A disease-related circular RNA network construction method based on multi-dimensional functional data

Abstract

The application discloses a disease-related circRNA network construction method based on multidimensional function data, which is composed of two parts. The first part integrates multidimensional function data, including a circRNA similar network, a disease similar network and a circRNA and disease adjacent network, so as to form a correlation network. The second part learns the characteristics of the correlation network by using an RWR algorithm to obtain a disease-related circRNA network. The application can be used for predicting the correlation between diseases and circRNAs, providing reliable input data for a prediction model, and thus obtaining good prediction results. The disease-related circRNA network based on multidimensional function data constructed by the application has good effects in subsequent experiments for predicting disease-related circRNAs, and the prediction accuracy is high.

Description

Technical Field

[0001] This invention belongs to the field of biomedical electrotechnology, specifically relating to a method for constructing a disease-related circular RNA network. Background Technology

[0002] Lei et al., in “Lei Xiujuan, Bian Chen. Integrating random walk with restart and k-Nearest Neighbor to identify novel circRNA-disease association. Scientific Reports. 2020; 10(1).”, constructed a feature matrix association network between diseases and circular RNA by integrating disease semantic similarity, GIP nuclear similarity, and circular RNA functional similarity. Deng et al., in “Deng Lei, Zhang Wei, Shi Yechuan, et al. Fusion of multiple heterogeneous networks for predicting circRNA-disease associations. Scientific Reports. 2019; 9.”, described how, due to the insufficient number of experimentally verified associations between circular RNA and diseases, they utilized protein-circular RNA association networks and protein-disease association networks to infer the association network between circular RNA and diseases. Zhao et al., in their paper "Zhao Qi, Yang Yingjuan, Ren Guofei, et al. Integrating Bipartite Network Projection and KATZ Measure to Identify Novel CircRNA-Disease Associations. IEEE Transactions on Nanobioscience. 2019; 18(4): 578-84," used a bipartite network projection algorithm to apply the resource score of circular RNA as an association score for a specific disease. Specifically, they used a hierarchical clustering algorithm to construct a biased rating of circular RNA, thereby obtaining an association network between circular RNA and disease. However, these methods do not consider integrating multi-dimensional functional data to construct the network, which may lead to a decrease in the performance of subsequent models using the network. Summary of the Invention

[0003] To overcome the shortcomings of existing technologies, this invention provides a method for constructing a disease-associated circular RNA (DRNA) network based on multi-dimensional functional data. The method consists of two parts: the first part integrates multi-dimensional functional data, including a circular RNA similarity network, a disease similarity network, and a circular RNA-disease adjacency network, thus forming an association network; the second part uses the RWR algorithm to learn the features of the association network, obtaining the disease-associated circular RNA network. This invention can be used to predict the association between diseases and circular RNAs, providing reliable input data for prediction models and thus obtaining good prediction results. The disease-associated circular RNA network constructed by this invention based on multi-dimensional functional data has shown good performance and high prediction accuracy in subsequent experiments predicting disease-associated circular RNAs.

[0004] The technical solution adopted by this invention to solve its technical problem includes the following steps:

[0005] Step 1: Construction of a miRNA-based circular RNA association network;

[0006] After obtaining circular RNA and miRNA association data from starBase, the similarity of circular RNAs was calculated using circular RNA-miRNA interactions; the formula for calculating similarity is:

[0007]

[0008] Among them, c i c represents the i-th type of circular RNA. j Let m represent the j-th circular RNA. i Indicates c i The number of relevant miRNAs, m = m i ∩m j That is, m is the number of miRNAs that are the same for the i-th type of circular RNA and the j-th type of circular RNA; CS mi (c i ,c j ) represents c i and c j Circular RNA-miRNA similarity;

[0009] Step 2: Construction of a circular RNA association network based on the binding protein RBP;

[0010] The similarity calculation formula based on the binding protein RBP is as follows:

[0011]

[0012] Where, r i Indicates c i The number of relevant RBPs, r = r i ∩r jThat is, r is the number of RBPs that are the same for the i-th type of circular RNA and the j-th type of circular RNA; CS rbp (c i ,c j ) represents c i and c j Circular RNA-RBP similarity;

[0013] Step 3: Construction of a circular RNA association network based on hybrid game representation CGR;

[0014] Step 3-1: Represent the position of each nucleotide in a plane, using the following formula:

[0015] P i =0.5*(P i-1 +S i i = 1...N

[0016] Let P0 be an arbitrarily given starting point; N represent the sequence length; S i This represents the i-th nucleotide in the sequence;

[0017] Step 3-2: Following step 3-1, the CGR graph is transformed into N. x Grid N x =2 s ×2 s s=3, called the frequency matrix FCGR of the CGR plot, and the frequency matrix grid is represented as:

[0018] grid i =(X i ,Y i Z i )

[0019] In the formula, X i and Y i Z represents the sum of the x and y coordinates of all points located in the i-th grid, respectively. i The z-score represents the circRNA nucleotides quantified as potential features in the i-th grid.

[0020] Step 3-3: Accumulate the x-coordinate (point.x) and y-coordinate (point.y) of each grid to quantify the position information. Construct the feature vector of the sequence using the x-axis, y-axis directions and their numerical features. The calculation formula is as follows:

[0021] X i =∑point.x if point in grid

[0022] Y i =∑point.y if point in grid

[0023] Steps 3-4: Calculate Z for each grid cell i The fraction of z is used to quantify nonlinear information, and the calculation formula is as follows:

[0024]

[0025] Among them, Num i It is the number of coordinate points in the frequency matrix grid;

[0026] Steps 3-5: Each grid can be represented by three attributes. These attributes are fused to construct a vector, and the sequence similarity of circular RNA is defined by the Pearson correlation coefficient.

[0027]

[0028]

[0029] Among them, vector(c i ) represents the sequence vector of the i-th circular RNA, vector(c i )·vector(c j ) is vector(c i ) and vector(c j The dot product of ) and CS seq =(c i ,c j ) represents c i and c j Circular RNA-CGR sequence similarity;

[0030] Step 4: Extraction of circular RNA features;

[0031] After calculating the three circular RNA similarity networks, features were extracted using a collaborative training method based on shared constraints, resulting in the final feature matrices CSF of the three networks. mi CSF rbp and CSF seq ;

[0032] Step 4-1: Learning the topology of the circular RNA association network based on restarted random walk (RWR);

[0033] The RWR algorithm is used to capture network information from node x. i Initially, the node is moved to another adjacent node with a restart probability c, and this process is repeated iteratively. In each iteration, the node returns to the initial node x with probability c. i The v obtained after iterative stabilization ij That is, from node x i to node x j The probability of A, i.e., the relevance score; let A kIndicates network G k The adjacency matrix, RWR formula is as follows:

[0034]

[0035]

[0036] Where t and t+1 represent the t-th and t+1-th steps of the RWR algorithm, respectively; T ij This represents the i-th row and j-th column of the transition probability matrix T, where T is the column normalization result of matrix A, e i Represents node x i The initial feature vector;

[0037] By using the RWR algorithm on the adjacency matrix A network, node feature representations with global network structure information are obtained;

[0038] Step 4-2: Establishing constraints in collaborative training;

[0039] The node feature representations obtained in step 4-1 are input into the autoencoder to reconstruct the node feature representations. For each autoencoder, a Laplacian matrix L is generated based on the reconstructed feature matrix, using the following formula:

[0040]

[0041] Where X is the node feature representation obtained using the RWR algorithm, where X i X is the feature vector of node i, and X′ is the node feature representation reconstructed after inputting X into the autoencoder, where X... i X′ is the reconstructed feature vector of node i, E is the identity matrix with the same dimension as X′, and D is the degree matrix of X′.

[0042] The Pearson correlation coefficient (PCC) is calculated as a constraint between node a and node b. The calculation formula is as follows:

[0043]

[0044] Finally, the Pearson correlation coefficient (PCC) is used to measure the similarity between nodes. The PCC values ​​of all node pairs are sorted, and the node pairs with the highest PCC values ​​are considered to be strongly correlated. The strong correlations are stored in the strong correlation matrix M and used as prior information for the next autoencoder.

[0045] Step 4-3: Collaborative training based on shared constraints;

[0046] Based on a semi-supervised autoencoder, hidden features and strong correlations are taken as inputs, and the feature matrix of the original network is finally obtained after multiple iterations.

[0047] An autoencoder consists of two parts: an encoder and a decoder. The encoder represents high-dimensional features as low-dimensional features, while the decoder reconstructs the original high-dimensional features from the encoded low-dimensional features. The autoencoder is optimized by minimizing the mean squared error. The loss function based on the reconstructed features is as follows:

[0048]

[0049] Where, x i It is the original high-dimensional feature, y i These are the features reconstructed by the decoder, where n is the number of nodes;

[0050] A semi-supervised autoencoder is used, and the loss function based on strong correlation is as follows:

[0051]

[0052] Where M is a strong correlation matrix, M i,j ∈(0,1), h i and h j These are low-dimensional features processed by the encoder, and k is the number of strongly correlated pairs.

[0053] A semi-supervised autoencoder integrates strong correlations into the autoencoder, which minimizes the joint objective function based on the two formulas mentioned above, as shown below:

[0054] L all =λ1L con +λ2L must

[0055] Where λ1 and λ2 are the balanced reconstruction errors L con and constraint error L must The weighting coefficients.

[0056] Step 5: Network fusion of circular RNAs;

[0057] The cosine similarity method is used to calculate the feature matrix CSF obtained through a collaborative training method based on shared constraints. mi CSF rbp and CSF seq To merge;

[0058] First, the three feature matrices are integrated into a single fused feature matrix. Then, cosine similarity is used for calculation, as shown in the following formula:

[0059]

[0060] Where A is the fusion feature matrix, A T It is the transpose of A;

[0061] The final circular RNA similarity matrix CS is constructed based on cosine similarity.

[0062] Step 6: Disease Similarity Network;

[0063] The FNSemSim method was used to calculate disease similarity;

[0064] Three functional association networks were used: the Human Genome Connectome (HGC), HumanNet, and FunCoup. HumanNet and FunCoup, two association networks with different scoring systems, were fused to calculate gene similarity. After obtaining the fused functional association network, the Restarted Random Walk (RWR) algorithm was used to analyze the relationship between any two genes in the fused network. The association between a gene g and a gene set G is defined as follows:

[0065]

[0066] Where PRWR represents the probability of a gene being associated with another gene in the network after RWR calculation, and AG is the gene functional association network; if a gene g and some genes in genome G are included in the functional association network, but g does not belong to G, then R... G The definition is the maximum value of PRWR across all gene pairs;

[0067] Gene set G a ={g a1 ,g a2 ,…} and G b ={g b1 ,g b2 ,…} respectively with disease d a and d b Related, disease d a and d b The similarity between them is defined as follows:

[0068]

[0069] Where num(G) a ) and num(G b ) respectively represent the disease d a and d b The number of related genes;

[0070] FNSemSim is defined as follows:

[0071]

[0072] Where |G a | and | G b | represents the size of the two gene sets, Ga and G b Respectively related to disease d in disease ontology a and d b Related; |G MICA |is for d a and d b The number of genes related to a common ancestor that provides the most information;

[0073] Step 7: Construction of a disease-associated circular RNA network based on multidimensional functional data;

[0074] Step 7-1: The relationship between circular RNA and disease is represented using the disease adjacency network (CD), which is represented as follows:

[0075]

[0076] Step 7-2: Integrate the circular RNA similarity network CS, the disease similarity network DS, and the circular RNA with the disease adjacency network CD to obtain the association network X. * :

[0077]

[0078] The RWR algorithm is then used to learn the features of the associated network X*, thereby obtaining the disease-related circular RNA network X.

[0079] Preferably, the circular RNA-miRNA similarity CS mi (c i ,c j ) and circular RNA-RBP similarity CS rbp (c i ,c j The value range of ) is [0,1].

[0080] Preferably, P0 = (0.5, 0.5).

[0081] The beneficial effects of this invention are as follows:

[0082] This invention can be used to predict the association between diseases and circular RNAs, providing reliable input data for prediction models and thus obtaining good prediction results. The disease-associated circular RNA network constructed in this invention based on multi-dimensional functional data has shown good performance and high accuracy in subsequent experiments predicting disease-associated circular RNAs. Attached Figure Description

[0083] Figure 1 This is a diagram of the method architecture of the present invention. Detailed Implementation

[0084] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0085] In existing technologies, the construction of disease-related circular RNA networks does not consider the integration of multi-dimensional data, which may lead to information loss. Therefore, this invention constructs disease-related circular RNA networks based on multi-dimensional functional data, providing reliable input data for subsequent prediction of disease-related circular RNA models.

[0086] This invention consists of two parts, as described in the reference. Figure 1 It is understood that the first part integrates multi-dimensional functional data, including circular RNA similarity networks, disease similarity networks, and circular RNA-disease adjacency networks, thereby forming association network X. * The second part uses the RWR algorithm to learn the features of the association network X*, and obtains the disease-related circular RNA network X.

[0087] 1) miRNA-based circular RNA association network construction method

[0088] After obtaining circular RNA and mircRNA association data from starBase, since circular RNAs associated with the same miRNA often have similar biological regulatory functions, circular RNA-miRNA interactions are used to calculate the similarity of circular RNAs. The formula for calculating the similarity is:

[0089]

[0090] Among them, c i Indicates the i-th type of circular RNA, m i Indicates c i The number of relevant miRNAs, m = m i ∩m j , where m is the number of miRNAs that are identical to the i-th and j-th circular RNAs. CS mi (c i ,c j ) represents c i and c j The similarity is calculated by taking the larger of the ratio of the number of identical miRNAs in the two circular RNAs to the number of their respective related miRNAs, with a value range of [0,1].

[0091] 2) Method for constructing circular RNA association networks based on binding proteins (RBPs)

[0092] Circular RNAs (RNAs) can serve as dynamic scaffold molecules regulating protein-protein interactions, and the interaction between RNAs and their binding proteins (RBPs) is considered a fundamental element of RNA function. Therefore, RNAs associated with the same RBPs often have similar functions. Similar to the calculation of RNA-miRNA similarity, the formula is as follows:

[0093]

[0094] Among them, c i R represents the i-th type of circular RNA. i Indicates c i The number of relevant RBPs, r = r i ∩r j That is, r is the number of RBPs that are the same for the i-th and j-th circular RNAs. CS rbp (c i ,c j ) represents c i and c j The similarity is determined by the larger of the ratio of the number of identical RBPs in the two circular RNAs to the number of their respective related RBPs, with a value range of [0,1].

[0095] 3) Method for constructing circular RNA association networks based on sequence similarity

[0096] Hybrid Game Representation (CGR) is an iterative mapping technique for processing sequences that obtains a vector representation of the sequences by combining positional information and nonlinear relationships. Finally, the Pearson correlation coefficient is used to quantify their correlation. The first advantage of this algorithm is that it can completely recover the original information of the sequences from the coordinate system without losing information during the mapping process. Secondly, each sequence has a unique mapping, meaning that positional information is preserved as part of the mapping.

[0097] The position of each nucleotide in the plane is:

[0098] P i =0.5*(P i-1 +S i i = 1...N

[0099] Let P0 be an arbitrarily given starting point, P0 = (0.5, 0.5); N represents the sequence length; S i The i-th nucleotide in the sequence corresponds to the fixed vertex coordinates of A = (0,0), C = (1,0), G = (1,1), and U = (0,1).

[0100] In this way, the CGR graph is converted into an Nx grid (N... x =2 s ×2 s s=3), is called the frequency matrix (FCGR) of the CGR plot. The frequency matrix grid can be represented as:

[0101] grid i =(X i ,Y i Zi )

[0102] In the formula, X i and Y i Z represents the sum of the x and y coordinates of all points located in the i-th grid, respectively. i The z-score represents the circRNA nucleotides quantified as potential features in the i-th grid.

[0103] The positional information is quantified by summing the x-coordinate (point.x) and y-coordinate (point.y) of each grid cell. The feature vector of the sequence is constructed using the x-axis, y-axis directions, and their numerical characteristics, calculated as follows:

[0104] X i =∑point.x if point in grid

[0105] Y i =∑point.y if point in grid

[0106] Then, calculate Z for each grid. i The fraction of z is used to quantify nonlinear information, and the calculation formula is as follows:

[0107]

[0108] Among them, Num i It represents the number of coordinate points in the frequency matrix grid.

[0109] Finally, each grid can be represented by three attributes, which are fused to construct a vector, and the sequence similarity of circular RNA is defined by the Pearson correlation coefficient.

[0110]

[0111]

[0112] Among them, c i Represents the i-th type of circular RNA, vector(c i ) represents the sequence vector of the i-th circular RNA, vector(c i )·vector(c j ) represents vector(c i ) and vector(c j The dot product of CS. seq (c i ,c j ) represents c i and c j Sequence similarity.

[0113] 4) Feature extraction of circular RNA

[0114] After calculating the three circular RNA similarity networks, features were extracted using a collaborative training method based on shared constraints, resulting in the final feature matrices CSF of the three networks. mi CSF rbp and CSF seq The method consists of three steps: learning the topology of circular RNA association networks based on restarted random walks (RWR), establishing constraints in co-training, and co-training based on shared constraints.

[0115] (1) Learning the topology of a circular RNA association network based on Restarted Random Walk (RWR): RWR is a local network diffusion process that can capture the global correlation between nodes in the network. RWR can extract node feature representations from the global structural information of the high-dimensional network. Compared with traditional methods for calculating distance on the graph, such as shortest path and maximum flow, RWR can capture multifaceted information about two nodes. Therefore, the RWR algorithm is used to capture network information from node x. i Initially, the node is moved to another adjacent node with a restart probability c, and this process is repeated iteratively. In each iteration, the node returns to the initial node x with probability c. i The v obtained after iterative stabilization ij That is, from node x i to node x j The probability, i.e., the relevance score. Let A... k Indicates network G k The adjacency matrix, RWR formula is as follows:

[0116]

[0117]

[0118] Where t and t+1 represent the t-th and t+1-th steps of the RWR algorithm, respectively. ij This represents the i-th row and j-th column of the transition probability matrix T, where T is the column normalization result of matrix A, e i Represents node x i The initial feature vectors were obtained. Node feature representations with global network structure information were obtained by using the RWR algorithm on network A.

[0119] (2) Constraint establishment method in collaborative training: Paired constraints can be divided into weak association and strong association. Strong association refers to node pairs that are highly similar or must be in the same cluster, while weak association refers to node pairs that are highly different or must be in different clusters. This paper only extracts strong association.

[0120] First, the node feature representations obtained through the RWR algorithm are input into the autoencoder to reconstruct the node feature representations. For each autoencoder, there is an additional reconstruction layer to obtain a feature matrix with the same shape as the original input feature matrix. Since the reconstructed feature matrix of each layer is a square matrix, a Laplacian matrix L is generated based on the reconstructed feature matrix, using the following formula:

[0121]

[0122] Where X is the node feature representation obtained using the RWR algorithm, where X i X is the feature vector of node i. X′ is the node feature representation reconstructed after inputting X into the autoencoder, where X is the feature vector of node i. i X′ is the reconstructed feature vector of node i. E is the identity matrix with the same dimension as X′, and D is the degree matrix of X′.

[0123] Then, the Pearson correlation coefficient (PCC) is calculated as a constraint between node a and node b, using the following formula:

[0124]

[0125] Finally, the Pearson correlation coefficient (PCC) value is used to measure the similarity between nodes. The PCC values ​​of all node pairs are sorted, and the node pairs with the highest PCC values ​​are considered strong associations. These strong associations are stored in a strong association matrix M, which can be used as prior information for the next autoencoder.

[0126] (3) Collaborative Training Method Based on Shared Constraints: This invention is based on a semi-supervised autoencoder, using hidden features and strong correlations as inputs, and obtaining the feature matrix of the original network after multiple iterations. Since the strong correlations extracted from different networks are not entirely the same, the intersection of these strong correlations is used as the final reliable constraint to make the results more accurate. A traditional autoencoder consists of an encoder and a decoder. The encoder can represent high-dimensional features as low-dimensional features, and the decoder reconstructs the encoded low-dimensional features into the original high-dimensional features. The autoencoder is optimized by minimizing the mean squared error, and the loss function formula based on the reconstructed features is as follows:

[0127]

[0128] Where, x i It is the original high-dimensional feature, y i These are the features reconstructed by the decoder, where n is the number of nodes.

[0129] However, traditional autoencoders cannot model strong correlations. Therefore, a semi-supervised autoencoder is used, and the loss function based on strong correlations is as follows:

[0130]

[0131] Where M is a strong correlation matrix, M i,j ∈(0,1), h i and h j is the low-dimensional feature processed by the encoder, and k is the number of strongly correlated pairs.

[0132] This embodiment integrates strong correlations into an autoencoder through a semi-supervised autoencoder. This encoder minimizes the joint objective function based on the two formulas mentioned above, as shown below:

[0133] L all =λ1L con +λ2L must

[0134] Where λ1 and λ2 are the balanced reconstruction errors L con and constraint error L must The weighting coefficients.

[0135] 5) Network fusion of circular RNAs

[0136] This invention employs a method for calculating cosine similarity, and uses the feature matrix CSF obtained through a collaborative training method based on shared constraints. mi CSF rbp and CSF seq The three feature matrices are first integrated into a single fused feature matrix. Then, cosine similarity is used for calculation, as shown in the following formula:

[0137]

[0138] Where A is the fusion feature matrix, A T It is the transpose of A.

[0139] The final circular RNA similarity matrix CS is constructed based on cosine similarity.

[0140] 6) Disease Similarity Network

[0141] This invention employs a fused functional association network to calculate disease similarity, using an improved method called FNSemSim. This invention utilizes three functional association networks: the Human Genome Connectome (HGC), HumanNet, and FunCoup. First, HumanNet and FunCoup, two association networks with different scoring systems, are fused to calculate gene similarity. After obtaining the fused functional association network, the Restarted Random Walk (RWR) algorithm is used to analyze the relationship between any two genes in the fused network. Therefore, the association between a gene g and a gene set G is defined as follows:

[0142]

[0143] Where PRWR represents the probability of a gene being associated with another gene in the network after RWR calculation, and AG is the gene functional association network. If a gene g and some genes in genome G are included in the functional association network, but g does not belong to G, then RWR... G The definition is the maximum PRWR across all gene pairs. Gene set G a ={g a1 ,g a2 ,…} and G b ={g b1 ,g b2 ,…} respectively with disease d a and d b Related, disease d a and d b The similarity between them is defined as follows:

[0144]

[0145] Where num(G) a ) and num(G b ) respectively represent the disease d a and d b The number of related genes. Because the semantic similarity between any two nodes in the ontology is positively correlated with their annotation count and negatively correlated with their MICA annotation count, FNSemSim can be defined as follows:

[0146]

[0147] Where |G a | and | G b | represents the size of the two gene sets, G a and G b Respectively related to disease d in disease ontology a and d b Related. |G MICA|is for d a and d b The number of genes associated with a common ancestor that provides the most information.

[0148] 7) Construction of disease-related circular RNA networks based on multidimensional functional data

[0149] To obtain a disease-associated circular RNA network based on multi-dimensional functional data, this invention starts with data from multiple dimensions. First, it integrates the circular RNA similarity network CS, the disease similarity network DS, and the circular RNA with the disease adjacency network CD to obtain the association network X. * :

[0150]

[0151] The RWR algorithm is then used to learn the features of the association network X*, thereby obtaining the disease-related circular RNA network X. The relationship between circular RNA and disease can be represented by the adjacency network CD, which can be expressed as:

[0152]

[0153] In experiments on a deep learning-based disease-related circular RNA prediction model, five-fold cross-validation and ten-fold cross-validation were used to evaluate the model's performance, with AUC value used as the evaluation criterion.

[0154] Cross-validation is a common method for verifying the predictive performance of a model. Its basic idea is to repeatedly use data, splitting the obtained samples and combining them into different training and test sets. The training set is used to train the model, and the test set is used to evaluate the model's predictive performance. This process is repeated multiple times to obtain a relatively objective evaluation result. The specific steps are as follows:

[0155] 1) Randomly divide the dataset into k disjoint subsets of the same size;

[0156] 2) Use k-1 subsets as the training set to train the model, and use the remaining subset as the test set to test the model;

[0157] 3) Evaluate model performance and calculate performance metrics;

[0158] 4) Repeat steps 1)-3) k times, ensuring that the selected validation set is different each time;

[0159] 5) The prediction performance of the model is obtained by combining the prediction results of k predictions.

[0160] AUC (Area Under Curve) is the area under the ROC curve and the coordinate axes, and its value will not exceed 1. AUC is typically used as a model evaluation metric because the ROC curve often doesn't clearly reflect the model's predictive performance, while AUC, as a numerical value, more intuitively reflects the model's predictive ability. The closer the AUC value is to 1, the better the model's predictive performance. When AUC equals 0.5, it's equivalent to random guessing, meaning the model has no predictive value. When AUC is less than 0.5, it performs better than random guessing when performing inverse prediction.

[0161] The mean value of the five-fold cross-validation was 0.9981, and the mean value of the ten-fold cross-validation was 0.9968.

[0162] The disease-associated circular RNA network constructed in this invention, based on multi-dimensional functional data, can be used to predict the association between diseases and circular RNAs, providing reliable input data for the prediction model and thus obtaining good prediction results.

[0163] The disease-related circular RNA network constructed by the method of this invention based on multi-dimensional functional data has good experimental results and high prediction accuracy in the deep learning-based disease-related circular RNA prediction model.

Claims

1.A method for constructing a disease-related circRNA network based on multi-dimensional functional data, characterized in that, Comprising the following steps: Step 1: Construction of the circular RNA association network based on miRNA; After obtaining the circular RNA-miRNA association data from starBase, the similarity of circular RNA is calculated using the circular RNA-miRNA interaction; The similarity formula is as follows: wherein, c i represents the number of miRNAs identical to the first i circular RNA, c j represents the number of miRNAs identical to the first j circular RNA, m i represents the number of miRNAs identical to the second c i circular RNA, m = m i represents the number of miRNAs identical to the third m j circular RNA, m i.e. the number of miRNAs identical to the first i circular RNA and the second j circular RNA; CS mi represents the circular RNA-miRNA similarity of the first c i , c j represents the circular RNA-miRNA similarity of the second c i , c j and the third Step 2: Construction of the circular RNA association network based on binding protein RBP; The similarity formula based on binding protein RBP is as follows: wherein, r i represents the number of RBPs associated with c i , r = r i ∩ r j , i.e. the number of RBPs that are identical to the first i circular RNA and the second j circular RNA; CS rbp ( c i , c j ) represents the circular RNA-RBP similarity of c i and c j . Step 3: Construction of the circular RNA association network based on mixed game representation of CGR; Step 3-1: Each nucleotide is represented by its position in the plane, and the formula is as follows: Let P 0 be an arbitrary starting point; N denote the length of the sequence; S i represent the nth nucleotide in the sequence; i ​ Step 3-2: By step 3-1, the CGR graph is converted into N x mesh The frequency matrix grid, called the CGR graph, FCGR, is represented as: wherein, X i and Y i represent the sum of the horizontal and vertical axis coordinates of all points located in the i grid, respectively, Z i represent the fraction of circRNA nucleotides in the i grid that are quantified as potential features, z ​ Step 3-3: Accumulate the horizontal coordinates in each grid point.x and vertical coordinates point.y to quantify the position information, using the x-axis, y-axis directions and their numerical characteristics to construct the feature vector of the sequence, the calculation formula is as follows: Step 3-4: Calculate each grid score Z i z The score of each grid is calculated to quantify the non-linear information as follows:​ wherein Num i is the number of coordinate points in the frequency matrix grid; Step 3-5: Each grid can be represented by three attributes, and these attributes are fused to construct a vector. The sequence similarity of circular RNA is defined by the Pearson correlation coefficient; wherein, vector ( c i ) denotes the sequence vector of the i thcircular RNA, vector ( c i ) •vector ( c j ) is vector ( c i ) and vector ( c j ) the dot product of CS seq = ( c i ,c j ) denotes c i and c j the circular RNA-CGR sequence similarity. Step 4: Feature extraction of circular RNA; After calculating the three circular RNA similarity networks, the features were extracted using the co-training method based on shared constraints to obtain the feature matrix of the final three networks CSF mi 、 CSF rbp and CSF seq ; Step 4-1: Topological structure learning of circular RNA association network based on restart random walk RWR; RWR algorithm is used to capture the network information, from node x i Start with restart probability c Move to other adjacent nodes and iterate repeatedly, each iteration with probability c Return to the initial node x i ; the obtained after iteration is stable v ij from the node x i to the node x j probability, that is, the correlation score; let A k represent the adjacency matrix of the network G k , and the RWR formula is as follows: wherein t and t+ 1 denote the first t and second t+1 steps of the RWR algorithm, respectively; T ij denotes the transition probability matrix T in the corresponding i row and j column, T is A the result of the row-wise normalization of the matrix e i denotes the initial feature vector of the node x i . By using the RWR algorithm on the adjacency matrix A The RWR algorithm is used on the network to obtain a node feature representation with global structure information of the network. Step 4-2: Establishment of constraint conditions in co-training; inputting the node feature representation obtained in step 4-1 into the autoencoder to reconstruct the feature representation of the node; for each autoencoder, generating a Laplacian matrix based on the reconstructed feature matrix L , and the formula is as follows: wherein, X is the node feature representation obtained using the RWR algorithm, wherein X i is the feature vector of the node , X ′ is the node feature representation reconstructed after inputting X to the autoencoder, wherein X i ′ is the reconstructed feature vector of the node , is the identity matrix of the same dimension as X ′ , is the degree matrix of X ′ . The value of the Pearson correlation coefficient PCC is calculated as a constraint between the nodes a and the node b The formula is as follows: Finally, the similarity between nodes is measured by the Pearson Correlation Coefficient (PCC) value, and the PCC values of all node pairs are sorted, and the node pair with the highest PCC value is taken as a strong association; the strong association is stored in the strong association matrix M where it is applied as prior information to the next autoencoder; Step 4-3: Co-training based on shared constraint conditions; Based on the semi-supervised autoencoder, the hidden features and strong associations are taken as input, and after multiple iterations, the feature matrix of the original network is finally obtained; The autoencoder consists of an encoder and a decoder. The encoder represents high-dimensional features as low-dimensional features, and the decoder reconstructs the encoded low-dimensional features into the original high-dimensional features. The autoencoder is optimized by minimizing the mean square error. The loss function formula based on the reconstructed features is as follows: wherein, x i is the original high-dimensional feature, y i is the decoder-reconstructed feature, n is the number of nodes; Based on the semi-supervised autoencoder, the loss function formula based on the strong association is as follows: wherein, M is a strong correlation matrix, M i,j ∈(0, 1), h i and h j is a low-dimensional feature processed by an encoder, k is the number of strong correlation pairs; Through the semi-supervised autoencoder, the strong association is integrated into the autoencoder. Based on the above two formulas, the joint objective function is minimized as follows: wherein, λ 1 and λ 2 are weight coefficients of the balanced reconstruction error L con and the constraint error L must . Step 5: Network fusion of circular RNA; The feature matrix obtained by the collaborative training method based on the shared constraint condition is fused by using a method of calculating cosine similarity CSF mi 、 CSF rbp and CSF seq ​ First, integrate the three feature matrices into a fusion feature matrix, and then use cosine similarity to calculate the formula as follows: wherein, A is a fused feature matrix, A T is A the transpose matrix of The final circular RNA similarity matrix is constructed according to the cosine similarity CS ; Step 6: Disease similarity network; The FNSemSim method is used to calculate the similarity of diseases; Three functional association networks are used, including human gene connection group HGC, HumanNet, and FunCoup. The two association networks with different scoring systems, HumanNet and FunCoup, are fused to calculate gene similarity. After obtaining the fused functional association network, the restart random walk RWR algorithm is used to analyze the relationship between any two genes in the fusion network. The association between a gene g and a gene set G is defined as follows: where P RWR represents the probability of a gene in the network to be associated with another gene after RWR computation, AG is the gene functional association network; if a gene is included in the functional association network, then is the probability of the gene to be associated with another gene in the network, is the probability of the gene to be associated with another gene in the network, is the probability of the gene to be associated with another gene in the network, R G is defined as the maximum value of P RWR over all gene pairs. Gene sets G a ={ g a1 , g a2 , …} and G b ={ g b1 , g b2 , …} are associated with diseases d a and d b , respectively, the similarity between diseases d a and d b is defined as follows: wherein num ( G a ) and num ( G b ) represent the number of genes associated with diseases d a and d b respectively; FNSemSim The following definitions apply: wherein G a | and G b | represent the size of the two gene sets, G a and G b respectively, are related to diseases d a and d b in the disease ontology; | G MICA | are the number of genes related to the common ancestor that provide the maximum amount of information; d a and d b the number of genes related to the common ancestor that provide the maximum amount of information. Step 7: Construction of disease-related circular RNA network based on multi-dimensional functional data; Step 7-1: Relationship of circular RNA to disease using disease adjacency network CD is represented by, CD is represented by: Step 7-2: Cyclic RNA Similarity Network CS、 Disease Similarity Network DS and Cyclic RNA and Disease Adjacency Network CD Integration to get Association Network X * : Learning relational networks from the features of the RWR algorithm X* to obtain disease-related circular RNA networks X . 2.The method of claim 1, wherein, The circular RNA-miRNA similarity CS mi ( c i , c j ) and the circular RNA-RBP similarity CS rbp ( c i , c j ) are all in the range of [0, 1]. 3.The method of claim 1, wherein, The P 0 = (0.5, 0.5).

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