A method and system for metabolomics sample normalization based on local similarity

Abstract

The application discloses a metabolomics sample normalization method and system based on local similarity, and the method comprises the following steps: an initialization step, giving a metabolomics data matrix to be normalized and initializing a normalization coefficient of the sample; a projection step, projecting the data matrix into a principal component analysis subspace to obtain a projected 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 projected data matrix, and obtaining the nearest neighbor set of each sample according to the correlation and distance indexes; a sample normalization step, calculating the normalization coefficient of the sample vector to obtain a normalized new data matrix; and an iteration step, iterating the subspace projection step to the sample normalization step until the relative change amount of the normalized data matrix is less than a given threshold. The application retains the local structure of the data, corrects the dilution effect, and makes the sample data more comparable.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of metabolomics data preprocessing, and particularly relates to a metabolomics sample normalization method and system based on local similarity. BACKGROUND

[0002] Metabolomics directly reflects the terminal and phenotypic information of organisms or biological samples, and provides new insights into the effects of diet, drugs and diseases [Idle, J. R.; Gonzalez, F. J. Metabolomics. Cell Metab 2007, 6(5), 348-351.]. In the process of preparing or obtaining metabolomics data, unnecessary systematic biases may be introduced, including technical errors (such as human error, instrument response bias) and biological bias, especially in samples such as cells, sweat, feces, saliva, urine, etc. [Wu, Y.; Li, L. Sample normalization methods in quantitative metabolomics. J Chromatogr A 2016, 1430, 80-95.]. For example, the concentration of urine samples can differ by more than 14 times [Tsuchiya, Y.; Takahashi, Y.; Jindo, T.; Furuhama, K.; Suzuki, K. T. Comprehensive evaluation of canine renal papillary necrosis induced by nefiracetam, an neurotransmission 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, L. P.; Lorenzi, P. L.; Purwaha, P.; Yong, V.; Hawke, D. H.; Weinstein, J. N. Measurement of DNA concentration as a normalization strategy for metabolomic data from adherent cell lines. Anal Chem 2013, 85(20), 9536-9542.], so the biological signal can be masked by this systematic bias. The above biological bias and technical errors cause linear shifts in data from the same batch of samples, such as overall signal reduction caused by experimental injection volume, which are collectively referred to as "dilution effect". Normalization is a key step in data preprocessing, as it can remove various sources of factors, 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-collection normalization and post-collection normalization. Post-collection normalization is a more convenient option, including total peak area normalization (CSN), probability quotient normalization (PQN) [

[0004] Dieterle, F.; Ross, A.; Schlotterbeck, G.; Senn, H. Probabilistic quotient normalization 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 constant, but in fact high-intensity variables have a major impact on the normalization result, so when some metabolites change dramatically, CSN will no longer be applicable. PQN assumes that the intensity of most metabolites is not affected by dramatic changes, so the median of the quotient of each sample and the reference spectrum is selected as the normalization factor, effectively solving the problem of CSN. However, when more than 50% of the metabolites change dramatically, PQN is no longer applicable. MDFC assumes that up-regulated and down-regulated metabolites are not always equal, so the maximum density estimate of the quotient is used instead of the median of the quotient used in PQN as the normalization factor. The above methods are all based on a common assumption that a global reference spectrum is used for the entire dataset, which is not suitable for multi-class datasets, and ignores the heterogeneity of the data distribution, so a more effective dilution effect correction method needs to be developed to restore the heterogeneity of various types of metabonomics data. SUMMARY

[0005] The present application aims to solve the problems in the prior art.

[0006] The technical scheme adopted by the present application to solve its technical problems is to provide a metabolomics sample normalization method based on local similarity, comprising the following steps:

[0007] A parameter initialization step, wherein the metabolomics data matrix to be normalized is given as X=(x ij ), i=1, 2, …, N; j=1, 2, …, M, wherein N is the number of samples; M is the number of variables, and the variable refers to metabolites; the normalization coefficient of the sample is initialized as

[0008] A subspace projection step, wherein the data matrix X is projected into a principal component analysis subspace, the first P components are retained, and the projected data matrix S=(s ij ), i=1, 2, …, N; j=1, 2, …, P is obtained.

[0009] A nearest neighbor set construction step, wherein the correlation between any two samples is calculated using the data matrix X, and the distance between any two samples is calculated using the projected data matrix S, the first K samples are selected according to the correlation and distance indicators respectively, and the union set of the two is taken to obtain the nearest neighbor set of each sample

[0010] A sample normalization step, wherein the normalization coefficient a i of any sample vector x i. is calculated, a new data matrix X is obtained by normalizing the data, and the normalized data a i ·x i· is close to the samples in its nearest neighbor set .

[0011] An algorithm iteration step, wherein the subspace projection step to the sample normalization step is iterated until the relative change of the normalized data matrix is less than a given threshold.

[0012] Preferably, the subspace projection step specifically calculates the PCA subspace mapping data matrix, which is represented as:

[0013] S=(s i· ) := PCA(X)

[0014] wherein s i. represents the score vector of x i· in the PCA model of X, and := represents assignment.

[0015] Preferably, the first P components are retained, specifically the number of principal components retaining 95% of the variance.

[0016] Preferably, the nearest neighbor set constructing step, the nearest neighbor set of each sample is constructed by two k-nearest neighbor sets and The union is:

[0017]

[0018] Wherein, is the sample x i. The K samples with the highest Pearson correlation coefficient with other samples, is the sample s i. The K samples with the shortest Euclidean distance with other samples.

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

[0020] According to the nearest neighbor set, the reference spectrum r i. of the sample x i· is calculated;

[0021] The quotient set between the sample x i· and its reference spectrum r i. is calculated, denoted as:

[0022]

[0023] The quotient set is divided into two subsets, denoted as:

[0024]

[0025] The normalization coefficient of the sample x i. is calculated based on the two subsets, denoted as:

[0026]

[0027] The data matrix is updated according to the normalization coefficient, denoted as:

[0028]

[0029] Preferably, the reference spectrum r i· of the sample x i· is calculated according to the nearest neighbor set, the median spectrum is taken as the reference spectrum, denoted as:

[0030]

[0031] Wherein, median represents taking the median of each variable of 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 value, expressed as:

[0033]

[0034] Wherein, CV t is the coefficient of variation of the variable at the tth iteration, and CV t is the relative change amount; ε is a preset threshold value.

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

[0036] A parameter initialization module, given the metabolomics data matrix to be normalized as X=(x ij ), i=1, 2, …, N; j=1, 2, …, M, wherein N is the number of samples; M is the number of variables, and the variable refers to metabolites; the normalization coefficient of the initialized sample is

[0037] A subspace projection module, projecting the data matrix X into a principal component analysis subspace, retaining the first P components, to obtain the projected data matrix S=(s ij ), i=1, 2, …, N; j=1, 2, …, P;

[0038] A nearest neighbor set construction module, calculating the correlation between any two samples using the data matrix X, and calculating the distance between any two samples using the projected data matrix S, and selecting the first K samples according to the correlation and distance indicators respectively, and taking the union of the two to obtain the nearest neighbor set of each sample

[0039] A sample normalization module, calculating the normalization coefficient α i. of any sample vector x i , to obtain a new data matrix X composed of normalized samples; the normalized data α i ·x i· is close to the samples in its nearest neighbor set .

[0040] An algorithm iteration module, iterating the subspace projection step to the sample normalization step, until the relative change amount of the normalized data matrix is less than a given threshold value.

[0041] The application has the following beneficial effects:

[0042] (1) The application selects reference spectra in the nearest neighbor, improves the accuracy of the normalization coefficient, has good robustness for data sets of different proportion difference metabolites, especially in data with more than 50% metabolite change proportion;

[0043] (2) The application iteratively corrects the dilution effect in the process of maintaining the local structure, better preserves 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) The application is a post-collection normalization method, is suitable for various types of metabolomics data (urine, cells, saliva, etc.), data collected by different platforms (GC-MS, LC-MS, NMR), and has universality, and is particularly suitable for multi-group data.

[0045] The application will be further described in detail below in combination with the drawings and examples, but the application is not limited to the examples. BRIEF DESCRIPTION OF DRAWINGS

[0046] Figure 1 The figure is a method step diagram of the embodiment of the application, including the following steps:

[0047] Figure 2 The figure is an RLA diagram of the data set of the embodiment of the application before and after correction of the dilution effect.

[0048] Figure 3 The figure is the effect of the data set of the embodiment of the application in pls-da models established after correction by different methods;

[0049] Figure 4 The figure is a system structure diagram of the embodiment of the application. DETAILED DESCRIPTION

[0050] The application aims to solve the problem that the existing dilution effect correction method ignores the heterogeneity recovery, proposes a novel sample normalization method based on local similarity, uses local samples as reference spectra (i.e., defines the nearest neighbor set for each sample), 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 dramatic change of metabolites, thereby effectively recovering the heterogeneity of sample distribution and the relationship between metabolites, and laying a more solid foundation for subsequent metabolomics data analysis.

[0051] Referring to Figure 1 The figure is a method step diagram of the embodiment of the application, including the following steps:

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

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

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

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

[0056] S105, an 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 embodiment of the present application is a study on the correlation between saliva and plasma of patients with glucose intolerance, which can be publicly obtained in the metabolomics workbench data repository (www.metabolomicsworkbench.org) with the number ST001905. It contains the saliva metabolic profiles of 31 patients with type Ⅱ diabetes and 30 healthy volunteers.

[0058] Specifically, in S101 of the embodiment of the present application, the given data matrix X=(x ij ), i=1, 2, …, N; j=1, 2, …, M, wherein N is the number of samples; M is the number of variables, and the variable refers 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 accounting for 95% of the variance, which is represented as:

[0060] S=(s i. ) := PCA(X)

[0061] Where s i. is the score vector of x i. in the PCA model of X.

[0062] Specifically, S103 is specifically: the nearest neighbor set of each sample is obtained by taking the union of two k-nearest neighbor sets and

[0063]

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

[0065] Specifically, S104 includes the following steps:

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

[0067]

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

[0069]

[0070] S1043 divides the quotient set into two subsets:

[0071]

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

[0073]

[0074] S1045, Update the sample data vector:

[0075]

[0076] Specifically, in S105, iterations from S102 to S104 are repeated until the relative change in the normalized data matrix is ​​less than a threshold, at which point the iteration terminates, as follows:

[0077]

[0078] In this embodiment, ε = 0.005, CV t The coefficient of variation of the variable at the t-th iteration is expressed as:

[0079]

[0080] The effectiveness and accuracy of the dilution effect correction effect of the embodiments of the present invention were verified by experiments.

[0081] join Figure 2 The image shows the RLA plots of the dataset before and after dilution effect correction in an embodiment of the present invention. First, the relative abundance (RLA) is used to visually display the data before normalization (…).Figure 2 Figure 6 shows the difference of the total sample concentration in a) and the box plot of b) after the normalization of the urine samples. For the relative abundance within group (RLA) plot, the median of each metabolite in each group was removed after log transformation, and the box plot of each sample was plotted to visually show the tightness of the within-group replicates, where the median should be close to zero, and the variation around the median should be small, and there should be no significant variation between the replicates. Figure 2 Figure 6a shows that the concentration difference between samples is large, while the box plot of the normalized data in Figure 6b tends to zero, indicating that there is a large dilution effect in the urine data set, and the present application (LSPN) can effectively eliminate this effect. Figure 2 Figure 2 Figure 6a shows that the concentration difference between samples is large, while the box plot of the normalized data in Figure 6b tends to zero, indicating that there is a large dilution effect in the urine data set, and the present application (LSPN) can effectively eliminate this effect.

[0082] For the classification task, sparse partial least squares discriminant analysis (PLS-DA) model was used for experiment, and the results are shown in Figure 7. Figure 3 Figure 7 shows that all normalization methods improve the within-group clustering and between-group separation to some extent, and the Q2 value of the model based on the normalization data corrected by the present application (LSPN) is relatively high, indicating that more sample information related to diabetes is retained, and the separation of data in different groups is improved. Figure 3 Figure 8 shows the PLS-DA results after adding noise interference, which shows that CSN, LSPN and PQN are basically not affected by noise, while MDFC fluctuates with the influence of noise.

[0083] From the above verification, it can be seen that the metabolic normalization method and system based on local similarity according to the present application perform well in removing dilution effect and retaining data heterogeneity analysis and classification tasks.

[0084] Figure 9 shows the system structure diagram of the embodiment of the present application, which comprises: Figure 4 Figure 9 shows the system structure diagram of the embodiment of the present application, which comprises:

[0085] The parameter initialization module 401 is given the metabolic data matrix to be normalized X=(x ij ), i=1, 2, …, N; j=1, 2, …, M, wherein N is the number of samples; M is the number of variables, and the variable refers to metabolites; the normalization coefficient of the sample is initialized

[0086] The 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 calculates the correlation between any two samples using the data matrix X and the distance between any two samples using the projected data matrix S. It then selects the top K samples based on both the correlation and distance indices, and takes the union of the two sets to obtain the nearest neighbor set for each sample.

[0088] Sample normalization module 404 calculates the normalization of any sample vector x. i. normalization coefficient α i This yields a new data matrix X, which is normalized; the normalized data α i ·x i· Its nearest neighbor set The samples are close together;

[0089] 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] As can be seen, the present invention effectively preserves the local structure of the data, while effectively correcting the dilution effect. After normalization, the data heterogeneity is well restored, thereby improving the reliability of downstream data analysis.

[0091] The above are merely 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 within the protection scope of the present invention.

Claims

1. A method for local similarity-based normalization of metabolomics samples, characterized in that, The method comprises the following steps: A parameter initialization step, given a metabolomics data matrix to be normalized as wherein, is the number of samples; is the number of variables, a variable refers to a metabolite; initializing the normalization coefficients of the samples ; said samples include saliva metabolomic profiles of diabetic patients and healthy volunteers; A subspace projection step projects the data matrix into a principal component analysis subspace, retaining the first principal components, to obtain a projected data matrix ; Nearest neighbor set construction step, utilizing data matrix Correlation between any two samples is calculated, and projection data matrix is utilized Distance between any two samples is calculated, and the first K samples are selected according to correlation and distance indexes respectively, and the union of the two is the nearest neighbor set of each sample ; a sample normalization step, calculating a normalization coefficient for any sample vector of the sample , obtaining a new data matrix of normalized composition ; normalized data and its nearest neighbors in the sample The algorithm iteration step, the subspace projection step to the sample normalization step, until the relative change of the normalized data matrix is less than a given threshold; so that the normalized sample retains more sample information related to diabetes in the classification task, and the separation degree of different group data is improved; The sample normalization step comprises the following steps: Calculating samples from nearest neighbor set Reference spectra of samples ; Computing the sample The quotient between its reference spectrum is denoted by: ； Commercial Collection Divided into two subsets, represented as: ； calculating the sample based on the two subsets the normalization coefficient is ； The data matrix is updated according to the normalization coefficient, and is expressed as: ； The calculation of samples based on nearest neighbors Reference spectrum Using the median spectrum as the reference spectrum, it is expressed as: ； wherein denotes taking the median value for each variable of the nearest neighbor set.

2. The local similarity based metabolomics sample normalization method of claim 1, wherein, The subspace projection step is specifically to calculate the PCA subspace mapping data matrix, and is expressed as: ； wherein represents the score vector of the PCA model of represents an assignment.​ 3. The local similarity based metabolomics sample normalization method of claim 1, wherein, The number of components, specifically the number of principal components that retain 95% of the variance. The number of components, specifically the number of principal components that retain 95% of the variance.

4. The local similarity based metabolomics sample normalization method of claim 1, wherein, The nearest neighbor set construction step, the nearest neighbor set of each sample is formed by two k-nearest neighbor sets and The union is obtained: ； wherein, is the sample is the sample is the sample is the sample 5. The local similarity based metabolomics sample normalization method of claim 1, wherein, In the algorithm iteration step, the relative change of the normalized data matrix is less than a given threshold, and is expressed as: ； ； wherein, represents the coefficient of variation of the variable at the tth iteration, and is the relative change amount; is a preset threshold value.

6. A local similarity based metabolomics sample normalization system, comprising: It comprises: a parameter initialization module, given a metabolomics data matrix to be normalized as wherein, is the number of samples; is the number of variables, where a variable refers to a metabolite; initializing the normalization coefficients of the samples ; the samples include saliva metabolomic profiles of diabetic patients and healthy volunteers; a subspace projection module that projects the data matrix into a principal component analysis subspace, retaining the first principal components, resulting in a projected data matrix ; Nearest neighbor set construction module, utilizing data matrix Correlation between any two samples is calculated, and projection data matrix is utilized Distance between any two samples is calculated, and the first K samples are selected according to correlation and distance indexes respectively, and the union of the two is the nearest neighbor set of each sample ; a sample normalization module, which calculates a normalization coefficient for any sample vector , resulting in a new data matrix of normalized components ; the normalized data is close to the samples in its nearest neighbor set ​​ The algorithm iteration module, the subspace projection step to the sample normalization step, until the relative change of the normalized data matrix is less than a given threshold; so that the normalized sample retains more sample information related to diabetes in the classification task, and the separation degree of different group data is improved; The sample normalization module comprises the following steps: Calculating samples from nearest neighbor set Reference spectra ; Computing the sample The quotient between its reference spectrum is denoted by: ； Commercial Collection Divided into two subsets, represented as: ； calculating the sample based on the two subsets the normalization coefficient is: ； The data matrix is updated according to the normalization coefficient, and is expressed as: ； The reference spectrum is calculated from the nearest neighbor set of samples with the median spectrum as reference spectrum, denoted as: ； wherein denotes taking the median value for each variable of the nearest neighbor set.

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