Metabonomics sample normalization method and system based on local similarity

Abstract

The invention discloses a metabonomics sample normalization method and system based on local similarity, and the method comprises the steps: an initialization step: giving a to-be-normalized metabonomics data matrix, and initializing the normalization coefficient of a sample; a projection step: projecting the data matrix into the principal component analysis subspace to obtain a projection data matrix; a nearest neighbor set construction step: calculating the correlation between any two samples by using the data matrix, calculating the distance between any two samples by using the projection data matrix, and obtaining the nearest neighbor set of each sample according to the correlation and the distance index; a sample normalization step: calculating a normalization coefficient of the sample vector to obtain a new data matrix formed by normalization; and an iteration step: iterating the subspace projection step to the sample normalization step until the relative variation of the normalized data matrix is smaller than a given threshold. According to the method, the local structure of the data is reserved, and meanwhile, the dilution effect is corrected, so that the sample data has better comparability.

Description

Technical Field

[0001] The present invention relates to the field of metabolomics data preprocessing, and in particular to a metabolomics sample normalization method and system based on local similarity. Background Art

[0002] Metabolomics directly reflects the terminal and phenotypic information of an organism or biological sample, and provides new insights into the effects of diet, drugs and diseases [Idle, JR; Gonzalez, FJ Metabolomics. Cell Metab 2007, 6 (5), 348-351.]. In the process of preparing or acquiring metabolomics data, unnecessary systematic biases may be introduced, including technical errors (such as human errors, instrument response bias) and biological biases, especially in samples such as cells, sweat, feces, saliva, and urine [Wu, Y.; Li, L. Sample normalization methods in quantitative metabolomics. J Chromatogr A 2016, 1430, 80-95.]. For example, the concentration of urine samples may differ by more than 14 times [Tsuchiya, Y.; Takahashi, Y.; Jindo, T.; Furuhama, K.; Suzuki, KT Comprehensive evaluation of canine renal papillary necrosis induced by nefiracetam, aneurotransmission enhancer. Eur J Pharmacol 2003, 475(1-3), 119-128.], and it is difficult to obtain accurate measurements of cell numbers for adherent cells [Silva, LP; Lorenzi, PL; Purwaha, P.; Yong, V.; Hawke, DH; Weinstein, JN Measurement of DNA concentration as a normalization strategy for metabolomic data from adherent cell lines. Anal Chem 2013, 85(20), 9536-9542.], so biological signals may be obscured by such systematic biases. The above biological deviations and technical errors cause linear shifts in the data of the same batch of samples, such as the overall signal drop caused by the experimental injection volume, which are collectively referred to as the "dilution effect". Normalization is a key step in data preprocessing because it can remove the above factors from various sources, ensure comparability between samples, and improve the reliability of metabolomics analysis.

[0003] A variety of sample normalization methods have been proposed, which can be divided into pre-acquisition normalization and post-acquisition normalization. Among them, post-acquisition normalization is a more convenient choice, including total peak area normalization (CSN), probability quotient normalization (PQN) [

[0004] Dieterle,F.;Ross,A.;Schlotterbeck,G.;Senn,H.Probabilistic quotientnormalization as robust method to account for dilution of complex biological mixtures.Application in 1H NMR metabonomics.Anal Chem 2006,78(13),4281-4290.], mPQN [An, Y.; Liu, S.; Hao, F.; Wang, Y.; Tang, H. Development and validation of an improved probabilistic quotient normalization method for LC / MS-and NMR-based metabonomic analysis. Chinese Chemical Letters 2020,31(7),1827-1830.], Maximum density fold change normalization (MDFC) [Yu, H.; Huan, T. MAFFIN: metabolomics sample normalization using maximal density fold change with high-quality metabolic features and corrected signal intensities.Bioinformatics 2022, 38(13), 3429-3437.], etc., among which PQN is the most commonly used. Existing normalization methods all make specific assumptions about the data. CSN assumes that the total signal intensity of each sample spectrum remains unchanged, but in fact high-intensity variables have a major impact on the normalization results, so when some metabolites change drastically, CSN will no longer be applicable. PQN assumes that the intensity of most metabolites is not affected by drastic changes, so the median of the quotient of each sample and the reference spectrum is selected as the normalization factor, which effectively solves the problem of CSN. However, when more than 50% of the metabolites change drastically, PQN is no longer applicable. MDFC assumes that upregulated and downregulated metabolites are not always equal, so the maximum density estimate of the quotient is used as the normalization factor instead of the median of the quotient used in PQN. The above methods are all based on a common assumption, that is, using a global reference spectrum for the entire data set, which is not applicable to multi-category data sets and ignores the heterogeneity of data distribution. Therefore, it is necessary to develop a more effective dilution effect correction method that is suitable for heterogeneity recovery of various types of metabolomics data. Summary of the invention

[0005] The object of the present invention is to solve the problems in the prior art.

[0006] The technical solution adopted by the present invention to solve the technical problem is: to provide a metabolomics sample normalization method based on local similarity, comprising the following steps:

[0007] In the parameter initialization step, the metabolomics data matrix to be normalized is given as X = (x ij ), i = 1, 2, ..., N; j = 1, 2, ..., M, where N is the number of samples; M is the number of variables, where variables refer to metabolites; the normalization coefficient of the initialized sample

[0008] Subspace projection step, project the data matrix X into the principal component analysis subspace, retain the first P components, and obtain the projected data matrix S = (s ij ), i=1,2,…,N; j=1,2,…,P;

[0009] In the step of constructing the nearest neighbor set, the data matrix X is used to calculate the correlation between any two samples, and the projection data matrix S is used to calculate the distance between any two samples. The first K samples are selected according to the correlation and distance indicators respectively, and the union of the two is taken to obtain the nearest neighbor set of each sample.

[0010] Sample normalization step, calculate any sample vector x i. The normalization coefficient α i , get the normalized new data matrix X; the normalized data α i ·x i· Its nearest neighbor The samples in are close;

[0011] The algorithm iterates from the subspace projection step to the sample normalization step until the relative change of the normalized data matrix is ​​less than a given threshold.

[0012] Preferably, the subspace projection step is specifically to calculate the data matrix of the PCA subspace mapping, which is expressed as:

[0013] S=(s i· )∶=PCA(X)

[0014] Among them, s i. In the PCA model of X, i· The score vector of , ∶= represents assignment.

[0015] Preferably, retaining the first P components specifically refers to retaining the number of principal components that retain 95% of the variance.

[0016] Preferably, in the step of constructing the nearest neighbor set, the nearest neighbor set of each sample consists of two k nearest neighbor sets and Find the union and we get:

[0017]

[0018] in, is the sample x i. The K most correlated samples are obtained by calculating the Pearson correlation coefficient with other samples. is a sample i. The K samples closest to each other are obtained by calculating the Euclidean distance with other samples.

[0019] Preferably, the sample normalization step comprises the following steps:

[0020] Calculate sample x based on the nearest neighbor set i. The reference spectrum r i· ;

[0021] Calculate sample x i· With its reference spectrum i. The quotient between is expressed as:

[0022]

[0023] The business group Divided into two subsets, represented as:

[0024]

[0025] Calculate the sample x based on two subsets i. The normalization coefficient is:

[0026]

[0027] Update the data matrix according to the normalization coefficient, expressed as:

[0028]

[0029] Preferably, the sample x is calculated according to the nearest neighbor set i· The reference spectrum r i· , taking the median spectrum as the reference spectrum, it is expressed as:

[0030]

[0031] Among them, median means taking the median value of each variable in the nearest neighbor set.

[0032] Preferably, in the algorithm iteration step, the relative change amount of the normalized data matrix is ​​less than a given threshold, which is expressed as:

[0033]

[0034] Among them, CV t Represents the coefficient of variation of the variable at the tth iteration, expressed as CV t As the relative change; ε is the preset threshold.

[0035] The present invention also provides a metabolomics sample normalization system based on local similarity, comprising:

[0036] The parameter initialization module is given by the metabolomics data matrix to be normalized as X = (x ij ), i = 1, 2, ..., N; j = 1, 2, ..., M, where N is the number of samples; M is the number of variables, where variables refer to metabolites; the normalization coefficient of the initialized sample

[0037] The subspace projection module projects the data matrix X into the principal component analysis subspace, retains the first P components, and obtains the projected data matrix S = (s ij ), i=1,2,…,N; j=1,2,…,P;

[0038] The nearest neighbor set construction module uses the data matrix X to calculate the correlation between any two samples, and uses the projection data matrix S to calculate the distance between any two samples. The first K samples are selected according to the correlation and distance indicators respectively, and the union of the two is taken to obtain the nearest neighbor set of each sample

[0039] Sample normalization module, calculates any sample vector x i. The normalization coefficient α i , get the normalized new data matrix X; the normalized data α i ·x i· Its nearest neighbor The samples in are close;

[0040] The algorithm iteration module iterates from the subspace projection step to the sample normalization step until the relative change of the normalized data matrix is ​​less than a given threshold.

[0041] The present invention has the following beneficial effects:

[0042] (1) The present invention improves the accuracy of the normalization coefficient by selecting the reference spectrum among the nearest neighbors, and has good robustness for data sets of metabolites with different proportions, especially in data with a metabolite change ratio of more than 50%;

[0043] (2) The present invention iteratively corrects the dilution effect while maintaining the local structure, better retains the heterogeneous distribution of data and the relationship between metabolite variables, and obtains more accurate classification results and identification of potential biomarkers in downstream analysis;

[0044] (3) As a post-collection normalization method, the present invention is applicable to various types of metabolomics data (urine, cells, saliva, etc.) and data collected by different platforms (GC-MS, LC-MS, NMR). It is universal and particularly suitable for multi-group data.

[0045] The present invention is further described in detail below in conjunction with the accompanying drawings and embodiments, but the present invention is not limited to the embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 A method step diagram of an embodiment of the present invention;

[0047] Figure 2 It is the RLA diagram of the data set before and after the dilution effect correction according to the embodiment of the present invention.

[0048] Figure 3 It is the effect of the data set of the embodiment of the present invention in the pls-da model established after correction by different methods;

[0049] Figure 4 4 is a system structure diagram of an embodiment of the present invention. DETAILED DESCRIPTION

[0050] The purpose of the present invention is to solve the problem of ignoring heterogeneity recovery in existing dilution effect correction methods, and propose a novel sample normalization method based on local similarity, which uses local samples as reference spectra (i.e., defines a nearest neighbor set for each sample), and iteratively approaches the median spectrum of the nearest neighbor sample set while maintaining the local data structure, so that the reference spectrum is less affected by the drastic changes of metabolites, thereby effectively restoring the heterogeneity of sample distribution and the relationship between metabolites, laying a more solid foundation for subsequent metabolomics data analysis.

[0051] See also Figure 1 FIG. 1 is a diagram showing steps of a method according to an embodiment of the present invention, comprising the following steps:

[0052] S101, parameter initialization step, given the metabolomics data matrix X to be normalized, initialize the normalization coefficient of the sample;

[0053] S102, a subspace projection step, projects the data matrix X into the principal component analysis subspace, retains the first P components, and obtains the projected data matrix S;

[0054] S103, the nearest neighbor set construction step, using the data matrix X to calculate the correlation between any two samples, and using the projection data matrix S to calculate the distance between any two samples, respectively selecting the first K samples according to the correlation and distance indicators, and taking the union of the two to obtain the nearest neighbor set of each sample;

[0055] S104, sample normalization step, calculating the normalization coefficient of any sample vector to obtain a normalized new data matrix X; the normalized data is close to the samples in its nearest neighbor set;

[0056] S105, algorithm iteration step, iterating the subspace projection step to the sample normalization step until the relative change of the normalized data matrix is ​​less than a given threshold.

[0057] The use case of the present invention is a study on the correlation between saliva and plasma in patients with glucose intolerance, which is publicly available in the Metabolomics Workbench Data Repository (www.metabolomicsworkbench.org) with the number ST001905. It contains the saliva metabolic profiles of 31 patients with type 2 diabetes and 30 healthy volunteers.

[0058] Specifically, in S101 of the embodiment of the present invention, the given data matrix X=(x ij ), i = 1, 2, ..., N; j = 1, 2, ..., M, where N is the number of samples; M is the number of variables, where variables refer to metabolites; the data matrix X contains 61 samples and 143 variables, and each sample is represented by a vector x i. =(x ij ),j=1,2,…,M.

[0059] Specifically, S102 calculates the data matrix of the PCA subspace mapping and retains the number of principal components of 95% variance, which is expressed as:

[0060] S=(s i. )∶=PCA(X)

[0061] Among them, s i. is the PCA model of X i. The score vector of .

[0062] Specifically, S103 is as follows: the nearest neighbor set of each sample consists of two k nearest neighbor sets and Find the union and we get:

[0063]

[0064] in, is the sample x i.The most relevant K samples are obtained by calculating the Pearson correlation coefficient with other samples. is a sample i. The K samples with the closest distance are obtained by calculating the Euclidean distance with other samples. In this embodiment, K=60%.

[0065] Specifically, S104 includes the following steps:

[0066] S1041, the specific reference spectrum of each sample in each round of iteration is the median of each variable in the nearest neighbor set to obtain the corresponding spectrum (median spectrum):

[0067]

[0068] S1042, calculate each sample x i With its reference spectrum i The business set between:

[0069]

[0070] S1043, divide the quotient set into two subsets:

[0071]

[0072] S1044, the normalization coefficient of this round of samples is:

[0073]

[0074] S1045, update the data vector of the sample:

[0075]

[0076] Specifically, in S105, S102 to S104 are iterated repeatedly until the relative change of the normalized data matrix is ​​less than a threshold value, and then the iteration is terminated, which is expressed as:

[0077]

[0078] In this embodiment, ε=0.005, CV t represents the coefficient of variation of the variable at the tth iteration, expressed as:

[0079]

[0080] The effectiveness and accuracy of the dilution effect correction effect of the embodiment of the present invention are verified through experiments.

[0081] join Figure 2 As shown in FIG. 1 , the RLA diagram of the data set before and after the dilution effect correction of the embodiment of the present invention is shown. First, relative abundance (RLA) is used to intuitively display the normalization before ( Figure 2 a) and after ( Figure 2 b) Differences in overall sample concentrations. For the relative abundance (RLA) graph within the group, after logarithmic transformation, the median of each metabolite in each group was removed, and a box plot of each sample was drawn to visually display the tightness of the repetition within the group. The median should be close to zero, with small changes near the median, and no significant changes between repeated samples. Figure 2 The a in the figure shows that the concentrations of the samples vary greatly, while the box plot of the normalized data ( Figure 2 b) in FIG. 1 tends to zero, which indicates that there are a large number of dilution-like effects in the urine data set, and the present invention (LSPN) can effectively eliminate this effect.

[0082] For the classification task, the sparse partial least squares discriminant analysis (PLS-DA) model was used for experiments, and the results are shown in Figure 3 As shown, all normalization methods improve the intra-group aggregation and inter-group separation to a certain extent, among which the model Q2 value of the normalized data corrected based on the present invention (LSPN) is relatively high, indicating that more sample information related to diabetes is retained and the separation of data from different groups is improved. Figure 3 Figure f shows the PLS-DA results after adding noise interference, indicating that CSN, LSPN and PQN are basically unaffected by noise, while MDFC fluctuates with the influence of noise.

[0083] It can be seen from the above verification that the metabolomics sample normalization method and system based on local similarity described in the present invention perform well in removing dilution effect and retaining data heterogeneity analysis and classification tasks.

[0084] join Figure 4 FIG. 1 is a system structure diagram of an embodiment of the present invention, including:

[0085] Parameter initialization module 401, given the metabolomics data matrix to be normalized as X = (x ij ), i = 1, 2, ..., N; j = 1, 2, ..., M, where N is the number of samples; M is the number of variables, where variables refer to metabolites; the normalization coefficient of the initialized sample

[0086] Subspace projection module 402 projects the data matrix X into the principal component analysis subspace, retains the first P components, and obtains the projected data matrix S = (s ij ), i=1,2,…,N; j=1,2,…,P;

[0087] The nearest neighbor set construction module 403 uses the data matrix X to calculate the correlation between any two samples, and uses the projection data matrix S to calculate the distance between any two samples. The first K samples are selected according to the correlation and distance indicators respectively, and the union of the two is taken to obtain the nearest neighbor set of each sample.

[0088] Sample normalization module 404 calculates any sample vector x i. The normalization coefficient α i , get the normalized new data matrix X; the normalized data α i ·x i· Its nearest neighbor The samples in are close;

[0089] The algorithm iteration module 405 iterates from the subspace projection step to the sample normalization step until the relative change of the normalized data matrix is ​​less than a given threshold.

[0090] It can be seen that the present invention effectively retains the local structure of the data and effectively corrects the dilution effect. The normalized data better restores the heterogeneity of the data, thereby improving the reliability of downstream data analysis.

[0091] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A metabolomics sample normalization method based on local similarity, characterized in that: The steps include: In the parameter initialization step, the metabolomics data matrix to be normalized is given as X = (x ij ), i = 1, 2, ..., N; j = 1, 2, ..., M, where N is the number of samples; M is the number of variables, where variables refer to metabolites; the normalization coefficient of the initialized sample Subspace projection step, project the data matrix X into the principal component analysis subspace, retain the first P components, and obtain the projected data matrix S = (s ij ), i=1,2,…,N; j=1,2,…,P; In the step of constructing the nearest neighbor set, the data matrix X is used to calculate the correlation between any two samples, and the projection data matrix S is used to calculate the distance between any two samples. The first K samples are selected according to the correlation and distance indicators respectively, and the union of the two is taken to obtain the nearest neighbor set of each sample. Sample normalization step, calculate any sample vector x i. The normalization coefficient α i , get the normalized new data matrix x; the normalized data α i ·x i· Its nearest neighbor The samples in are close; The algorithm iterates from the subspace projection step to the sample normalization step until the relative change of the normalized data matrix is ​​less than a given threshold.

2. The method for normalizing metabolomics samples based on local similarity according to claim 1, characterized in that: The subspace projection step is specifically to calculate the data matrix of the PCA subspace mapping, which is expressed as: S=(s i· )∶=PCA(X) Among them, s i. In the PCA model of X, i. The score vector of , ∶= represents assignment.

3. The method for normalizing metabolomics samples based on local similarity according to claim 1, characterized in that: The retaining of the first P components specifically refers to the number of principal components retaining 95% of the variance.

4. The method for normalizing metabolomics samples based on local similarity according to claim 1, characterized in that: In the nearest neighbor set construction step, the nearest neighbor set of each sample consists of two k nearest neighbor sets and Find the union and we get: in, is the sample x i. The K most correlated samples are obtained by calculating the Pearson correlation coefficient with other samples. is a sample i. The K samples closest to each other are obtained by calculating the Euclidean distance with other samples.

5. The method for normalizing metabolomics samples based on local similarity according to claim 1, characterized in that: The sample normalization step comprises the following steps: Calculate sample x based on the nearest neighbor set i. The reference spectrum r i· ; Calculate sample x i· With its reference spectrum i. The quotient between is expressed as: The business group Divided into two subsets, represented as: Calculate the sample x based on two subsets i. The normalization coefficient is: Update the data matrix according to the normalization coefficient, expressed as:

6. The method for normalizing metabolomics samples based on local similarity according to claim 1, characterized in that: The sample x is calculated according to the nearest neighbor set i. The reference spectrum r i· , taking the median spectrum as the reference spectrum, it is expressed as: Among them, median means taking the median value of each variable in the nearest neighbor set.

7. The method for normalizing metabolomics samples based on local similarity according to claim 1, characterized in that: In the algorithm iteration step, the relative change of the normalized data matrix is ​​less than a given threshold, which is expressed as: Among them, CV t Represents the coefficient of variation of the variable at the tth iteration, expressed as CV t As the relative change; ε is the preset threshold.

8. A metabolomics sample normalization system based on local similarity, characterized in that: include: The parameter initialization module is given by the metabolomics data matrix to be normalized as X = (x ij ), i = 1, 2, ..., N; j = 1, 2, ..., M, where N is the number of samples; M is the number of variables, where variables refer to metabolites; the normalization coefficient of the initialized sample The subspace projection module projects the data matrix X into the principal component analysis subspace, retains the first P components, and obtains the projected data matrix S = (s ij ), i=1,2,…,N; j=1,2,…,P; The nearest neighbor set construction module uses the data matrix X to calculate the correlation between any two samples, and uses the projection data matrix S to calculate the distance between any two samples. The first K samples are selected according to the correlation and distance indicators respectively, and the union of the two is taken to obtain the nearest neighbor set of each sample Sample normalization module, calculates any sample vector x i· The normalization coefficient α i , get the normalized new data matrix X; the normalized data α i ·x i· Its nearest neighbor The samples in are close; The algorithm iteration module iterates from the subspace projection step to the sample normalization step until the relative change of the normalized data matrix is ​​less than a given threshold.

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