CN113345593A - Method for predicting disease association relation in biological association network - Google Patents

Method for predicting disease association relation in biological association network Download PDF

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CN113345593A
CN113345593A CN202110287525.8A CN202110287525A CN113345593A CN 113345593 A CN113345593 A CN 113345593A CN 202110287525 A CN202110287525 A CN 202110287525A CN 113345593 A CN113345593 A CN 113345593A
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郭菲
王浩
唐继军
丁漪杰
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Abstract

The invention discloses a method for predicting disease association relation in a biological association network, which comprises the following steps: s1 creating a polynuclear representation of non-coding RNAs
Figure DDA0002981104660000011
And multi-nuclear representation of disease
Figure DDA0002981104660000012
S2, respectively fusing the non-coding RNA multi-core and disease multi-core by adopting a central core alignment calculation method to obtain an optimal core
Figure DDA0002981104660000013
And
Figure DDA0002981104660000014
s3, calculating method by using singular value decompositionThe fused optimal kernel is decomposed into two matrices, i.e.
Figure DDA0002981104660000015
And
Figure DDA0002981104660000016
s4 matrix pair method using hypergraph regular term three-matrix decomposition
Figure DDA0002981104660000017
And
Figure DDA0002981104660000018
calculating to obtain a hypergraph Laplace matrix
Figure DDA0002981104660000019
And
Figure DDA00029811046600000110
s5, performing cross validation on the Laplace matrix of the hypergraph
Figure DDA00029811046600000111
And
Figure DDA00029811046600000112
calculating to obtain a new incidence relation matrix, Y*＝AΘBT(ii) a The invention solves the problem of incidence relation prediction of non-coding RNA and diseases, adds the Laplacian regularization term of the hypergraph into the three-matrix decomposition calculation, and adopts a multi-core fusion method of central core alignment, thereby obviously improving the prediction precision.

Description

Method for predicting disease association relation in biological association network
Technical Field
The invention belongs to the field of biological association network prediction algorithms in bioinformatics, and particularly relates to a method for predicting disease association relationship in a biological association network.
Background
The precise correlation between non-coding RNA and disease is of great help for the treatment of human biomedical research. However, the conventional techniques are applied to only one non-coding RNA or one specific disease, and the separation of the two is performed, and the experimental method is time-consuming and expensive. Based on known non-coding RNAs and disease-related information, many computational tools have been proposed to detect new associations. Since non-coding rnas (ncrnas), including circular rnas (circrnas), micro rnas (mirnas), and long non-coding rnas (lncrnas), are closely related to the progression of various diseases in humans, it is important to develop an effective computational method to predict ncRNA-disease association.
Disclosure of Invention
In view of the problems in the prior art, the present invention aims to provide a method for predicting disease association relationship in a biological association network. The method uses a multi-core learning algorithm with central core alignment to fuse a plurality of cores, and then uses a three-matrix decomposition method based on a hypergraph regular term to train, so as to predict the new incidence relation between non-coding RNA and diseases.
In order to solve the problems in the prior art, the invention adopts the following technical scheme:
a method for disease association prediction in a biological association network, comprising the steps of:
s1 creating a polynuclear representation of non-coding RNAs
Figure BDA0002981104640000011
And multi-nuclear representation of disease
Figure BDA0002981104640000012
Wherein u and v are the number of nuclei in the expression space of the non-coding RNA and the disease;
s2, fusing the non-coding RNA nucleus and the disease nucleus respectively by adopting a central nucleus alignment method to obtain the optimal nucleus
Figure BDA0002981104640000013
And
Figure BDA0002981104640000014
s3, decomposing the fused optimal kernel into two matrixes by using a singular value decomposition method, namely
Figure BDA0002981104640000015
And
Figure BDA0002981104640000016
the calculation process is as follows:
Figure BDA0002981104640000017
Figure BDA0002981104640000018
wherein, A and B are low rank approximate matrixes; r isncAnd rdPotential characteristic spatial dimensions of non-coding RNA and disease, respectively;
s4 matrix pair method using hypergraph regular term three-matrix decomposition
Figure BDA0002981104640000019
And
Figure BDA00029811046400000110
calculating to obtain a hypergraph Laplace matrix
Figure BDA00029811046400000111
And
Figure BDA00029811046400000112
s5, performing cross validation on the Laplace matrix of the hypergraph
Figure BDA0002981104640000021
And
Figure BDA0002981104640000022
calculating to obtain a new incidence relation matrix, Y*＝AΘBT。
Further, the laplace matrix of the hypergraph in the step S4
Figure BDA0002981104640000023
And
Figure BDA0002981104640000024
the calculation formula is as follows:
Lh＝I-Θ
Figure BDA0002981104640000025
where I is the identity matrix.
Further, in the step S5, the laplace matrix of the hypergraph is processed by the cross validation method
Figure BDA0002981104640000026
And
Figure BDA0002981104640000027
the calculation process is as follows:
ATAΘBTB+λ1ATL1AΘBTB+λ2ATAΘBTL2B＝ATYtrainB
AΘBT+λ1L1AΘBT+λ2AΘBTL2＝Ytrain
(I+λ1L1)AΘBT+λ2AΘBTL2＝Ytrain
A-1(I+λ1L1)AΘ+λ2ΘBTL2(BT)-1＝A-1Ytrain(BT)-1
wherein the content of the first and second substances,
Figure BDA0002981104640000028
is a correlation matrix of known ncRNA-diseases;
Figure BDA0002981104640000029
is a double projection matrix; lambda [ alpha ]1And λ2Regularizing coefficients for two different graphs, each set to 1;
Figure BDA00029811046400000210
and
Figure BDA00029811046400000211
is shown as a drawingThe normalized laplacian matrix is calculated as follows:
Figure BDA00029811046400000212
Figure BDA00029811046400000213
wherein the content of the first and second substances,
Figure BDA00029811046400000214
and
Figure BDA00029811046400000215
is a diagonal matrix of the angles,
Figure BDA00029811046400000216
and
Figure BDA00029811046400000217
advantageous effects
The project utilizes a multi-core fusion method to identify the association relationship between non-coding RNA and diseases. And searching for important features influencing the incidence relation by using an efficient multi-core learning algorithm, evaluating the importance of the core matrix, and reducing the deviation brought by core fusion. A reasonable kernel matrix evaluation method is constructed, weight coefficients are calculated for different kernel matrices, the kernel matrix containing noise can be effectively filtered, useful kernel matrices are reserved to the maximum extent, and a foundation is provided for improving the prediction accuracy of the model. Each kernel matrix represents information of different heterogeneous data, the weight coefficient of each kernel matrix reflects the contribution degree of different information in a prediction model, and key information influencing the ncRNA-disease associated prediction accuracy can be further found. The prediction accuracy of the method is better than that of other methods in the prior art. The method is high in prediction accuracy, simple and efficient, solves the problem that the accuracy of ncRNA-disease association identification is not high in the existing method, and has important significance for promoting non-coding RNA research.
Drawings
FIG. 1 is a flow chart of the computational process of the present invention;
FIG. 2, weight of each core in five data sets;
FIG. 3 compares AUC and AUPR for different kernel functions by 5-fold cross validation of 5 data sets;
FIG. 4 compares AUC and AUPR of different matrix factorization methods by 5-fold cross validation of 5 data sets;
FIG. 5, different rdAnd rncAUC of parameters under 5-fold cross validation;
FIG. 6, different rdAnd rncAUPR with parameters under 5-fold cross validation;
FIG. 7, optimal parameter r calculated over five data setsncAnd rd；
FIG. 8 compares AUC results of prior excellent methods by 5-fold cross validation and leave-one-fold cross validation;
FIG. 9 shows ten new correlations of lung cancer, liver cancer and pancreatic cancer.
Detailed Description
The invention is described in detail below with reference to the attached drawing figures:
as shown in figure 1, the invention realizes the accurate identification of the association relationship between non-coding RNA and diseases, and is greatly helpful for disease treatment of human biomedical research. However, conventional techniques are only applied to one non-coding RNA or one specific disease, and the experimental method is time-consuming and expensive. Based on known non-coding RNAs and disease-related information, many computational tools have been proposed to detect new associations. Since ncRNAs (circRNAs, miRNAs, and lncRNAs) are closely related to various disease progression in humans, development of an efficient computational method is crucial for ncRNA-disease association prediction.
The basic idea of the invention is: fusing a plurality of nuclei of non-coding RNA and a plurality of nuclei of diseases by adopting a central nucleus alignment method, and predicting a new incidence relation by adopting a three-matrix decomposition method of a hypergraph regular term.
The invention mainly comprises the following steps: firstly, obtaining non-coding RNA nuclei and disease nuclei as much as possible, then fusing the non-coding RNA nuclei and the disease nuclei by adopting a central nucleus alignment method, decomposing the fused nuclei into two matrixes by using a singular value decomposition method, and finally obtaining a new incidence relation matrix by using a three-matrix decomposition method of hypergraph regular terms in a cross validation mode. The method comprises the following specific steps:
a method for disease association prediction in a biological association network, comprising the steps of:
s1 construction of non-coding RNA nuclei
Figure BDA0002981104640000031
And nucleus of disease
Figure BDA0002981104640000032
Wherein u and v are the number of nuclei in the non-coding RNA and the disease space;
s2, fusing the non-coding RNA nucleus and the disease nucleus to obtain the optimal nucleus by adopting a central nucleus alignment method
Figure BDA0002981104640000041
And
Figure BDA0002981104640000042
the parity value of the invention can describe the similarity of two kernels; CKA-MKL the relationship between the ideal nuclear matrix and ncRNA nuclei (or disease nuclei) was calculated as follows:
Figure BDA0002981104640000043
Figure BDA0002981104640000044
βp≥0,p＝1,2,…,N
Figure BDA0002981104640000045
wherein, KidealIs an idealThe core is a core of a plurality of cores,
Figure BDA0002981104640000046
and
Figure BDA0002981104640000047
is an ideal inner core of ncRNA and disease constructed by known correlation;
s3, decomposing the fused optimal kernel into two matrixes by adopting a singular value decomposition method, namely
Figure BDA0002981104640000048
And
Figure BDA0002981104640000049
the calculation process is as follows:
Figure BDA00029811046400000410
Figure BDA00029811046400000411
wherein, A and B are low rank approximate matrixes; r isncAnd rdPotential characteristic space dimensions of ncRNA and disease respectively;
s4, three-matrix decomposition method matrix using hypergraph regular term
Figure BDA00029811046400000412
And
Figure BDA00029811046400000413
calculating to obtain a hypergraph Laplacian matrix
Figure BDA00029811046400000414
And
Figure BDA00029811046400000415
the laplace matrix of the hypergraph in the step S4
Figure BDA00029811046400000416
And
Figure BDA00029811046400000417
the calculation formula is as follows:
Lh＝I-Θ
Figure BDA00029811046400000418
where I is the identity matrix.
S5, performing cross validation on the Laplace matrix of the hypergraph
Figure BDA00029811046400000419
And
Figure BDA00029811046400000420
calculating to obtain a new incidence relation matrix, Y*＝AΘBT。
The cross validation method in the step S5 is used for the Laplacian moment of the hypergraph
Figure BDA00029811046400000421
And
Figure BDA00029811046400000422
the matrix calculation process is as follows:
ATAΘBTB+λ1ATL1AΘBTB+λ2ATAΘBTL2B＝ATYtrainB
AΘBT+λ1L1AΘBT+λ2AΘBTL2＝Ytrain
(I+λ1L1)AΘBT+λ2AΘBTL2＝Ytrain
A-1(I+λ1L1)AΘ+λ2ΘBTL2(BT)-1＝A-1Ytrain(BT)-1
wherein the content of the first and second substances,
Figure BDA0002981104640000051
is a correlation matrix of known ncRNA-diseases;
Figure BDA0002981104640000052
is a double projection matrix; lambda [ alpha ]1And λ2Regularizing coefficients for two different graphs, each set to 1;
Figure BDA0002981104640000053
and
Figure BDA0002981104640000054
the laplacian matrix is normalized for the graph as calculated:
Figure BDA0002981104640000055
Figure BDA0002981104640000056
wherein the content of the first and second substances,
Figure BDA0002981104640000057
and
Figure BDA0002981104640000058
in the form of a diagonal matrix,
Figure BDA0002981104640000059
and
Figure BDA00029811046400000510
the invention calculates the new incidence relation matrix through the steps S1-S5, and can obtain the identification accuracy of the new incidence relation through inquiring and verifying in other databases.
The implementation process of the invention comprises the following steps:
according to the calculation method, the invention obtains the optimal r of the D1 data set by using a grid search methodncAnd rd. The present invention uses 100 steps to test for different values from 100 to the maximum. The rest data sets use the same grid searching method, and the optimal parameters r of different data setsncAnd rdAs shown in fig. 7. Meanwhile, fig. 5 and 6 are different from each other in rdAnd rncAUC and aucr under 5-fold cross validation of the model. Here, rnc(horizontal axis) and rdThe (vertical axis) setting ranges from 100 to 1500, step size 100.
The invention counts the performance of multi-core and single-core applications on 5 data sets. Fig. 2 shows the weights for each core in the five data sets. It can be seen that the semantic similarity of diseases is given almost the greatest weight. Non-coding RNAs that function similarly are of greater weight, which means that they have more potent information.
Figure 3 shows the results of 5-fold cross validation (AUC and aucr) on 5 data sets for different kernel functions. It can be seen that the process of the invention (CKA-HGRTMF) gives the best performance (AUC) on D2(0.9775), D3(0.9023), D4(0.8809) and D5 (0.9185). The method (CKA-HGRTMF) of the invention achieves the best AUPR performance on 5 data sets. For a single core, CKA-HGRTMF selects different combinations of cores in two feature spaces and tests are performed using the HGRTMF model. It was found experimentally that both ncRNA and the most weighted nuclei of the disease feature set gave better results than the other methods.
Comparing HGRTMF and other MF based computational models, including three matrix factorization (CMF), graph regularization term matrix factorization (GRMF), Three Matrix Factorization (TMF), NRLMF, and graph regularization term three matrix factorization (GRTMF), the results are shown in fig. 4. The method (CKA-HGRTMF) of the present invention performed the best AUPRs at D1 (AUPR: 0.9173), D2 (AUPR: 0.7712), D3 (AUPR: 0.6224) and D5 (AUPR: 0.5017), and performed the best AUCs at D2 (AUC: 0.9775), D3 (AUC: 0.9023), D4 (AUC: 0.8809) and D5 (AUC: 0.9185), which are superior to other MF-based computational models. The AUPRs of CKA-HGRTMF on 5 datasets were 0.8957, 0.7456, 0.6014, 0.3992 and 0.4250, respectively, and the AUCs were 0.9857, 0.9746, 0.8991, 0.8774 and 0.8991, respectively. The AUCs and AUPRs of CKA-GRTMF at D1, D2 and D5 are all higher than CKA-TMF. The result shows that the addition of the calculation model of the graph regularization term is beneficial to improving the prediction performance.
In order to evaluate the performance of the CKA-GRTMF model, the method is compared with other existing methods. Fig. 8 shows the results of 5-fold cross validation and leave-one cross validation of AUCs. The method of the invention (CKA-GRTMF) achieved the best results in both 5-fold cross validation on D2, D3, D4, D5 and one-leave cross validation on 5 datasets. The calculation method of the invention finds ten new association relations among lung cancer, liver cancer and pancreatic cancer, and the result is shown in figure 9.
In conclusion, the invention solves the problem of predicting the association relationship between non-coding RNA and diseases. Adding a Laplace regularization term of the hypergraph into three-matrix decomposition, and adopting a center kernel alignment method to obviously improve the prediction precision. The calculation process of the invention has the characteristics of simplicity, easy realization and the like, and the hardware equipment and the calculation resources required by calculation are also lower, thus having wide usability. The method is realized by C + + and MATLAB, is applied to a computer with a common 2.5GHz8 core CPU and a 24GB memory, and can complete the prediction tasks of thousands of samples in a short time.

Claims (3)

1. A method for disease association prediction in a biological association network, comprising the steps of:
s1 creating a polynuclear representation of non-coding RNAs
Figure FDA0002981104630000011
And multi-nuclear representation of disease
Figure FDA0002981104630000012
Wherein: u and v are the number of nuclei in the feature space of the non-coding RNA and the disease;
s2, fusing the non-coding RNA multi-core and disease multi-core by adopting a central core alignment calculation method to obtain an optimal core
Figure FDA0002981104630000013
And
Figure FDA0002981104630000014
s3, decomposing the fused optimal kernel into two matrixes by adopting a singular value decomposition calculation method, namely
Figure FDA0002981104630000015
And
Figure FDA0002981104630000016
the calculation process is as follows:
Figure FDA0002981104630000017
Figure FDA0002981104630000018
wherein, A and B are low rank approximate matrixes; r isncAnd rdPotential feature space dimensions for non-coding RNA and disease, respectively;
s4 matrix pair method using hypergraph regular term three-matrix decomposition
Figure FDA0002981104630000019
And
Figure FDA00029811046300000110
calculating to obtain a hypergraph Laplace matrix
Figure FDA00029811046300000111
And
Figure FDA00029811046300000112
s5, drawing the hypergraph by a cross validation methodThe placian matrix
Figure FDA00029811046300000113
And
Figure FDA00029811046300000114
calculating to obtain a new incidence relation matrix, Y*＝AΘBT。
2. The method for disease association prediction in biological association network as claimed in claim 1, wherein said step S4 is executed by using the laplace matrix of hypergraph
Figure FDA00029811046300000115
And
Figure FDA00029811046300000116
the calculation formula is as follows:
Lh＝I-Θ
Figure FDA00029811046300000117
where I is the identity matrix.
3. The method for disease association prediction in biological association network as claimed in claim 1, wherein the step S5 is performed by cross-validation of the laplacian matrix of the hypergraph
Figure FDA00029811046300000118
And
Figure FDA00029811046300000119
the calculation process is as follows:
ATAΘBTB+λ1ATL1AΘBTB+λ2ATAΘBTL2B＝ATYtrainB
AΘBT+λ1L1AΘBT+λ2AΘBTL2＝Ytrain
(I+λ1L1)AΘBT+λ2AΘBTL2＝Ytrain
A-1(I+λ1L1)AΘ+λ2ΘBTL2(BT)-1＝A-1Ytrain(BT)-1
wherein the content of the first and second substances,
Figure FDA0002981104630000021
a correlation matrix of known non-coding RNAs with disease;
Figure FDA0002981104630000022
is a double projection matrix; lambda [ alpha ]1And λ2Regularizing coefficients for two different graphs, each set to 1;
Figure FDA0002981104630000023
and
Figure FDA0002981104630000024
for the graph normalized Laplace matrix, the formula is as follows:
Figure FDA0002981104630000025
Figure FDA0002981104630000026
wherein the content of the first and second substances,
Figure FDA0002981104630000027
and
Figure FDA0002981104630000028
is a diagonal matrix of the angles,
Figure FDA0002981104630000029
and
Figure FDA00029811046300000210
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