula above, we obtain the corresponding feature representation matrices.

[0132] S3: Dynamically fuses low-order local features of circRNA and disease obtained from graph convolutional networks and high-order global features of circRNA and disease obtained from hypergraph convolutional networks through an attention aggregation mechanism, and uses contrastive learning to promote information interaction between features; including:

[0133] S3.1: We take the hypergraph H as an example. SAC And Figure G SAC After performing hypergraph convolution and graph convolution operations, the two feature matrices obtained are and Let's take an example to illustrate. and The i-th row represents the feature representation of the i-th circRNA, and the feature matrix... and The attention score is calculated by transforming the i-th row respectively:

[0134]

[0135] Among them, W i It is a weight matrix, and tanh is the activation function. This indicates that the graph convolutional network starts from the graph adjacency matrix G. SAC The low-order local features of the i-th circRNA extracted from it are represented as follows: This indicates that the hypergraph convolutional network starts from the hypergraph adjacency matrix H. SAC The high-order global feature representation of the i-th circRNA extracted, q i It is a trainable parameter vector. yes Attention score yes Attention score;

[0136] S3.2: To make attention scores comparable, we normalize them using the exp exponential function. and

[0137]

[0138] in, Indicates to Process the resulting new attention score, Indicates to The resulting new attention score is processed, where exp is an exponential function.

[0139] S3.3: Using the obtained attention score and Aggregate feature matrix and The feature representation of the i-th row yields C. SAC (i,:):

[0140]

[0141] Finally, we aggregate the feature matrix using the formula described above. and The feature representation of each row can be used to obtain the final feature representation matrix C. SAC Similarly, we consider the characteristic matrix and and and An attention aggregation mechanism is also used to obtain the feature representation matrix: C SCS D SAD D SDS ;

[0142] S3.4: Next, we will perform the feature matrix C of the two circRNAs obtained after attention fusion. SAC and C SCS Comparative learning is performed, and the calculation formula for comparative learning is as follows:

[0143]

[0144] Where τ is the temperature hyperparameter in contrastive learning, sim(,) is the function for calculating cosine similarity, and M is C SAC and C SCS The number of rows, C SAC (i,:) and C SCS (i,:) represent C SAC and C SCS The feature representation of the i-th row of the matrix, L c It yields the contrastive learning loss value, where log is a logarithmic function;

[0145] We will perform attention fusion to obtain the feature matrices D of the two diseases. SAD and D SDS Comparative learning is performed, and the calculation formula for comparative learning is as follows:

[0146]

[0147] Where τ is the temperature hyperparameter in contrastive learning, sim(,) is the function for calculating cosine similarity, and N is the D... SAD and D SDS The number of rows, D SAD (i,:) and D SDS (i,:) represent D respectively SAD and D SDSThe feature representation of the i-th row of the matrix, L d This yields the contrastive learning loss value;

[0148] S3.5: Therefore, the total learning loss value is compared as follows:

[0149] L c+d =L c +L d

[0150] During training, the model optimizes to obtain four feature matrices related to the final disease and circRNA by minimizing the loss value of contrastive learning: C SAC C SCS D SAD D SDS .

[0151] S4: Extracting circRNAs and nonlinear features of the disease from ACD using a variational autoencoder; including:

[0152] S4.1: Considering the importance of the known association between circRNA and disease, the model uses a variational autoencoder (VAE) to obtain nonlinear features of circRNA and disease. Here, we take obtaining the nonlinear features of circRNA as an example:

[0153]

[0154] Where ACD is the association matrix of circRNA-disease, W CD It is the weight matrix of ACD, b CD W is the deviation matrix of ACD. CD and b CD Given by a variational autoencoder, It is the feature matrix after activation processing, and tanh is an activation function;

[0155] S4.2: Next, we use two independent fully connected layers to obtain the mean M of the features. c Sum of variance U c The calculation is as follows:

[0156]

[0157] Among them, W Mc and W Uc yes The learnable weight matrix, b Mc and b Uc yes The deviation matrix, W Mc W Uc b Mc b UcGiven by the variational autoencoder, tanh is an activation function;

[0158] S4.3: Finally, the nonlinear characteristics of the circRNA obtained by VAE are calculated using the following formula:

[0159] C v =M c +U c ⊙ε

[0160] Where ε is a random vector sampled from the standard normal distribution, and ⊙ represents element-wise multiplication. Similarly, we can also use ACD. T The input is fed into a variational autoencoder to obtain the nonlinear features D of the disease. v .

[0161] S5: Integrating multiple circRNAs and disease features, a circRNA-disease association score matrix is ​​obtained to predict key circRNAs associated with the disease, including:

[0162] S5.1: Integrating circRNAs and disease features obtained through attention fusion graph-hypergraph convolutional networks and contrastive learning:

[0163]

[0164] Here, sigmoid is an activation function because C SAC and D SAD Both are cosine similarity matrices calculated based on ACD, so here we use the product of these two feature matrices and activate them to obtain the circRNA-disease score matrix CD1,C. SCS and D SDS After multiplication and activation, the circRNA-disease score matrix CD2 is obtained.

[0165] The obtained CD1 and CD2 are smoothed as follows:

[0166] CD e =βCD1+(1-β)CD2

[0167] Where β is a parameter that balances the contributions of CD1 and CD2;

[0168] S5.2: Integrating circRNAs and disease features obtained through a variational autoencoder:

[0169]

[0170] Where sigmoid is an activation function, C v and D v The circRNA and disease feature matrix obtained through an autoencoder, CDv This indicates that by integrating C v and D v The resulting circRNA-disease score matrix;

[0171] S5.3: Finally, the final circRNA-disease score matrix CD is obtained:

[0172] CD = λCD e +(1-λ)CD v

[0173] Where λ is the equilibrium CD e and CD v The parameters of the contribution.

[0174] Simulation experiment:

[0175] We trained the model and then predicted potentially disease-associated circRNAs. Finally, we obtained a circRNA-disease score matrix, with rows representing circRNAs and columns representing diseases. To demonstrate our model's ability to predict circRNA-disease associations, we conducted a case study. We chose a common hallmark disease: lung cancer. Lung cancer is the most common cancer globally. Based on the predicted scores for lung cancer and related circRNAs, we selected the top 10 lung cancer-associated circRNAs and validated them using the document PMID numbers in the PubMed medical database, proving that our predicted top 10 circRNAs were indeed associated with lung cancer. We then performed a miRNA regulatory analysis on the predicted circRNAs. Previous studies have shown that circRNAs often exert their effects on diseases by regulating corresponding miRNAs. For example, hsa_circ_0000284 promotes the proliferation of NCI-H1299 and NCI-H2170 cells through miR-379 and its target IGF1, potentially making it a lung tumor biomarker. First, we obtained lung cancer-associated miRNAs from the HMDD database. We then linked these miRNAs with the top 10 predicted circRNAs to obtain a relational chord diagram. The diagram revealed that 7 of the top 10 predicted lung cancer-associated circRNAs interacted with 35 lung cancer-associated miRNAs, further supporting our prediction of a lung cancer association. Figure 2 The matching results of the top 10 circRNAs with the highest lung cancer scores and their corresponding PMID numbers from the literature were listed, along with a chord diagram showing the relationship between circRNAs and miRNAs.

[0176] Subsequently, we compared the proposed method AGHCL with other state-of-the-art methods (HGCNMDA (Peng W, Che Z, Dai W, Wei S, Lan W. Predicting miRNA-Disease Associations From miRNA-Gene-Disease Heterogeneous Network With Multi-Relational Graph Convolutional Network Model. IEEE / ACM Trans Comput Biol Bioinform. 2023; 20(6):3363-3375.), AGAEMDA (Zhang H, Fang J, Sun Y, Xie G, Lin Z, Gu G. Predicting miRNA-Disease Associations via Node-Level Attention Graph Auto-Encoder. IEEE / ACM Trans Comput Biol Bioinform. 2023; 20(2):1308-1318.), GATCL2CD (Peng L, Yang C, Chen Y, Liu W. Predicting CircRNA-Disease Associations via Feature Convolutional Network Model). The study compared two models: * **Learning with Heterogeneous Graph Attention Network (IEEE J Biomed Health Inform. 2023; 27(6):3072-3082.)** and * **MHCLMDA (Peng W, He Z, Dai W, Lan W. MHCLMDA: multihypergraph contrastive learning for miRNA-disease association prediction. Brief Bioinform. 2023; 25(1): bbad524.)**. Five metrics were used to evaluate the model's predictive performance: AUC, AUPR, F1SCORE, PRECISION, and RECALL. Figure 3 This is a comparison of our method with other methods.

[0177] Figure 1 This describes the algorithm flow. Figure 2It predicts the matching of the top 10 circRNAs associated with lung cancer with the PMID numbers in the literature, as well as the relationship chord diagram between circRNAs and miRNAs. Figure 3 This is a comparison of our method AGHCL with other methods.

[0178] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A method for predicting circRNA-disease associations based on attention fusion graph-hypergraph convolutional networks, characterized in that: include: S1: Based on database information, construct the circRNA-disease association matrix (ACD), circRNA association cosine similarity matrix (SAC), disease association cosine similarity matrix (SAD), circRNA functional second-order similarity matrix (SCS), and disease semantic second-order similarity matrix (SDS). S2: Based on four similarity matrices (SAC, SAD, CSC, SDS), corresponding graph adjacency matrices and hypergraph adjacency matrices are constructed respectively. Graph convolutional networks are used to extract low-order local feature representations of circRNAs and diseases in the graph, and hypergraph convolutional networks are used to extract high-order global feature representations of circRNAs and diseases in the hypergraph. S3: Dynamically fuse low-order local features of circRNA and disease obtained from graph convolutional networks and high-order global features of circRNA and disease obtained from hypergraph convolutional networks through an attention aggregation mechanism, and use contrastive learning to promote information interaction between features; S4: Extracting circRNA and nonlinear features of the disease from ACD using a variational autoencoder; S5: Integrate multiple circRNAs and disease features to obtain a circRNA-disease association score matrix to predict key circRNAs associated with diseases.

2. The circRNA-disease association prediction method based on attention fusion graph-hypergraph convolutional network according to claim 1, characterized in that: S1 includes: S1.1: The method for constructing the circRNA-disease association matrix (ACD) is as follows: We obtain m circRNAs, n diseases, and association information between circRNAs and diseases from known databases, and use this data to construct a circRNA-disease association matrix. For any element ACD(i,j) in ACD, if there is a correlation between circRNA i and disease j, then ACD(i,j) = 1, otherwise it is 0; S1.2: Constructing the cosine similarity matrix of circRNA associations The calculation formula is: Where ACD is the association matrix between circRNA and disease, ACD(i,:) is the vector in the i-th row of ACD, ACD(j,:) is the vector in the j-th row of ACD, ||ACD(i,:)|| is the modulus of ACD(i,:), ||ACD(j,:)|| is the modulus of ACD(j,:), and SAC(i,j) represents the cosine similarity between the i-th and j-th circRNAs. According to the above formula, we calculate the cosine similarity between each circRNA to obtain the circRNA association cosine similarity matrix (SAC). S1.3: Constructing a cosine similarity matrix of disease associations The calculation formula is: Where ACD is the association matrix of circRNA-disease, ACD(:,i) is the vector in the i-th column of ACD, ACD(:,j) is the vector in the j-th column of ACD, ||ACD(:,i)|| is the modulus of ACD(:,i), ||ACD(:,j)|| is the modulus of ACD(:,j), and SAD(i,j) represents the cosine similarity between the i-th and j-th diseases. According to the above formula, we calculate the cosine similarity between each disease to obtain the disease association cosine similarity matrix (SAD). S1.4: Constructing a second-order semantic similarity matrix for diseases We use the Bioconductor package in R to calculate the semantic similarity between diseases, which yields a disease semantic similarity matrix. We calculate the second-order semantic similarity SDS(i,j) of a disease based on its semantic similarity matrix, using the following formula: Where SD is the disease semantic similarity matrix, SD(i,:) is the vector in the i-th row of SD, SD(j,:) is the vector in the j-th row of SD, ||SD(i,:)|| is the modulus of SD(i,:), ||SD(j,:)|| is the modulus of SD(j,:), and SDS(i,j) represents the semantic second-order similarity between the i-th and j-th diseases. Based on the above formula, we calculate the cosine similarity between each disease to obtain the disease semantic second-order similarity matrix. S1.5: The method for constructing the second-order functional similarity matrix (SCS) of circRNAs is as follows: Based on the property that two circRNAs with similar disease groups often have similar functions, a functional similarity matrix of circRNAs can be obtained. We calculate the second-order functional similarity (SCS(i,j)) of circRNAs based on the functional similarity matrix of circRNAs, using the following formula: Here, SC is the circRNA functional similarity matrix, SC(i,:) is the vector in the i-th row of SC, SC(j,:) is the vector in the j-th row of SC, ||SC(i,:)|| is the modulus of SC(i,:), ||SC(j,:)|| is the modulus of SC(j,:), and SCS(i,j) represents the functional second-order similarity between the i-th and j-th circRNAs. Based on the above formula, we calculate the functional second-order similarity between each circRNA, thus obtaining the circRNA functional second-order similarity matrix.

3. The circRNA-disease association prediction method based on attention fusion graph-hypergraph convolutional network according to claim 2, characterized in that: S2 includes: S2.1: Methods for constructing graph adjacency matrices using the four similarity matrices mentioned above: In a simple graph, each edge connects only two nodes. We construct an adjacency matrix to reflect the relationship between any two nodes by finding the nodes most similar to each node. In this study, if the graph is constructed using a circRNA similarity matrix, the nodes represent each circRNA; if the graph is constructed using a disease similarity matrix, the nodes represent each disease. For example, in the adjacency matrix of the graph, if node i and node j are connected, then G(i,j) = 1, indicating that the i-th circRNA and the j-th circRNA are related or the i-th disease and the j-th disease are related; otherwise, it is 0. Based on the second-order similarity matrix of circRNA function, the cosine similarity matrix of disease association, the second-order similarity matrix of disease semantics, and the cosine similarity matrix of circRNA association, their corresponding graph adjacency matrices are constructed, resulting in the graph adjacency matrix G. SCS G SAD G SDS G SAC ; S2.2: Methods for constructing hypergraph adjacency matrices using the four similarity matrices mentioned above: A hypergraph is a special form of graph where a hyperedge can connect any number of nodes, representing common associations between them. Therefore, a hypergraph can represent higher-order relationships between nodes. We construct hyperedges by collecting the nodes most similar to each node; the number of hyperedges corresponds to the number of nodes. In this study, a hypergraph constructed using a circRNA similarity matrix represents each circRNA, while a hypergraph constructed using a disease similarity matrix represents each disease. For example, in the hypergraph adjacency matrix, if node a is contained in hyperedge e, then H(a,e) = 1, indicating that hyperedge e contains either the a-th circRNA or the a-th disease; otherwise, it is 0. Based on the second-order similarity matrix of circRNA function, the cosine similarity matrix of disease association, the second-order similarity matrix of disease semantics, and the cosine similarity matrix of circRNA association, their corresponding hypergraph adjacency matrices are constructed respectively, resulting in hypergraph adjacency matrices denoted as: H SCS H SAD H SDS H SAC ; S2.3: The calculation formula for the graph convolutional network described in S2 is: Where G is the input graph adjacency matrix, D is the degree matrix corresponding to the input graph adjacency matrix, and X... G (l) It is a graph convolutional network X G The feature matrix of the l-th layer, where each row of the matrix represents the feature representation of a node (circRNA or disease) in the l-th layer. X is the weight matrix of the l-th layer in a graph convolutional network. G (l+1) is the feature matrix of the (l+1)th layer output by the graph convolutional network. Each row of the matrix represents the feature representation of a node (circRNA or disease) in the (l+1)th layer, and σ represents the non-linear activation function. We will respectively view Figure G SCS Figure G SAD Figure G SAC And Figure G SDS Substituting these values ​​into the above graph convolutional network formula, we obtain the corresponding feature representation matrices. S2.4: The calculation formula for the hypergraph convolutional network described in S2 is as follows: Where H is the input hypergraph adjacency matrix, X H (l) This represents the feature matrix of the l-th layer in a hypergraph convolutional network. D represents the weight matrix of the l-th layer in a hypergraph convolutional network. e This is the hyperedge degree matrix of the input hypergraph adjacency matrix. This matrix is ​​a diagonal matrix describing the degree of each hyperedge, i.e., the sum of the number of nodes (circRNAs or diseases) connected by that hyperedge. D v is a matrix of vertex degrees of the hypergraph adjacency matrix. This matrix is ​​a diagonal matrix that describes the degree of each vertex, i.e., the sum of the number of hyperedges to which the node (circRNA or disease) belongs. P is the weight matrix of the hyperedges. Specifically, during hypergraph convolution, nodes connected by common hyperedges propagate more widely. Hyperedges with larger weights should be regarded as more reliable feature propagation carriers and occupy a higher proportion in the information aggregation process. We will respectively define the hypergraph H SCS Hypergraph H SAD Hypergraph H SAC He Chaotu H SDS Substituting these values ​​into the hypergraph convolutional network formula above, we obtain the corresponding feature representation matrices.

4. The circRNA-disease association prediction method based on attention fusion graph-hypergraph convolutional network according to claim 3, characterized in that: S3 includes: S3.1: We take the hypergraph H as an example. SAC And Figure G SAC After performing hypergraph convolution and graph convolution operations, the two feature matrices obtained are and Let's take an example to illustrate. and The i-th row represents the feature representation of the i-th circRNA, and the feature matrix... and The attention score is calculated by transforming the i-th row respectively: Among them, W i It is a weight matrix, and tanh is the activation function. This indicates that the graph convolutional network starts from the graph adjacency matrix G. SAC The low-order local features of the i-th circRNA extracted from it are represented as follows: This indicates that the hypergraph convolutional network starts from the hypergraph adjacency matrix H. SAC The high-order global feature representation of the i-th circRNA extracted, q i It is a trainable parameter vector. yes Attention score yes Attention score; S3.2: To make attention scores comparable, we normalize them using the exp exponential function. and in, Indicates to Process the resulting new attention score, Indicates to The resulting new attention score is processed, where exp is an exponential function. S3.3: Using the obtained attention score and Aggregate feature matrix and The feature representation of the i-th row yields C. SAC (i,:): Finally, we aggregate the feature matrix using the formula described above. and The feature representation of each row can be used to obtain the final feature representation matrix C. SAC Similarly, we consider the characteristic matrix and and and An attention aggregation mechanism is also used to obtain the feature representation matrix: C SCS D SAD D SDS ; S3.4: Next, we will perform the feature matrix C of the two circRNAs obtained after attention fusion. SAC and C SCS Comparative learning is performed, and the calculation formula for comparative learning is as follows: Where τ is the temperature hyperparameter in contrastive learning, sim(,) is the function for calculating cosine similarity, and M is C SAC and C SCS The number of rows, C SAC (i,:) and C SCS (i,:) represent C SAC and C SCS The feature representation of the i-th row of the matrix, L c It yields the contrastive learning loss value, where log is a logarithmic function; We will perform attention fusion to obtain the feature matrices D of the two diseases. SAD and D SDS Comparative learning is performed, and the calculation formula for comparative learning is as follows: Where τ is the temperature hyperparameter in contrastive learning, sim(,) is the function for calculating cosine similarity, and N is the D... SAD and D SDS The number of rows, D SAD (i,:) and D SDS (i,:) represent D respectively SAD and D SDS The feature representation of the i-th row of the matrix, L d It yields the contrastive learning loss value, where log is a logarithmic function; S3.5: Therefore, the total learning loss value is compared as follows: L c+d =L c +L d During training, the model optimizes to obtain four feature matrices related to the final disease and circRNA by minimizing the loss value of contrastive learning: C SAC C SCS D SAD D SDS .

5. The circRNA-disease association prediction method based on attention fusion graph-hypergraph convolutional network according to claim 4, characterized in that: S4 include: S4.1: Considering the importance of the known association between circRNA and disease, the model uses a variational autoencoder (VAE) to obtain nonlinear features of circRNA and disease. Here, we take obtaining the nonlinear features of circRNA as an example: Where ACD is the association matrix of circRNA-disease, W CD It is the weight matrix of ACD, b CD W is the deviation matrix of ACD. CD and b CD Given by a variational autoencoder, It is the feature matrix after activation processing, and tanh is an activation function; S4.2: Next, we use two independent fully connected layers to obtain the mean M of the features. c Sum of variance U c The calculation is as follows: Among them, W Mc and W Uc yes The learnable weight matrix, b Mc and b Uc yes The deviation matrix, W Mc W Uc b Mc b Uc Given by the variational autoencoder, tanh is an activation function; S4.3: Finally, the nonlinear characteristics of the circRNA obtained by VAE are calculated using the following formula: C v =M c +U c ⊙ε Where ε is a random vector sampled from the standard normal distribution, and ⊙ represents element-wise multiplication. Similarly, we can also use ACD. T The input is fed into a variational autoencoder to obtain the nonlinear features D of the disease. v .

6. The circRNA-disease association prediction method based on attention fusion graph-hypergraph convolutional network according to claim 5, characterized in that: S5 include: S5.1: Integrating circRNAs and disease features obtained through attention fusion graph-hypergraph convolutional networks and contrastive learning: Here, sigmoid is an activation function because C SAC and D SAD Both are cosine similarity matrices calculated based on ACD, so here we use the product of these two feature matrices and activate them to obtain the circRNA-disease score matrix CD1,C. SCS and D SDS After multiplication and activation, the circRNA-disease score matrix CD2 is obtained. The obtained CD1 and CD2 are smoothed as follows: CD e =βCD1+(1-β)CD2 Where β is a parameter that balances the contributions of CD1 and CD2; S5.2: Integrating circRNAs and disease features obtained through a variational autoencoder: Where sigmoid is an activation function, C v and D v The circRNA and disease feature matrix obtained through an autoencoder, CD v This indicates that by integrating C v and D v The resulting circRNA-disease score matrix; S5.3: Finally, the final circRNA-disease score matrix CD is obtained: CD=λCD e +(1-λ)CD v Where λ is the equilibrium CD e and CD v The parameters of the contribution.

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