A lncRNA-disease association prediction method based on weighted kernel norm regularization algorithm

Abstract

The present invention provides a lncRNA-disease association prediction method based on a weighted kernel canonical regularization algorithm, comprising the following steps: S1: obtaining the lncRNA-disease adjacency matrix LD; S2: calculating the lncRNA expression similarity LS exp , lncRNA functional similarity LS fun , lncRNA Gaussian similarity LS gau , lncRNA linear neighborhood similarity LS lin , disease semantic similarity DS sem , disease Gaussian similarity DS gau , disease linear neighborhood similarity DS lin S3: The k-nearest-neighbor centered kernel alignment algorithm is used to integrate the similarities of lncRNAs and diseases into the same space. S4: A heterogeneous matrix is ​​constructed using the lncRNA-disease association matrix and the optimal similarity kernel matrix of lncRNAs and diseases as the target matrix for matrix completion. S5: The heterogeneous matrix is ​​input into a weighted kernel canonical regularization model for completion, ultimately obtaining the predicted lncRNA-disease association. This method utilizes the k-nearest-neighbor centered kernel alignment algorithm to integrate similarity information for auxiliary prediction and constructs a weighted kernel canonical regularization model to complete the heterogeneous matrix, achieving more accurate lncRNA-disease association prediction.

Description

Technical Field

[0001] The present invention relates to the field of combining matrix completion algorithms with biological genes, and more specifically, to a lncRNA-disease association prediction method based on a weighted kernel canonical regularization algorithm. Background Art

[0002] LncRNAs are endogenous RNAs composed of over 200 nucleotides and possess little protein-coding capacity, translated from the genome. Various noncoding RNAs comprise 98% of the human genome, but are often considered "transcriptional noise." However, recent experimental evidence indicates that lncRNAs play important roles in many key biological processes, including epigenetic regulation, protein transport, and cell development and growth. LncRNA dysregulation and mutations are closely associated with the development of complex diseases, including renal, prostate, and colon cancers. LncRNA PCA3 has been shown to be associated with prostate cancer invasion, while lncRNA UCA1 can be used for bladder cancer diagnosis. Currently, there are two approaches to identifying lncRNA-disease associations: biological experimental verification and computational prediction. However, using traditional biological experiments to investigate the mechanisms and interactions between lncRNAs and diseases is time-consuming and labor-intensive. Therefore, effectively exploring the potential associations between lncRNAs and diseases is of paramount importance.

[0003] An increasing number of scientists are seeking to use computational methods to more efficiently and cost-effectively uncover potential lncRNA-disease associations. This could accelerate the discovery of potential drug targets and biomarkers, thereby improving the diagnosis and treatment of complex diseases. Numerous computational methods for predicting potential lncRNA-disease associations have been proposed and have demonstrated promising predictive performance in validation with biological experimental data. Current methods for predicting lncRNA-disease associations can be broadly categorized into three categories: machine learning, network propagation-based methods, and matrix completion.

[0004] Machine learning methods based on classifier training are widely used in bioinformatics research. Many common machine learning algorithms are used for lncRNA-disease association prediction, such as support vector machines, Bayesian classifiers, and random forests. However, most machine learning methods require negative samples as training sets, which significantly impacts their predictive performance. This is because negative samples are often difficult to obtain. Furthermore, most machine learning methods face challenges in selecting hyperparameters and biological features for classifier training. With the increasing research in deep learning within the machine learning field, an increasing number of researchers are applying deep learning to the problem of lncRNA-disease association prediction. Deep learning neural networks are capable of extracting low-dimensional representations from high-dimensional features of biological entities, enabling efficient prediction. However, these methods fail to fully utilize the rich information in similarity networks, ultimately impacting the quality of the representation of lncRNA and disease features.

[0005] Network propagation-based methods are based on the assumption that similar lncRNAs tend to be associated with similar diseases. Most biological network-based methods perform random walks on established heterogeneous networks, basing association predictions on the underlying topological information within these networks. Consequently, predictions may favor lncRNAs associated with more known diseases and diseases associated with more known lncRNAs. Furthermore, the rigid domain relationships exploited in random walk algorithms can affect the richness of molecular signature information.

[0006] Matrix completion methods supplement unknown entries in known lncRNA-disease association matrices based on the assumption that unknown associations can be derived from known associations. However, previous studies have shown that biomolecules with similar structures often do not exhibit identical functions. This lack of known relevant information significantly impacts the predictive performance of matrix completion methods. Furthermore, many matrix completion methods implicitly assume that all data sources have the same relevance to the prediction target and fail to differentiate between the quality of different data sources, resulting in predictive performance being severely impacted by data source noise. When completing low-rank matrices, matrix completion methods assign equal weight to each association, ignoring the underlying principal direction of the association, making the model less flexible for solving the completion problem.

[0007] The discovery of potential lncRNA-disease associations is undoubtedly a significant contribution to understanding disease pathogenesis and developing treatments for human diseases. Therefore, developing computational methods to uncover previously unknown associations between lncRNAs and diseases will not only facilitate understanding of the primary functions of lncRNAs in the pathology and molecular changes of human diseases, but also aid in the prognosis, treatment, and prevention of complex diseases. Because current methods fail to fully utilize feature similarity information and lack the flexibility to address the problem of completeness, this paper proposes a novel approach for predicting lncRNA-disease associations. Summary of the Invention

[0008] The present invention provides a lncRNA-disease association prediction method based on a weighted kernel canonical regularization algorithm to better predict the lncRNA-disease association.

[0009] In order to solve the above technical problems, the technical solutions of the present invention are as follows:

[0010] The lncRNA-disease association prediction method based on the weighted kernel norm regularization algorithm includes the following steps:

[0011] S1: Obtain the lncRNA-disease adjacency matrix LD, which is used to describe the lncRNA-disease association relationship;

[0012] S2: Calculate lncRNA expression similarity LS exp , lncRNA functional similarity LS fun , lncRNA Gaussian similarity LS gau , lncRNA linear neighborhood similarity LS lin , disease semantic similarity DS sem , Disease Gaussian Similarity DS gau , disease linear neighborhood similarity DS lin ;

[0013] S3: The k-nearest neighbor center kernel alignment algorithm is used to integrate the similarities of lncRNA and disease into the same space, and the optimal similarity kernel matrices LS and DS of lncRNA and disease are obtained respectively;

[0014] S4: A heterogeneous matrix was constructed using the lncRNA-disease association matrix and the optimal similarity kernel matrix of lncRNA and disease;

[0015] S5: The heterogeneous matrix is ​​input into the weighted kernel norm regularization model for completion, and the predicted lncRNA-disease association is finally obtained.

[0016] Preferably, the lncRNA-disease adjacency matrix LD in step S1 is specifically:

[0017] The lncRNA-disease association data were downloaded from the LncRNADisease v2.0 (http: / / www.rnanut.net / lncrnadisease / ) and Lnc2Cancer3.0 databases. After removing duplicate lncRNAs and diseases and replacing terms without relevant annotations with broader categories, this method constructed an adjacency matrix LD∈R nL×nD To represent the association between lncRNA and disease, nL and nD represent the number of lncRNAs and diseases. If a lncRNA is confirmed to be associated with a disease, LD(i,j) is set to 1, otherwise LD(i,j) is set to 0.

[0018] Preferably, in step S2, the lncRNA expression similarity LS exp , specifically:

[0019] This method downloaded about 50,000 lncRNA expression profiles from 53 human tissues and cell types to form a dataset. The Spearman correlation coefficient between each pair of lncRNA expression profiles was calculated to represent the similarity of lncRNA expression. The matrix LS exp (L i ,L j ) to describe lncRNA L i and lncRNA L j The similarity of expression is between 0 and 1.

[0020] Preferably, in step S2, the lncRNA functional similarity LS fun , specifically:

[0021] By calculating the similarity between two groups of diseases associated with two lncRNAs, the functional similarity between two lncRNAs can be quantitatively calculated. i and L j If lncRNA L i and L j Functional similarity LS between fun (L i ,L j ) is calculated as follows:

[0022]

[0023] Among them, DS(D i ,D') represents the disease set D i The similarity value between the disease set D' and the top k diseases with the highest similarity (this paper uses the semantic similarity of diseases).

[0024] Preferably, in step S2, the lncRNA Gaussian similarity LS gau , specifically:

[0025] Gaussian kernel similarity is also called radial basis function kernel similarity. By calculating the Euclidean distance between different nodes in the node network, the similarity weight between nodes can be obtained. i ) represents the i-th row vector in the Gaussian kernel eigenvector (L i represents the association between the i-th lncRNA and other diseases in LD), the Gaussian kernel similarity LS between lncRNAs gau The calculation method is:

[0026] LS gau (L i ,L j )=exp(-γ L ||Q(L i )-Q(L j )|| 2 ),

[0027]

[0028] where γ' L is the initial kernel parameter, by default γ' L =1.

[0029] Preferably, the lncRNA linear neighborhood similarity LS in step S2 lin , specifically:

[0030] Each data node and its neighboring nodes tend to be located at or near local linear segments, and linear coefficients can be used to characterize the local geometry of these linear segments. Therefore, linear coefficients are used to reconstruct the data points in the neighborhood. A lncRNA set is considered as a feature vector L i , the reconstructed linear coefficient can be obtained from L i Each data node is calculated as follows:

[0031]

[0032]

[0033]

[0034]

[0035] Where λ is the regularization parameter, and by default, λ=1. i ) represents k LThe set of nearest neighbors (calculated by Euclidean distance), L ij It's L i The jth neighbor of L' ij Indicates L ij The reconstruction linear coefficients of The reconstructed linear coefficients can be obtained using standard quadratic programming. Finally, it is easy to obtain the linear coefficient matrix LS of lncRNA lin ∈R nL×nL , which can be used as the linear neighborhood similarity of lncRNA.

[0036] Preferably, the disease semantic similarity DS in step S2 sem , specifically:

[0037] The semantic similarity between diseases was calculated using a directed acyclic graph (DAG). DAG is constructed based on MeSH description information (the original data of disease semantic information) and can be downloaded from the National Library of Medicine. i )=(T(D i ),E(D i )) to describe the disease D i DAG, where T(D i ) is disease D i and its own ancestor node E(D i ) between the corresponding connecting edges. First, in DAG (D i ) Disease D i The semantic similarity SV(D i ) is calculated as follows:

[0038]

[0039]

[0040] Among them D t ∈T(D i ), ω is the semantic contribution attenuation factor, which is ω=0.5 by default. Then, based on the common ancestor nodes in DAG, the disease D is calculated. i and D j The semantic similarity DS between sem (D i ,D j )for:.

[0041]

[0042] Preferably, the disease Gaussian similarity DS in step S2 gau , specifically:

[0043] The disease Gaussian similarity DS gau The calculation method is similar to lncRNA Gaussian similarity LS gau The calculation method is the same.

[0044] Preferably, the disease linear neighborhood similarity DS in step S2 lin , specifically:

[0045] The disease linear neighborhood similarity DS lin The calculation method is similar to lncRNA linear neighborhood similarity LS lin The calculation method is the same.

[0046] Preferably, in step S3, the k-nearest neighbor center kernel alignment algorithm is used to integrate lncRNA similarities to obtain the optimal similarity kernel matrix LS, specifically:

[0047] The four lncRNA similarity kernel matrices (LS exp ,LS fun ,LS gau ,LS lin ∈R nL×nL ) into the same space and calculate the optimal combined similarity kernel LS of lncRNA:

[0048]

[0049] Among them LS i Represents the similarity matrix of the lncRNA similarity kernel matrix set. ω i It represents the weight coefficient of the combination, which is calculated based on the degree of alignment between the base core and the central core. The degree of alignment between the cores is positively correlated with the correlation between the cores. The alignment score CKA(LS i ,CK) can be expressed by cosine correlation as follows:

[0050]

[0051] in <LS i ,CK> F =Trace(LS i T CK) is the Frobenius inner product, is the Frobenius parameterization. It can be further transformed into an optimization problem of the objective function:

[0052]

[0053]

[0054]

[0055] IK=LD·LD T

[0056] U=I-ll T / nL

[0057] Where I is an nL-order unit matrix and l is an nL-order unit vector. i Indicates lncRNAL i The top k with the highest similarity s ×nL lncRNAs, k s ∈[0,1] is the quantity coefficient. It is simplified to a combinatorial optimization problem as follows:

[0058]

[0059]

[0060] N=(<ULS1U,CK> F ,<ULS2U,CK> F ,…, <ULS nS U,CK. F ) T

[0061]

[0062] M p,q = <ULS p U,ULS q U> F ,p,q=1,2,…,nS

[0063] Finally, the optimal combination similarity kernel is obtained by quadratic programming

[0064] Preferably, in step S3, the k-nearest neighbor center kernel alignment algorithm is used to integrate disease similarities to obtain the optimal similarity kernel matrix DS, specifically:

[0065] The calculation method of the disease optimal similarity kernel matrix DS is the same as the calculation method of the lncRNA optimal similarity kernel matrix LS.

[0066] Preferably, the heterogeneous matrix in step S4 is specifically:

[0067] Heterogeneous network X'∈R (nL+nD)×(nL+nD) Defined as:

[0068] Preferably, the weighted kernel norm regularization model in step S5 is specifically:

[0069] Complete the target matrix by solving the rank minimization problem:

[0070]

[0071] sT Ω (X) = P Ω (X')

[0072]

[0073] Where rank(·) is the rank function, X'∈R (nL+nD)×(nL×nD) is the target matrix to be constructed. Ω is a set of index pairs (i, j) containing all known lncRNA-disease associations in X'. Ω is the projection operator on Ω. However, directly solving the rank minimization in the above matrix completion is an NP-hard problem, which can be simplified to a nuclear norm minimization:

[0074]

[0075] sT Ω (X) = P Ω (X')

[0076]

[0077] in represents the weighted nuclear norm of matrix X, σ i (X) represents the i-th largest singular value of the matrix X and satisfies σ1(X)≥σ2(X≥…≥σ n (X). ω=[ω1,ω2,…,ω n ] is assigned to σ i After constraining the predicted value to be within the interval [0,1] and adding a tolerable noise term, the model is converted to the following ADMM form:

[0078]

[0079] stX=M,0≤M≤1

[0080] where α is the error term of the balanced nuclear norm, is the Frobenius parameterization. M is an auxiliary matrix used to accelerate the convergence of the model. Finally, the augmented Lagrangian function is transformed into:

[0081]

[0082] Where Z is the Lagrange multiplier, and β>0 represents the adaptive penalty parameter of the augmentation term. An iterative method is used, with the initial value set to X1=M1=Z1=P Ω (X'), and solve M through k iterations respectivelyk+1 and X K+1 , Z k+1 .

[0083] For M k+1 , calculated by fixing the other two terms. Using the inverse operator, the optimal closed-form solution becomes:

[0084]

[0085]

[0086] For X k+1 , iterate in the same way:

[0087]

[0088]

[0089] where σ i (X k ) represents X k The i-th singular value of X. ε is a small constant and C is the weight coefficient. k+1 The closed form solution of can be obtained from the formula:

[0090]

[0091] in represents the singular value contraction operator, which is defined as:

[0092]

[0093]

[0094] a i =σ(Y) i -ε,

[0095] b i =(σ(Y) i +ε) 2 -4C.

[0096] Where σ(Y) i is the i-th singular value of Y in descending order, and u i and v i is σ(Y) i The corresponding left and right singular vectors.

[0097] For Z k+1 , Z k+1 =Z k +β(X k+1 -M k+1 ).

[0098] When the iteration meets and The iteration is terminated. The final updated heterogeneous network can be obtained Finally, the completed association probability matrix can be obtained

[0099] Compared with the prior art, the beneficial effects of the technical solution of the present invention are:

[0100] The present invention calculates multiple-angle similarity information to assist in association prediction between lncRNA and disease, proposes a k-nearest neighbor center kernel alignment algorithm to integrate similarity information to obtain the optimal combined similarity kernel matrix, and designs a weighted kernel norm regularization model for association prediction, achieving more accurate lncRNA-disease association prediction. BRIEF DESCRIPTION OF THE DRAWINGS

[0101] Figure 1 Flow chart of the method of the present invention.

[0102] Figure 2 This is the algorithm structure diagram of the present invention.

[0103] Figure 3 In the embodiment, WNNRLDA and RWRlncD, BRWLDA are implemented based on LOOCV.

[0104] Schematic diagram of AUCs of SIMCLDA, GMCLDA, and HOPMCLDA.

[0105] Figure 4 Schematic diagram of AUCs achieved based on 5-fold CV using WNNRLDA and RWRlncD, BRWLDA, SIMCLDA, GMCLDA, and HOPMCLDA in the examples. DETAILED DESCRIPTION

[0106] The accompanying drawings are for illustrative purposes only and are not to be construed as limiting this patent;

[0107] In order to better illustrate this embodiment, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product size;

[0108] It is understandable to those skilled in the art that some well-known structures and descriptions thereof may be omitted in the drawings.

[0109] The technical solution of the present invention is further described below with reference to the accompanying drawings and embodiments.

[0110] Example 1

[0111] This embodiment provides a lncRNA-disease association prediction method based on a weighted kernel canonical regularization algorithm, such as Figure 1 As shown, the following steps are included:

[0112] S1: Obtain the lncRNA-disease adjacency matrix LD, which is used to describe the lncRNA-disease association relationship;

[0113] S2: Calculate lncRNA expression similarity LS exp , lncRNA functional similarity LS fun , lncRNA Gaussian similarity LS gau , lncRNA linear neighborhood similarity LS lin , disease semantic similarity DS sem , Disease Gaussian Similarity DS gau , disease linear neighborhood similarity DS lin ;

[0114] S3: The k-nearest neighbor center kernel alignment algorithm is used to integrate the similarities of lncRNA and disease into the same space, and the optimal similarity kernel matrices LS and DS of lncRNA and disease are obtained respectively;

[0115] S4: A heterogeneous matrix was constructed using the lncRNA-disease association matrix and the optimal similarity kernel matrix of lncRNA and disease;

[0116] S5: The heterogeneous matrix is ​​input into the weighted kernel norm regularization model for completion, and the predicted lncRNA-disease association is finally obtained.

[0117] The lncRNA-disease adjacency matrix LD in step S1 is specifically:

[0118] The lncRNA-disease association data were downloaded from the LncRNADisease v2.0 (http: / / www.rnanut.net / lncrnadisease / ) and Lnc2Cancer3.0 databases. After removing duplicate lncRNAs and diseases and replacing terms without relevant annotations with broader categories, this method constructed an adjacency matrix LD∈R nL×nD To represent the association between lncRNA and disease, nL and nD represent the number of lncRNAs and diseases. If a lncRNA is confirmed to be associated with a disease, LD(i,j) is set to 1, otherwise LD(i,j) is set to 0.

[0119] lncRNA expression similarity LS in step S2 exp , specifically:

[0120] This method downloaded about 50,000 lncRNA expression profiles from 53 human tissues and cell types to form a dataset. The Spearman correlation coefficient between each pair of lncRNA expression profiles was calculated to represent the similarity of lncRNA expression. The matrix LS exp (L i ,L j ) to describe lncRNA L i and lncRNA L j The similarity of expression is between 0 and 1.

[0121] lncRNA functional similarity LS in step S2 fun , specifically:

[0122] By calculating the similarity between two groups of diseases associated with two lncRNAs, the functional similarity between two lncRNAs can be quantitatively calculated. i and L j If lncRNA L i and L j Functional similarity LS between fun (L i ,L j ) is calculated as follows:

[0123]

[0124]

[0125] Among them, DS(D i ,D') represents the disease set D i The similarity value between the disease set D' and the top k diseases with the highest similarity (this paper uses the semantic similarity of diseases).

[0126] lncRNA Gaussian similarity LS in step S2 gau , specifically:

[0127] Gaussian kernel similarity is also called radial basis function kernel similarity. By calculating the Euclidean distance between different nodes in the node network, the similarity weight between nodes can be obtained. i ) represents the i-th row vector in the Gaussian kernel eigenvector (L i represents the association between the i-th lncRNA and other diseases in LD), the Gaussian kernel similarity LS between lncRNAs gau The calculation method is:

[0128] LS gau (Li ,L j )=exp(-γ L ||Q(L i )-Q(L j )|| 2 )

[0129]

[0130] where γ' L is the initial kernel parameter, by default γ' L =1.

[0131] lncRNA linear neighborhood similarity LS in step S2 lin , specifically:

[0132] Each data node and its neighboring nodes tend to be located at or near local linear segments, and linear coefficients can be used to characterize the local geometry of these linear segments. Therefore, linear coefficients are used to reconstruct the data points in the neighborhood. A lncRNA set is considered as a feature vector L i , the reconstructed linear coefficient can be obtained from L i Each data node is calculated as follows:

[0133]

[0134]

[0135]

[0136]

[0137] Where λ is the regularization parameter, and by default, λ=1. i ) represents k L The set of nearest neighbors (calculated by Euclidean distance), L ij It's L i The jth neighbor of L' ij Indicates L ij The reconstruction linear coefficients of The reconstructed linear coefficients can be obtained using standard quadratic programming. Finally, it is easy to obtain the linear coefficient matrix LS of lncRNA lin ∈R nL×nL , which can be used as the linear neighborhood similarity of lncRNA.

[0138] Disease semantic similarity DS in step S2 sem , specifically:

[0139] The semantic similarity between diseases was calculated using a directed acyclic graph (DAG). DAG is constructed based on MeSH description information (the original data of disease semantic information) and can be downloaded from the National Library of Medicine. i )=(T(D i ),E(D i )) to describe the disease D i DAG, where T(D i ) is disease D i and its own ancestor node E(D i ) between the corresponding connecting edges. First, in DAG (D i ) Disease D i The semantic similarity SV(D i ) is calculated as follows:

[0140]

[0141]

[0142] Among them D t ∈T(D i ), ω is the semantic contribution attenuation factor, which is ω=0.5 by default. Then, based on the common ancestor nodes in DAG, the disease D is calculated. i and D j The semantic similarity DS between sem (D i ,D j )for:.

[0143]

[0144] Disease Gaussian similarity DS in step S2 gau , specifically:

[0145] The disease Gaussian similarity DS gau The calculation method is similar to lncRNA Gaussian similarity LS gau The calculation method is the same.

[0146] Disease linear neighborhood similarity DS in step S2 lin , specifically:

[0147] The disease linear neighborhood similarity DS lin The calculation method is similar to lncRNA linear neighborhood similarity LS lin The calculation method is the same.

[0148] In step S3, the k-nearest neighbor center kernel alignment algorithm is used to integrate lncRNA similarity to obtain the optimal similarity kernel matrix LS, specifically:

[0149] The four lncRNA similarity kernel matrices (LS exp ,LS fun ,LS gau ,LS lin ∈R nL×nL ) into the same space and calculate the optimal combined similarity kernel LS of lncRNA:

[0150]

[0151] Among them LS i Represents the similarity matrix of the lncRNA similarity kernel matrix set. ω i It represents the weight coefficient of the combination, which is calculated based on the degree of alignment between the base core and the central core. The degree of alignment between the cores is positively correlated with the correlation between the cores. The alignment score CKA(LS i ,CK) can be expressed by cosine correlation as follows:

[0152]

[0153] in <LS i ,CK> F =Trace(LS i T CK) is the Frobenius inner product, is the Frobenius parameterization. It can be further transformed into an optimization problem of the objective function:

[0154]

[0155]

[0156]

[0157] IK=LD·LD T

[0158] U=I-ll T / nL

[0159] Where I is an nL-order unit matrix and l is an nL-order unit vector. i Indicates lncRNAL i The top k with the highest similarity s ×nL lncRNAs, k s ∈[0,1] is the quantity coefficient. It is simplified to a combinatorial optimization problem as follows:

[0160]

[0161]

[0162] N=(<ULS1U,CK> F ,<ULS2U,CK> F ,…, <ULS nS U,CK> F ) T

[0163]

[0164] M p,q = <ULS p U,ULS q U> F ,p,q=1,2,…,nS

[0165] Finally, the optimal combination similarity kernel is obtained by quadratic programming

[0166] Preferably, in step S3, the k-nearest neighbor center kernel alignment algorithm is used to integrate disease similarities to obtain the optimal similarity kernel matrix DS, specifically:

[0167] The calculation method of the disease optimal similarity kernel matrix DS is the same as the calculation method of the lncRNA optimal similarity kernel matrix LS.

[0168] The heterogeneous matrix in step S4 is specifically:

[0169] Heterogeneous network X'∈R (nL+nD)×(nL+nD) Defined as:

[0170] The weighted kernel norm regularization model in step S5 is specifically:

[0171] Complete the target matrix by solving the rank minimization problem:

[0172]

[0173] sT Ω (X) = P Ω (X')

[0174]

[0175] Where rank(·) is the rank function, X'∈R (nL+nD)×(nL×nD) is the target matrix to be constructed. Ω is a set of index pairs (i, j) containing all known lncRNA-disease associations in X'. Ω is the projection operator on Ω. However, directly solving the rank minimization in the above matrix completion is an NP-hard problem, which can be simplified to a nuclear norm minimization:

[0176]

[0177] sT Ω (X) = P Ω (X')

[0178]

[0179] in represents the weighted nuclear norm of matrix X, σ i (X) represents the i-th largest singular value of the matrix X and satisfies σ1(X)≥σ2(X≥…≥σ n (X). ω=[ω1,ω2,…,ω n ] is assigned to σ i After constraining the predicted value to be within the interval [0,1] and adding a tolerable noise term, the model is converted to the following ADMM form:

[0180]

[0181] stX=M,0≤M≤1

[0182] where α is the error term of the balanced nuclear norm, is the Frobenius parameterization. M is an auxiliary matrix used to accelerate the convergence of the model. Finally, the augmented Lagrangian function is transformed into:

[0183]

[0184] Where Z is the Lagrange multiplier, and β>0 represents the adaptive penalty parameter of the augmentation term. An iterative method is used, with the initial value set to X1=M1=Z1=P Ω (X'), and solve M through k iterations respectively k+1 and X K+1 , Z k+1 .

[0185] For M k+1 , calculated by fixing the other two terms. Using the inverse operator, the optimal closed-form solution becomes:

[0186]

[0187]

[0188] For X k+1 , iterate in the same way:

[0189]

[0190]

[0191] where σ i (X k ) represents X k The i-th singular value of X. ε is a small constant and C is the weight coefficient. k+1 The closed form solution of can be obtained from the formula:

[0192]

[0193] in represents the singular value contraction operator, which is defined as:

[0194]

[0195]

[0196] a i =σ(Y) i -ε,

[0197] b i =(σ(Y) i +ε) 2 -4C.

[0198] Where σ(Y) i is the i-th singular value of Y in descending order, and u i and v i is σ(Y) i The corresponding left and right singular vectors.

[0199] For Z k+1 , Z k+1 =Z k +β(X k+1 -M k+1 ).

[0200] When the iteration meets and The iteration is terminated. The final updated heterogeneous network can be obtained Finally, the completed association probability matrix can be obtained

[0201] In order to test the prediction accuracy of the method (WNNRLDA) of this embodiment, WNNRLDA is compared with five advanced methods: RWRlncD, BRWLDA, SIMCLDA, GMCLDA, and HOPMCLDA. Figure 2It can be seen that under the LOOCV framework, the area under the WNNRLDA curve AUC is 0.9340, which is larger than other calculation methods (RWRlncD 0.8630, BRWLDA 0.8312, SIMCLDA 0.7675, GMCLDA 0.8425, HOPMCLDA 0.8686), indicating that the performance of WNNRLDA is better than other calculation methods. In order to further verify the prediction performance of WNNRLDA, the 5-fold CV framework was used for verification. Figure 3 As can be seen, WNNRLDA can achieve a reliable AUC of 0.9275 ± 0.0043, far exceeding the AUC values ​​of 0.8136 ± 0.0038, 0.8083 ± 0.0026, 0.7351 ± 0.0057, 0.8421 ± 0.0039, and 0.8431 ± 0.0061. This means that WNNRLDA is more effective than other methods under the 5-fold CV framework. These results fully demonstrate that the WNNRLDA method is superior to the comparative method and is more conducive to predicting lncRNA-disease associations.

[0202] WNNRLDA is also used to predict the application of known lncRNAs in actual lncRNA-disease prediction. In the process of predicting new lncRNA-disease associations, this method uses the known lncRNA-disease correlations as the training data set of WNNRLDA, and then calculates the prediction score of each unknown lncRNA-disease pair and ranks them. This method selects cervical cancer, gastric cancer and breast cancer as case studies. The top 10 cancer lncRNAs were verified in third-party databases (Lnc2Cancer and MNDR). The results shown in Tables 1, 2 and 3 show that 90%, 100% and 90% of the predicted lncRNAs are related to cancer, respectively.

[0203] In addition, WNNRLDA predicts some unproven lncRNA-disease relationships, including TINCR and cervical cancer, and FTX and breast cancer. These predicted associations have not yet been reported in the literature, but may be more likely to exist, and medical researchers are awaiting further study and verification.

[0204] Table 1 Top 10 potential lncRNAs associated with cervical cancer predicted by WNNRLDA

[0205]

[0206]

[0207] Table 2 Top 10 potential lncRNAs associated with gastric cancer predicted by WNNRLDA

[0208]

[0209] Table 3 Top 10 potential lncRNAs associated with breast cancer predicted by WNNRLDA

[0210]

[0211]

[0212] The same or similar reference numerals correspond to the same or similar components;

[0213] The terms used in the drawings to describe positional relationships are for illustrative purposes only and should not be construed as limiting this patent;

[0214] Obviously, the above embodiments of the present invention are merely examples for the purpose of clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Those skilled in the art will appreciate that other variations or modifications can be made based on the above description. It is not necessary and impossible to enumerate all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the claims of the present invention.

Claims

1. A lncRNA-disease association prediction method based on a weighted kernel canonical regularization algorithm, characterized in that: The following steps are involved: S1: Obtain the lncRNA-disease adjacency matrix LD, which is used to describe the lncRNA-disease association relationship; S2: Calculate lncRNA expression similarity LS exp , lncRNA functional similarity LS fun , lncRNA Gaussian similarity LS gau , lncRNA linear neighborhood similarity LS lin , disease semantic similarity DS sem , disease Gaussian similarity DS gau , disease linear neighborhood similarity DS lin ; S3: The k-nearest neighbor center kernel alignment algorithm is used to integrate the similarities of lncRNA and disease into the same space, and the optimal similarity kernel matrices LS and DS of lncRNA and disease are obtained respectively; S4: A heterogeneous matrix was constructed using the lncRNA-disease association matrix and the optimal similarity kernel matrix of lncRNA and disease; S5: Input the heterogeneous matrix into the weighted kernel norm regularization model for completion, and finally obtain the predicted lncRNA-disease association. The specific steps are as follows: Complete the target matrix by solving the rank minimization problem: stP Ω (X)=P Ω (X') Where rank(·) is the rank function, X'∈R (nL+nD)×(nL×nD) is the target matrix to be constructed; Ω is a set of index pairs (i, j) containing all known lncRNA-disease associations in X'; P Ω is the projection operator on Ω; however, directly solving the rank minimization in the above matrix completion is an NP-hard problem, which can be simplified to a nuclear norm minimization: stP Ω (X)=P Ω (X') where ||X|| ω,* represents the weighted nuclear norm of matrix X, σ i (X) represents the i-th largest singular value of the matrix X and satisfies σ1(X)≥σ2(X≥…≥σ n (X);ω=[ω1,ω2,…,ω n ] is assigned to σ i (X); After constraining the predicted value to be in the interval [0,1] and adding a tolerable noise term, the model is converted to the following ADMM form: stX=M,0≤M≤1 where α is the error term of the balanced nuclear norm, is the Frobenius parameterization; M is an auxiliary matrix used to accelerate the convergence of the model; finally, it is transformed into an augmented Lagrangian function: Where Z is the Lagrange multiplier, β>0 represents the adaptive penalty parameter of the augmentation term; an iterative method is used to set the initial value to X1=M1=Z1=Ρ Ω (X'), and solve M through k iterations respectively k+1 and X K+1 , Z k+1 ; When the iteration ends, the final updated heterogeneous network can be obtained Finally, the completed association probability matrix can be obtained 2. The lncRNA-disease association prediction method based on the weighted kernel canonical regularization algorithm according to claim 1, characterized in that: The lncRNA-disease adjacency matrix LD in step S1 is specifically: lncRNA-disease association data were downloaded from the LncRNADisease v2.0 and Lnc2Cancer 3.0 databases. After removing duplicate lncRNAs and diseases, and replacing category terms without relevant annotations with their broader category terms, an adjacency matrix LD∈R was constructed. nL×nD to represent the association between lncRNA and disease, where nL and nD represent the number of lncRNA and disease; if a lncRNA is confirmed to be associated with a disease, LD(i,j) is set to 1, otherwise LD(i,j) is set to 0.

3. The lncRNA-disease association prediction method based on the weighted kernel canonical regularization algorithm according to claim 1, characterized in that: lncRNA expression similarity LS in step S2 exp , specifically: More than 50,000 lncRNA expression profiles from 53 human tissues and cell types were downloaded to form a dataset. The Spearman correlation coefficient between each lncRNA pair expression profile was calculated to represent the expression similarity of lncRNA. The matrix LS was used to exp (L i ,L j ) to describe lncRNA L i and lncRNA L j The similarity of expression is between 0 and 1.

4. The lncRNA-disease association prediction method based on the weighted kernel canonical regularization algorithm according to claim 1, characterized in that: lncRNA functional similarity LS in step S2 fun , specifically: If a disease set D containing m diseases and a disease set D' containing n diseases are respectively i and L j If lncRNA L i and L j Functional similarity LS between fun (L i ,L j ) can quantitatively calculate the functional similarity between two lncRNAs by calculating the similarity between the two groups of diseases associated with them respectively.

5. The lncRNA-disease association prediction method based on the weighted kernel canonical regularization algorithm according to claim 1, characterized in that: lncRNA Gaussian similarity LS in step S2 gau , specifically: Gaussian kernel similarity is also called radial basis function kernel similarity; vector Q(L i ) represents the i-th row vector in the Gaussian kernel feature vector; the similarity weights between nodes can be obtained by calculating the Euclidean distance between different nodes in the node network to obtain the Gaussian kernel similarity LS between lncRNAs. gau ; lncRNA linear neighborhood similarity LS in step S2 lin , specifically: Each data node and its neighboring nodes tend to be located at or near local linear segments, and linear coefficients can be used to characterize the local geometry of these linear segments. Therefore, this method uses linear coefficients to reconstruct the data points in the neighborhood. The reconstructed linear coefficients can be obtained using standard quadratic programming. Finally, it is easy to obtain the linear coefficient matrix LS of lncRNA. lin ∈R nL×nL , which can be used as the linear neighborhood similarity of lncRNA; Disease semantic similarity DS in step S2 sem , specifically: The semantic similarity between diseases is calculated using a directed acyclic graph (DAG); DAG is constructed based on MeSH description information and can be downloaded from the National Library of Medicine. i )=(T(D i ),E(D i )) to describe the disease D i DAG, where T(D i ) is disease D i and its own ancestor node E(D i ) between the corresponding connecting edges; first calculate DAG (D i ) Disease D i The semantic similarity SV(D i ), then based on the common ancestor nodes in the DAG, the disease D i and D j The semantic similarity DS between sem (D i ,D j ).

6. The lncRNA-disease association prediction method based on the weighted kernel canonical regularization algorithm according to claim 1, characterized in that: Disease Gaussian similarity DS in step S2 gau , specifically: The disease Gaussian similarity DS gau The calculation method is similar to lncRNA Gaussian similarity LS gau The calculation method is the same; Disease linear neighborhood similarity DS in step S2 lin , specifically: The disease linear neighborhood similarity DS lin The calculation method is similar to lncRNA linear neighborhood similarity LS lin The calculation method is the same.

7. The lncRNA-disease association prediction method based on the weighted kernel canonical regularization algorithm according to claim 1, characterized in that: In step S3, the k-nearest neighbor center kernel alignment algorithm is used to integrate lncRNA similarity to obtain the optimal similarity kernel matrix LS, specifically: The four lncRNA similarity kernel matrices (LS exp ,LS fun ,LS gau ,LS lin ∈R nL×nL ) into the same space and calculate the optimal combined similarity kernel LS of lncRNA: Among them LS i Represents the similarity matrix of the lncRNA similarity kernel matrix set; ω i It represents the weight coefficient of the combination, which is calculated based on the degree of alignment between the base core and the central core. The degree of alignment between the cores is positively correlated with the correlation between the cores. The alignment score CKA(LS i ,CK) can be transformed into the optimization problem of the objective function by using cosine correlation. I=LD·LD T U=I-ll T / nL Where I is the nL-order unit matrix, l is the nL-order unit vector; N i Indicates lncRNAL i The top k with the highest similarity s ×nL lncRNAs, k s ∈[0,1] is the quantity coefficient; finally, the optimal combination similarity kernel is obtained by quadratic programming LS i ∈R nL×nL .

8. The lncRNA-disease association prediction method based on the weighted kernel canonical regularization algorithm according to claim 1, characterized in that: In step S3, the k-nearest neighbor center kernel alignment algorithm is used to integrate disease similarities to obtain the optimal similarity kernel matrix DS, which is specifically: The calculation method of the disease optimal similarity kernel matrix DS is the same as the calculation method of the lncRNA optimal similarity kernel matrix LS.

9. The lncRNA-disease association prediction method based on the weighted kernel canonical regularization algorithm according to claim 1, characterized in that: The heterogeneous matrix in step S4 is specifically: Heterogeneous network X'∈R (nL+nD)×(nL+nD) Defined as:

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