A lncRNA-disease association prediction method based on collaborative matrix factorization with high-order perturbations and flexible ternary regularization

Abstract

The invention discloses a method for predicting the association between lncRNA and disease based on a collaborative matrix decomposition of high-order perturbations and flexible ternary regularization, which belongs to the technical field of matrix decomposition and biological gene combination. The method comprises the following specific steps: obtaining the association matrix Z of lncRNA and disease; calculating the functional similarity matrix R of lncRNA based on the known association matrix Z; s and the semantic similarity matrix D of the disease s ; The multi-order correlation matrix calculated based on the known correlation matrix is ​​added to the known correlation matrix as a high-order perturbation; the global nonlinear structural similarity information of the similarity matrix is ​​obtained through similarity learning of flexible ternary regular terms; the objective function is optimized and iterated based on the collaborative matrix decomposition method to obtain the final prediction score matrix, so that the final prediction of lncRNA-disease association is more accurate.

Description

Technical Field

[0001] The invention relates to the technical field of matrix decomposition and biological gene combination, and in particular to a lncRNA-disease association prediction method based on collaborative matrix decomposition of high-order perturbation and flexible ternary regularization. Background Art

[0002] Non-coding RNA (ncRNA) is mainly divided into small RNA, medium RNA and long non-coding RNA (LncRNA) according to the number of nucleotides. Among them, long non-coding RNA plays a very important role in the regulation of disease expression in animals and plants. Current biological studies have shown that in the development of lung adenocarcinoma, long non-coding RNA HAGLR inhibits tumor growth, so this LncRNA is confirmed as a tumor suppressor. At the same time, in the study of esophageal cancer, LncRNA (ADAMTS9-AS2) can effectively inhibit the proliferation, invasion and migration of cancer cells. It can be seen that the study of the potential association between LncRNA and disease is helpful for the prevention, detection and treatment of related diseases. Traditional biological experimental methods have high accuracy in discovering potential correlations, but the process is complicated and time-consuming. Therefore, it is of great significance to develop an efficient and convenient computational method based on the rapidly developing computer technology to detect the association between LncRNA and disease.

[0003] It is known that the effective information of the LncRNA-disease association matrix is ​​very sparse, and most LncRNAs are only associated with a single disease, which means that the overall number of LncRNAs and diseases is large, but the interactive information between them is too little. This situation often leads to a cold start problem in the decomposition system. Insufficient interactive data will make it difficult to build a complete and accurate prediction model. In short, it is difficult to further mine the remaining diseases (LncRNAs) that have never been exposed to LncRNAs (diseases) with a single sparse interactive data. The LncRNA-disease association prediction methods that have previously dealt with the cold start problem mainly include methods based on the mean enhancement of neighbor action spectra and random walk preprocessing. In the prior art, the interaction map of lncRNA is recalculated by using the mean of the neighbor node interaction spectrum, thereby effectively alleviating the cold start problem. However, this method has obvious disadvantages. While each LncRNA node is enhanced, its own unique information will be assimilated by the mean, which means that while the effective information of a part of the LncRNA is enhanced, it will cause some strongly correlated nodes to be weakened and weak noise to be amplified. The approach of using the average of the neighbor's interaction spectra to recalculate the lncRNA interaction map is mainly to obtain some unmined similarity information from the perspective of the lncRNA similarity matrix, and also from the perspective of the sparser known association matrix, based on the theoretical knowledge of random walks, simulate the jumps of different probability nodes of the lncRNA-disease association matrix network to obtain new association information, and the use of random walks does not destroy the original information of the original association matrix. However, this method also has limitations. It has poor robustness when facing data sets with dynamic changes or noise interference. It is easy to produce wrong prediction results based on random probability to infer the possibility of lncRNA-disease interaction. In short, on the problem of cold start, the existing methods cannot effectively avoid the impact of noise on the results in the process of enhancing effective information, and do not consider mining deeper effective information from a high-order perspective.

[0004] Among the existing matrix decomposition methods used to predict potential associations, the learning methods for the similarity between LncRNA and diseases are mainly divided into two similarity learning methods: graph regularization and binary orthogonal fitting similarity. The purpose of graph regularization is to maintain the similarity between LncRNA (disease) neighbor nodes in order to better predict the potential association between LncRNA and disease. In the graph regularization of LncRNA-disease association prediction, the neighborhood graph is basically constructed based on K-nearest neighbor (KNN), which plans a uniform domain range for each node, but cannot plan different domain ranges for each node, which leads to the inability of some information nodes to capture the local optimal distribution of neighbor nodes. Moreover, since the graph regularization method based on KNN is local, the nonlinear structure it learns mainly reflects the relationship between nodes in their local neighborhood. However, this local perspective makes it unable to fully capture the global nonlinear structural information in the similarity matrix, resulting in the problem of partial global nonlinear information loss. The binary orthogonal fitting similarity method is different from the graph regularization method in preserving local feature structures, and it pays more attention to the global structure of similarity features. However, this two-factor orthogonal decomposition is highly restrictive. This method attempts to approximate the original high-dimensional data through a small number of linear combinations, so it cannot effectively learn the nonlinear structural information of the similarity matrix. Whether it is the calculation method of the similarity matrix of LncRNA or disease, it often introduces a nonlinear structure to the calculated similarity information matrix. For example, semantic similarity is based on the data structure of the graph to calculate the semantic value of each node. The complex structure of the graph often leads to a nonlinear structure in the similarity matrix. For example, the difference in expression spectrum and the calculation process of the Pearson correlation coefficient will cause the similarity matrix to present a nonlinear structure. Therefore, when the binary orthogonal fitting similarity method uses a simple linear combination to fit the similarity matrix with a nonlinear structure, it will cause a large fitting error, resulting in the loss of similarity information. In short, whether the similarity information of LncRNA (disease) can be accurately learned and retained is crucial to the performance of the LncRNA-disease algorithm model. However, the current model methods based on graph regularization and binary orthogonal fitting similarity are difficult to effectively learn the global nonlinear structural information of the similarity matrix, resulting in the loss of some global nonlinear similarity information. Therefore, a lncRNA-disease association prediction method based on collaborative matrix decomposition with high-order perturbation and flexible ternary regularization was invented. Summary of the invention

[0005] In view of the above problems and / or the existing problems in the LncRNA-disease association prediction method based on collaborative matrix decomposition of high-order perturbations and flexible ternary regularization, the present invention is proposed.

[0006] Therefore, the purpose of the present invention is to provide a LncRNA-disease association prediction method based on collaborative matrix decomposition of high-order perturbations and flexible ternary regularization, which can solve the above-mentioned existing problems.

[0007] To solve the above technical problems, according to one aspect of the present invention, the present invention provides the following technical solutions:

[0008] A lncRNA-disease association prediction method based on collaborative matrix decomposition of high-order perturbations and flexible ternary regularization includes the following specific steps:

[0009] S1: Obtain the LncRNA-disease association matrix Z;

[0010] S2: Based on the known association matrix Z, calculate the LncRNA functional similarity matrix R s and the semantic similarity matrix D of the disease s ;

[0011] S3: adding the multi-order correlation matrix calculated based on the known correlation matrix as a high-order perturbation to the known correlation matrix;

[0012] S4: Obtain global nonlinear structural similarity information of similarity matrix through similarity learning of flexible ternary regularization terms;

[0013] S5: Integrate high-order perturbations and flexible ternary regularization into collaborative matrix factorization, iteratively optimize and eliminate the interference of high-order perturbations to obtain the final prediction score matrix.

[0014] As a preferred solution of the LncRNA-disease association prediction method based on high-order perturbation and flexible ternary regularization collaborative matrix decomposition described in the present invention, the steps of obtaining the LncRNA-disease association matrix Z in S1 are as follows:

[0015] S11: The first dataset is from LncRNADisease2.0;

[0016] S12: To facilitate in-depth case analysis of the prediction results, standard MeSH disease terms and broader category terms were used to replace the terms in the original dataset;

[0017] S13: Clean the data, delete duplicate entries and entries of non-human lncRNA and disease, and finally get 1690 lncRNA-disease association pairs confirmed by biological experiments, covering 447 lncRNAs and 218 diseases, which are used as the experimental data set. On this basis, the association matrix Z of the defined lncRNA and disease is expressed as follows:

[0018]

[0019] As a preferred solution of the LncRNA-disease association prediction method based on high-order perturbation and flexible ternary regularization collaborative matrix decomposition described in the present invention, wherein: the semantic similarity matrix D of the disease in S2 s The calculation steps are as follows:

[0020] S21: construct a directed acyclic graph (DAG(d)=(T(d), E(d))) based on the Mesh database, where T(d) represents the set of disease ancestor nodes including disease d itself, and E=(d) represents the set of edges directly connecting the ancestor nodes of the disease node to the child nodes;

[0021] S22: Based on the constructed DAG, the contribution of the disease itself and its ancestor nodes to itself is judged. The equation expression is as follows:

[0022]

[0023] where disease t∈T(d);

[0024] S23: The semantic value score of the disease can be calculated using the following formula:

[0025]

[0026] S24: On this basis, calculate the disease d i and diseases j The semantic similarity between them is then used to obtain the final disease semantic similarity matrix D s :

[0027]

[0028] As a preferred solution of the LncRNA-disease association prediction method based on high-order perturbation and flexible ternary regularization collaborative matrix decomposition described in the present invention, wherein: the functional similarity matrix R of the LncRNA in S2 s The calculation steps are as follows:

[0029] S25: Assumption D i and D j They are respectively related to the R i and R j Related disease groups;

[0030] S26: LncRNA functional similarity matrix is ​​defined as R s ;

[0031] S27: R i and R jThe similarity value between is calculated as follows:

[0032]

[0033] Where |D i | indicates R i The number of diseases associated with |D j | indicates R j The number of diseases associated with it, S(d m ,D j ) is related to LncRNA R i Related diseases m and LncRNA j Related disease cluster D j The similarities between.

[0034] As a preferred solution of the LncRNA-disease association prediction method based on high-order perturbation and flexible ternary regularization collaborative matrix decomposition described in the present invention, the specific steps of adding the multi-order association matrix calculated based on the known association matrix as a high-order perturbation to the known association matrix in S3 are as follows:

[0035] S31: Construct a high-order connection matrix C based on the known association matrix:

[0036] C=min(1,Z T ·Z)

[0037] in is the known incidence matrix, m and n represent the number of rows and columns of the known incidence matrix Z, respectively. T Z represents the medium through which LncRNA and disease can interact. In order to avoid errors in subsequent analysis caused by numerical differences, all values ​​greater than 1 are restricted to 1, thereby constructing a high-order connection matrix C. This binary matrix represents whether LncRNA and disease can interact;

[0038] S32: Construct different order correlation matrices based on the high order connection matrix C:

[0039] Hyperconnection(Z,i)=min(1,Z·C i-1 )

[0040] In the experiment of the data set, it was observed that the high-order correlation matrix after the 4th-order correlation matrix remained basically unchanged. Therefore, only the 2nd-4th-order high-order correlation matrix was used as the final high-order correlation matrix.

[0041]

[0042] S33: Calculate the high-order perturbation matrix Hop:

[0043]

[0044] stW = 0.1 * rand (size (Z));

[0045] Where ⊙ represents the Hadamard product of the matrix, and the random value W represents the probability of interaction at the position determined by the high-order correlation matrix. When constructing the high-order correlation matrix, only the positions other than the original correlation matrix Z are determined, that is, A random value W is added to the position where the value is not 0, because the effective information of the original correlation matrix Z should be retained while avoiding the influence of the high-order correlation matrix processing on the original matrix. In order to ensure that the importance of the correlation information in the original matrix is ​​retained and the initial value is different from the value of the original matrix, the range of the random value W needs to be set between 0 and 0.1 to ensure that it can effectively reflect the possibility of correlation while reducing the interference to the original matrix;

[0046] Therefore, the new incidence matrix can be expressed as:

[0047] Z new =Z+Hop.

[0048] As a preferred solution of the LncRNA-disease association prediction method based on collaborative matrix decomposition of high-order perturbation and flexible ternary regularization described in the present invention, the specific steps of obtaining the global nonlinear structural similarity information of the similarity matrix in S4 are as follows:

[0049] S41: Based on the principle of collaborative matrix decomposition, the expression of collaborative matrix decomposition is designed for the problem of predicting the association between LncRNA and diseases:

[0050]

[0051] where α 1 , α 2 and λ are the hyperparameters of the regularization term, and They represent the decomposed low-dimensional matrices of LncRNA term and disease term respectively, i is the number of subspace dimensions, is the Frobenius norm;

[0052] S42: Adding additional factors M and N between the two variables of binary orthogonality preserves the global nonlinear structural information for similarity learning. Therefore, the expression of matrix decomposition with flexible ternary regularization is as follows:

[0053]

[0054] in, and is the factor matrix attached to the orthogonal variables of LncRNA and disease similarity, σ is the hyperparameter controlling the additional factors M and N, and in order to avoid complex non-convex coupling terms when minimizing the objective function, a proxy matrix variable of penalty is introduced Make it similar to UV T , therefore, the above formula can also be expressed as:

[0055]

[0056] in It is UV T The proxy matrix variable of .

[0057] As a preferred solution of the LncRNA-disease association prediction method based on collaborative matrix decomposition of high-order perturbation and flexible ternary regularization described in the present invention, the specific steps of integrating high-order perturbation and flexible ternary regularization into collaborative matrix decomposition in S5 are as follows:

[0058] S511: Based on high-order perturbations and flexible ternary regularization, the specific objective function of the proposed matrix decomposition with high-order perturbations and flexible ternary regularization is finally expressed as follows:

[0059]

[0060] S512: In order to avoid the cumbersome non-convex coupling terms when solving the objective function minimization problem and reduce the optimization difficulty caused by the high power of the dependent variable, we introduce and Two variables, used to fit UM and VN respectively;

[0061] S513: Finally, after these transformations, the above objective function can also be expressed as:

[0062]

[0063]

[0064] Similarly, β 1 and β 2 is also a set of hyperparameters.

[0065] As a preferred solution of the LncRNA-disease association prediction method based on collaborative matrix decomposition of high-order perturbation and flexible ternary regularization described in the present invention, the specific steps of iterative optimization in S5 are as follows:

[0066] S521: Update X

[0067]

[0068] Among them, matrices B and Y are temporary matrix variables used for transition in the gradient descent process, s is a hyperparameter of the iterative process, and r is the gradient step size. In order to simplify the experimental process and avoid introducing too many hyperparameters while ensuring the convergence of the optimization algorithm, the value of r is set to 0.1;

[0069] S522: Update U

[0070]

[0071] make:

[0072]

[0073] but:

[0074]

[0075] U p Represents the previous iteration data U of U t-1 , E is an identity matrix; S523: Update V

[0076]

[0077] Based on the update formula of U, we can infer by analogy:

[0078]

[0079] Similarly, V p Represents the previous iteration data V of V t-1 ;

[0080] S524: Update W

[0081]

[0082] Among them, matrices T and Y are temporary matrix variables used for transition during the gradient descent process; S525: Update Q

[0083]

[0084] make:

[0085]

[0086] but:

[0087]

[0088] Q=(β 1 UM+α 1 R s U)(β 1E+α 1 U T U) -1 ;

[0089] S526: Update P

[0090]

[0091] make:

[0092]

[0093] Then the partial derivative of the factor matrix P is:

[0094]

[0095] The update formula steps based on Q can also be derived by analogy:

[0096] P=(β 2 VN+α 2 D s V)(β 2 E+α 2 V T V) -1 ;

[0097] S527: Update M

[0098]

[0099] make:

[0100]

[0101] but:

[0102]

[0103] M=(β 1 U T U+σE) -1 (β 1 U T Q);

[0104] S528: Update N

[0105]

[0106] make:

[0107]

[0108] but:

[0109]

[0110] Based on the optimization steps of M, we can infer by analogy:

[0111] N=(β 2 V T V+σE) -1 (β 2 V T P).

[0112] As a preferred solution of the LncRNA-disease association prediction method based on high-order perturbation and flexible ternary regularization collaborative matrix decomposition described in the present invention, the specific steps of obtaining the final prediction score matrix in S5 are as follows:

[0113] S531: After the iteration process meets the following conditions:

[0114]

[0115] S532: Calculate and obtain an approximate score matrix:

[0116]

[0117] S533: After eliminating the influence of high-order perturbations on the results, the final score matrix is ​​obtained:

[0118]

[0119] Compared with existing technologies:

[0120] The present invention performs high-order connection processing on the original known association matrix in the matrix decomposition stage to obtain a high-order association matrix, adds high-order information to the original known association matrix as "new" association interaction information, increases the possibility that LncRNA (disease) has a connection with a disease (LncRNA) that currently has no interaction, and then adds additional factors between binary variables in the binary orthogonal method to further provide the necessary degrees of freedom to obtain a good factor decomposition. The additional factors can reveal the correlation between similarity information in different row and column clusters, thereby providing a communication bridge for LncRNA and disease to interact, and then learn the global nonlinear structure of the similarity matrix to obtain more complete similarity information; finally, based on the collaborative matrix decomposition method, the objective function is optimized and iterated to obtain the final prediction score matrix, so that the final prediction of the association between lncRNA and disease is more accurate. BRIEF DESCRIPTION OF THE DRAWINGS

[0121] Figure 1 is a flow chart of the present invention;

[0122] Figure 2A schematic diagram of AUCs of HPTRMF, SCCPMD, LDGRNMF, CKA-HGRTMF, DSCMF, LDCMFC, PMFILDA and WGRCMF implemented by the present invention based on LOOCV;

[0123] Figure 3 This is a schematic diagram of AUCs achieved by the present invention based on 5-fold-CV using HPTRMF, SCCPMD, LDGRNMF, CKA-HGRTMF, DSCMF, LDCMFC, PMFILDA and WGRCMF. DETAILED DESCRIPTION

[0124] In order to make the objectives, technical solutions and advantages of the present invention more clear, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0125] The present invention provides a LncRNA-disease association prediction method based on high-order perturbation and flexible ternary regularization collaborative matrix decomposition, please refer to Figure 1-Figure 3 , including the following specific steps:

[0126] S1: Obtain the LncRNA-disease association matrix Z;

[0127] The LncRNA-disease association matrix Z mentioned above is specifically generated as follows:

[0128] The first dataset is from LncRNADisease2.0. In order to facilitate in-depth case analysis of the prediction results, standard MeSH disease terms and broader category terms are used to replace the terms of the original dataset. In addition, the data is cleaned and duplicate entries and non-human LncRNA and disease entries are deleted. Finally, 1,690 lncRNA-disease association pairs confirmed by biological experiments are obtained, covering 447 lncRNAs and 218 diseases. They are used as the experimental dataset. On this basis, the association matrix Z of the defined LncRNA and disease is expressed as follows:

[0129]

[0130] S2: Based on the known association matrix Z, calculate the LncRNA functional similarity matrix R s and the semantic similarity matrix D of the disease s ;

[0131] Among them, the semantic similarity matrix D of the mentioned diseases s , and its specific generation method is:

[0132] Disease semantic similarity is often used to predict the potential association between LncRNA and disease. The disease semantic similarity calculation method is based on the directed acyclic graph (DAG(d) = (T(d), E(d))) constructed based on the Mesh database, where T(d) represents the set of disease ancestor nodes including the disease d itself, and E = (d) represents the edge set of the ancestor nodes of the disease node directly connected to the child nodes. Then, the contribution of the disease itself and its ancestor nodes to itself is judged based on the constructed DAG. The equation expression is as follows:

[0133]

[0134] where disease t∈T(d),

[0135] Finally, the semantic value score of the disease can be calculated using the following formula:

[0136]

[0137] On this basis, the disease d can be calculated i and diseases j The semantic similarity between them is then used to obtain the final disease semantic similarity matrix D s :

[0138]

[0139] Among them, the functional similarity matrix R of the LncRNA mentioned s , and its specific generation method is:

[0140] Based on the assumption that similar LncRNAs are often associated with similar diseases, the functional similarity of LncRNAs is further calculated according to the semantic similarity of diseases. i and D j They are respectively related to the R i and R j Related disease groups, the lncRNA functional similarity matrix is ​​defined as R s , R i and R j The similarity value between is calculated as follows:

[0141]

[0142] Where |D i | indicates R i The number of diseases associated with |D j | indicates R j The number of diseases associated with it, S(d m ,D j ) is related to LncRNA Ri Related diseases m and LncRNA j Related disease cluster D j similarities between;

[0143] S3: adding the multi-order correlation matrix calculated based on the known correlation matrix as a high-order perturbation to the known correlation matrix;

[0144] Among them, the new correlation matrix obtained by constructing a high-order perturbation method based on the known correlation matrix Z is specifically:

[0145] First, a high-order connection matrix C is constructed based on the known association matrix:

[0146] C=min(1,Z T ·Z)

[0147] in is the known incidence matrix, m and n represent the number of rows and columns of the known incidence matrix Z, respectively. T Z represents the medium through which LncRNA and disease can interact. In order to avoid errors in subsequent analysis caused by numerical differences, all values ​​greater than 1 are restricted to 1, thereby constructing a high-order connection matrix C. This binary matrix represents whether LncRNA and disease can interact;

[0148] The following constructs the correlation matrix of different orders based on the high-order connection matrix C:

[0149] Hyperconnection(Z,i)=min(1,Z·C i-1 )

[0150] In the experiment of the data set, it was observed that the high-order correlation matrix after the 4th-order correlation matrix remained basically unchanged. Therefore, only the 2nd-4th-order high-order correlation matrix was used as the final high-order correlation matrix.

[0151]

[0152] Based on this, the high-order perturbation matrix Hop is finally calculated:

[0153]

[0154] stW=0.1*rand(size(Z))

[0155] Where ⊙ represents the Hadamard product of the matrix, and the random value W represents the probability of interaction at the position determined by the high-order correlation matrix. When constructing the high-order correlation matrix, only the positions other than the original correlation matrix Z are determined, that is, A random value W is added to the position where the value is not 0, because the effective information of the original correlation matrix Z should be retained while avoiding the influence of high-order correlation matrix processing on the original matrix. In order to ensure that the importance of the correlation information in the original matrix is ​​retained and the initial value is different from the value of the original matrix, the range of the random value W needs to be set between 0 and 0.1 to ensure that it can effectively reflect the possibility of correlation while reducing the interference to the original matrix.

[0156] Therefore, the new incidence matrix can be expressed as:

[0157] Z new =Z+Hop;

[0158] S4: Obtain global nonlinear structural similarity information of similarity matrix through similarity learning of flexible ternary regularization terms;

[0159] Among them, the flexible ternary regularization method is specifically:

[0160] Based on the principle of collaborative matrix decomposition, the expression of collaborative matrix decomposition is designed for the problem of predicting the association between LncRNA and diseases:

[0161]

[0162] where α 1 , α 2 and λ are the hyperparameters of the regularization term, and They represent the decomposed low-dimensional matrices of LncRNA term and disease term respectively, i is the number of subspace dimensions, is the Frobenius norm;

[0163] Next, we add additional factors M and N between the two variables of binary orthogonality to retain the global nonlinear structural information for similarity learning. Therefore, the expression of matrix decomposition with flexible ternary regularization is as follows:

[0164]

[0165] in, and is the factor matrix attached to the orthogonal variables of LncRNA and disease similarity, σ is the hyperparameter controlling the additional factors M and N, and in order to avoid complex non-convex coupling terms when minimizing the objective function, a proxy matrix variable of penalty is introduced Make it similar to UV T , therefore, the above formula can also be expressed as:

[0166]

[0167] in It is UV T Proxy matrix variables of ;

[0168] S5: Integrate high-order perturbations and flexible ternary regularization into collaborative matrix factorization, iteratively optimize and remove the interference of high-order perturbations to obtain the final prediction score matrix;

[0169] Among them: high-order perturbations and flexible ternary regularization are integrated into the collaborative matrix factorization, specifically:

[0170] Based on high-order perturbations and flexible ternary regularization, the specific objective function of the proposed matrix decomposition with high-order perturbations and flexible ternary regularization is finally expressed as follows:

[0171]

[0172] In order to avoid the cumbersome non-convex coupling terms when solving the objective function minimization problem and reduce the optimization difficulty caused by the high power of the dependent variable, we introduce and Two variables are used to fit UM and VN respectively. Finally, after these transformations, the above objective function can also be expressed as:

[0173]

[0174] Similarly, β 1 and β 2 It is also a set of hyperparameters;

[0175] Among them, the objective function is optimized, specifically:

[0176] During the optimization process, the gradient descent step is applied to the factor matrices X and W, and the proximal gradient descent step is used for other factor matrices. The specific optimization process is as follows:

[0177] (1) Update X

[0178]

[0179] Among them, matrices B and Y are temporary matrix variables used for transition in the gradient descent process, s is a hyperparameter of the iterative process, and r is the gradient step size. In order to simplify the experimental process and avoid introducing too many hyperparameters while ensuring the convergence of the optimization algorithm, the value of r is set to 0.1.

[0180] (2) Update U

[0181]

[0182] make:

[0183]

[0184] but:

[0185]

[0186]

[0187]

[0188] U p Represents the previous iteration data U of U t-1 , E is an identity matrix,

[0189] (3) Update V

[0190]

[0191] Based on the update formula of U, we can infer by analogy:

[0192]

[0193] Similarly, V p Represents the previous iteration data V of V t-1 ;

[0194] (4) Update W

[0195]

[0196] Among them, matrices T and Y are temporary matrix variables used for transition during the gradient descent process.

[0197] (5) Update Q

[0198]

[0199] make:

[0200]

[0201] but:

[0202]

[0203] Q=(β 1 UM+α 1 R s U)(β 1 E+α 1 U T U) -1

[0204] (6) Update P

[0205]

[0206] make:

[0207]

[0208] Then the partial derivative of the factor matrix P is:

[0209]

[0210] Based on the update formula steps of Q, we can get the following by analogy:

[0211] P=(β 2 VN+α 2 D s V)(β 2 E+α 2 V T V) -1

[0212] (7) Update M

[0213]

[0214] make:

[0215]

[0216] but:

[0217]

[0218] (8) Update N

[0219]

[0220] make:

[0221]

[0222] but:

[0223]

[0224] Based on the optimization steps of M, we can infer by analogy:

[0225] N=(β 2 V T V+σE) -1 (β 2 V T P);

[0226] Among them, after optimization, the influence of high-order disturbances on the results is eliminated to obtain the final score matrix, which is:

[0227] After the iteration process meets the following conditions:

[0228]

[0229] The approximate score matrix can be calculated:

[0230]

[0231] After eliminating the influence of high-order perturbations on the results, the final score matrix is ​​obtained:

[0232]

[0233] In order to verify the prediction accuracy of the method (HPTRMF) of this embodiment, HPTRMF is compared with 7 advanced methods including SCCPMD, LDGRNMF, CKA-HGRTMF, DSCMF, LDCMFC, PMFILDA and WGRCMF. Figure 2 It can be seen that under the LOOCV framework, the area under the HPTRMF curve AUC is 0.9846, which is larger than other calculation methods (SCCPMD 0.9727, LDGRNMF 0.9564, CKA-HGRTMF 0.9294, DSCMF 0.8959, LDCMFC 0.9419, PMFILDA 0.9301 and WGRCMF 0.8836), indicating that the performance of HPTRMF is better than other calculation methods. In order to further verify the prediction performance of HPTRMF, the 5-fold CV framework was used for verification. Figure 3 It can be seen that HTRMF can obtain a reliable AUC of 0.9824, far exceeding the AUC values ​​of 0.9505, 0.0.9412, 0.9136, 0.8823, 0.8891, 0.8706 and 0.8709 of the seven comparison models. This means that HPTRMF is also more effective than other methods under the 5-fold-CV framework. The above results fully demonstrate that the HPTRMF method is superior to the benchmark method and is more conducive to the prediction of lncRNA-disease correlation.

[0234] HPTRMF is also used to predict the application of known lncRNAs in actual lncRNA-disease prediction. In the process of predicting new lncRNA-disease associations, the known lncRNA-disease correlations are used as the training data set of HPTRMF, and then the prediction scores of each unknown lncRNA-disease pair are calculated and ranked. In the experiment of the present invention, endometriosis and obesity were used as case studies, and the top 10 cancer lncRNAs were verified in the PubMed database. The results are shown in Tables 1 and 2, and 70% and 80% of the predicted lncRNAs are associated with cancer, respectively.

[0235] In addition, HPTRMF predicts some unproven lncRNA-diseases, including PVT1 and endometriosis, CDKN2B-AS1 and obesity, etc. These predicted associations have not been reported in current literature, but they are likely to exist, and medical researchers are waiting to study and verify these associations.

[0236] Table 1 Top 10 potential lncRNAs associated with endometriosis predicted by HPTRMF

[0237]

[0238]

[0239] Table 2 Top 10 potential lncRNAs related to obesity predicted by HPTRMF

[0240]

[0241] In summary, therefore, in the present invention, first, in the matrix decomposition stage, the original known association matrix is ​​subjected to high-order connection processing to obtain a high-order association matrix, and high-order information is added to the original known association matrix as "new" associated interaction information, which increases the possibility that LncRNA (disease) has a connection with a disease (LncRNA) that does not currently interact. Secondly, additional factors are added between binary variables in the method similar to binary orthogonal fitting to further provide the necessary degrees of freedom to obtain a good factor decomposition. The additional factors can reveal the correlation between similarity information in different row and column clusters, thereby providing a communication bridge for LncRNA and disease to interact, and then learn the global nonlinear structure of the similarity matrix, and obtain more complete similarity information. Finally, the objective function is optimized and iterated based on the method of collaborative matrix decomposition to obtain the final prediction score matrix.

[0242] Although the present invention has been described above with reference to the embodiments, various modifications may be made thereto and parts thereof may be replaced by equivalents without departing from the scope of the present invention. In particular, as long as there is no structural conflict, the various features in the embodiments disclosed in the present invention may be used in combination with each other in any manner, and the fact that these combinations are not exhaustively described in this specification is only for the sake of omitting space and saving resources. Therefore, the present invention is not limited to the specific embodiments disclosed herein, but includes all technical solutions falling within the scope of the claims.

Claims

1. A lncRNA-disease association prediction method based on collaborative matrix decomposition with high-order perturbation and flexible ternary regularization, characterized in that: The specific steps are as follows: S1: Obtain the LncRNA-disease association matrix Z; S2: Based on the known association matrix Z, calculate the LncRNA functional similarity matrix R s and the semantic similarity matrix D of the disease s ; S3: adding the multi-order correlation matrix calculated based on the known correlation matrix as a high-order perturbation to the known correlation matrix; S4: Obtain global nonlinear structural similarity information of similarity matrix through similarity learning of flexible ternary regularization terms; S5: Integrate high-order perturbations and flexible ternary regularization into collaborative matrix factorization, iteratively optimize and remove the interference of high-order perturbations to obtain the final prediction score matrix; The steps for obtaining the LncRNA-disease association matrix Z in S1 are as follows: S11: The first dataset is from LncRNADisease2.0; S12: To facilitate in-depth case analysis of the prediction results, standard MeSH disease terms and broader category terms were used to replace the terms in the original dataset; S13: Clean the data, delete duplicate entries and entries of non-human lncRNA and disease, and finally get 1690 lncRNA-disease association pairs confirmed by biological experiments, covering 447 lncRNAs and 218 diseases, which are used as the experimental data set. On this basis, the association matrix Z of the defined lncRNA and disease is expressed as follows: The semantic similarity matrix D of the diseases in S2 s The calculation steps are as follows: S21: construct a directed acyclic graph (DAG(d)=(T(d), E(d))) based on the Mesh database, where T(d) represents the set of disease ancestor nodes including disease d itself, and E=(d) represents the set of edges directly connecting the ancestor nodes of the disease node to the child nodes; S22: Based on the constructed DAG, the contribution of the disease itself and its ancestor nodes to itself is judged. The equation expression is as follows: where disease t∈T(d); S23: The semantic value score of the disease can be calculated using the following formula: S24: On this basis, calculate the disease d i and diseases j The semantic similarity between them is then used to obtain the final disease semantic similarity matrix D s : The functional similarity matrix R of LncRNA in S2 s The calculation steps are as follows: S25: Assumption D i and D j They are respectively related to the R i and R j Related disease groups; S26: LncRNA functional similarity matrix is ​​defined as R s ; S27: R i and R j The similarity value between is calculated as follows: Where |D i | indicates R i The number of diseases associated with |D j | indicates R j The number of diseases associated with it, S(d m ,D j ) is related to LncRNA R i Related diseases m and LncRNA j Related disease cluster D j similarities between; The specific steps of adding the multi-order correlation matrix calculated based on the known correlation matrix as a high-order disturbance to the known correlation matrix in S3 are as follows: S31: Construct a high-order connection matrix C based on the known association matrix: C=min(1,Z T ·WITH) in is the known incidence matrix, m and n represent the number of rows and columns of the known incidence matrix Z, respectively. T Z represents the medium through which LncRNA and disease can interact. In order to avoid errors in subsequent analysis caused by numerical differences, all values ​​greater than 1 are restricted to 1, thereby constructing a high-order connection matrix C. This binary matrix represents whether LncRNA and disease can interact; S32: Construct different order correlation matrices based on the high order connection matrix C: Hyperconnection(Z,i)=min(1,Z·C i-1 ) In the experiment of the data set, it was observed that the high-order correlation matrix after the 4th-order correlation matrix remained basically unchanged. Therefore, only the 2nd-4th-order high-order correlation matrix was used as the final high-order correlation matrix. S33: Calculate the high-order perturbation matrix Hop: stW=0.1*rand(size(Z)) Where ⊙ represents the Hadamard product of the matrix, and the random value W represents the probability of interaction at the position determined by the high-order correlation matrix. When constructing the high-order correlation matrix, only the positions other than the original correlation matrix Z are determined, that is, A random value W is added to the position where the value is not 0, because the effective information of the original correlation matrix Z should be retained while avoiding the influence of the high-order correlation matrix processing on the original matrix. In order to ensure that the importance of the correlation information in the original matrix is ​​retained and the initial value is different from the value of the original matrix, the range of the random value W needs to be set between 0 and 0.1 to ensure that it can effectively reflect the possibility of correlation while reducing the interference to the original matrix; Therefore, the new incidence matrix can be expressed as: WITH new =Z+Hop; The specific steps of obtaining the global nonlinear structural similarity information of the similarity matrix in S4 are as follows: S41: Based on the principle of collaborative matrix decomposition, the expression of collaborative matrix decomposition is designed for the problem of predicting the association between LncRNA and diseases: Where α1, α2 and λ are the hyperparameters of the regularization term, and They represent the decomposed low-dimensional matrices of LncRNA term and disease term respectively, i is the number of subspace dimensions, is the Frobenius norm; S42: Adding additional factors M and N between the two variables of binary orthogonality preserves the global nonlinear structural information for similarity learning. Therefore, the expression of matrix decomposition with flexible ternary regularization is as follows: in, and is the factor matrix attached to the orthogonal variables of LncRNA and disease similarity, σ is the hyperparameter controlling the additional factors M and N, and in order to avoid complex non-convex coupling terms when minimizing the objective function, a proxy matrix variable of penalty is introduced Make it similar to UV T , therefore, the above formula can also be expressed as: in It is UV T Proxy matrix variables of ; The specific steps of integrating high-order perturbations and flexible ternary regularization into collaborative matrix factorization in S5 are as follows: S511: Based on high-order perturbations and flexible ternary regularization, the specific objective function of the proposed matrix decomposition with high-order perturbations and flexible ternary regularization is finally expressed as follows: S512: In order to avoid the cumbersome non-convex coupling terms when solving the objective function minimization problem and reduce the optimization difficulty caused by the high power of the dependent variable, we introduce and Two variables, used to fit UM and VN respectively; S513: Finally, after these transformations, the above objective function can also be expressed as: Similarly, β1 and β2 are also a set of hyperparameters; The specific steps of iterative optimization in S5 are as follows: S521: Update X str∈(0,2),s>0,Y≥0 Among them, matrices B and Y are temporary matrix variables used for transition in the gradient descent process, s is a hyperparameter of the iterative process, and r is the gradient step size. In order to simplify the experimental process and avoid introducing too many hyperparameters while ensuring the convergence of the optimization algorithm, the value of r is set to 0.1; S522: Update U make: but: s.t.s>0,U p =U t-1 U p Represents the previous iteration data U of U t-1 , E is an identity matrix; S523: Update V Based on the update formula of U, we can infer by analogy: s.t.s>0,V p =V t-1 Similarly, V p Represents the previous iteration data V of V t-1 ; S524: Update W str∈(0,2),s>0,Y≥0 Among them, matrices T and Y are temporary matrix variables used for transition during the gradient descent process; S525: Update Q make: but: Q=(β1UM+α1R s U)(β1E+α1U T U) -1 ; S526: Update P make: Then the partial derivative of the factor matrix P is: The update formula steps based on Q can also be derived by analogy: P=(β2VN+α2D s V)(β2E+α2V T V) -1 ; S527: Update M make: but: M=(β1U T U+σE) -1 (β1U T Q); S528: Update N make: but: Based on the optimization steps of M, we can infer by analogy: N=(β2V T V+σE) -1 (β2V T P); The specific steps for obtaining the final prediction score matrix in S5 are as follows: S531: After the iteration process meets the following conditions: S532: Calculate and obtain an approximate score matrix: S533: After eliminating the influence of high-order perturbations on the results, the final score matrix is ​​obtained:

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