JP2021009540A - Data analysis device and method - Google Patents

Abstract

To enable various data analyses while considering orders among statistic samples.SOLUTION: A data analysis device (5) performs a multivariate analysis of a plurality of statistic samples about a plurality of data items. The data analysis device includes a storage part (52) and a control part (51). The storage part 52 records statistic data (X) for managing a plurality of data items in each sample, and order information (D) showing orders among the plurality of statistic samples. The control part performs arithmetic processing based on the statistic data and the order information. The control part calculates a first vector (wx) corresponding to an explanatory variable and a second vector (wy) corresponding to an auxiliary variable so as to optimize covariance between the explanatory variable (t) in a main component analysis of the statistic data and the auxiliary variable (s) undergoing setting of a constraint condition following the order information (S12), and calculates a score corresponding to the plurality of statistic samples on the basis of at least one of the first and second vectors (S13).SELECTED DRAWING: Figure 9

Description

The present invention relates to a data analysis device, method and program for performing data analysis by a statistical method.

Conventionally, for example, in metabolomics, principal component analysis (PCA: Principal Component Analysis) and partial least squares regression (PLS: Partial Least Squares) are often used as multivariate analysis methods for analyzing data of a large number of metabolites. (Refer to Non-Patent Document 1 and the like).

Patent Document 1 discloses a method called kernel PLS-ROG, which introduces the concept of the kernel method into PLS-ROG (Rank Order of Groups) to which PLS is applied. According to the kernel PLS-ROG, integrated analysis of various statistical data can be performed while reflecting the order of the groups formed by the statistical samples in the score, and various data analysis can be performed while considering the order of the groups.

International Publication No. 2017/090566

Hiroyuki Yamamoto, et al., "Dimensionality reduction for metabolome data using PCA, PLS, OPLS, and RFDA with differential penalties to latent variables", Chemom. Intell. Lab. Syst., 98 (2009) 136-142. Yasumune Nakayama, et al., "Novel Strategy for Non-Targeted Isotope-Assisted Metabolomics by Means of Metabolic Turnover and Multivariate Analysis" Metabolites 2014, 4 (3), 722-739 Pongsuwan W, et al., "Prediction of Japanese green tea ranking by gas chromatography / mass spectrometry-based hydrophilic metabolite fingerprinting." J Agric Food Chem. 2007 Jan 24; 55 (2): 231-6.

PLS is a type of supervised dimensionality reduction method, while PCA is an unsupervised method. The inventor of the present application has conducted extensive research on a method that enables various data analysis such as a loading hypothesis test while reflecting the order between samples in a score in an analysis method such as PCA.

An object of the present invention is to provide a data analysis device and method that enable various data analysis while considering the order between statistical samples.

The data analysis device according to the present invention is a device that performs multivariate analysis on a plurality of data items on a plurality of statistical samples. The data analysis device includes a storage unit and a control unit. The storage unit records statistical data for managing a plurality of data items for each statistical sample, and order information indicating the order between the plurality of statistical samples. The control unit performs predetermined arithmetic processing based on statistical data and order information. The control unit uses the first vector corresponding to the explanatory variable to optimize the covariance between the explanatory variable in the principal component analysis of the statistical data and the auxiliary variable for which the constraint condition according to the order information is set. A second vector corresponding to the auxiliary variable is calculated, and a score for a plurality of statistical samples is calculated based on at least one of the first vector and the second vector.

The data analysis method according to the present invention is a method in which a computer performs multivariate analysis on a plurality of data items on a plurality of statistical samples. In the storage unit 52 of the computer, statistical data for managing a plurality of data items for each statistical sample and order information indicating the order among the plurality of statistical samples are recorded. In this method, the first method corresponds to the explanatory variables so that the computer optimizes the covariance between the explanatory variables in the principal component analysis of the statistical data and the auxiliary variables for which the constraints according to the order information are set. A step of calculating a vector and a second vector corresponding to an auxiliary variable, and a step of calculating a score for a plurality of statistical samples based on at least one of the first vector and the second vector. Including.

According to the data analysis apparatus and method according to the present invention, statistics are obtained by applying a theory that optimizes the covariance between the explanatory variables in the principal component analysis of statistical data and the auxiliary variables for which constraint conditions according to ordinal information are set. It is possible to analyze various data while considering the order between samples.

Diagram for explaining the theory of OS-PCA The figure which shows the analysis result of PCA in the case 1 of data analysis. The figure which shows the analysis result of OS-PCA in the case 1 of data analysis. Chart showing an example of hypothesis testing of OS-PCA loading in case 1 of data analysis The figure which shows the analysis result of PCA in the case 2 of data analysis. The figure which shows the analysis result of OS-PCA in the case 2 of data analysis. Block diagram showing the configuration of the data analysis apparatus according to the first embodiment Flowchart showing data analysis processing by data analysis device Flowchart showing OS-PCA arithmetic processing in data analysis processing

Hereinafter, embodiments of the data analysis apparatus, method, and program according to the present invention will be described with reference to the accompanying drawings. In each of the following embodiments, the same reference numerals are given to the same components.

(Embodiment 1)
1. 1. Outline An outline of statistical analysis by the data analysis method according to the first embodiment of the present invention will be described. The application example of this data analysis method to metabolomics will be described below.

Metabolomics is a research field that comprehensively analyzes low-molecular-weight metabolites in vivo. In metabolomics, for example, biological samples (samples) such as animal tissues, microbial cells, human blood and urine are measured by various analyzers, and the concentration of biotransforms contained in the samples is analyzed. The metabolome data in which the measured concentrations of various biotransforms and the like are recorded is represented in the form of the data matrix X of n rows and q columns as shown below.

Here, n is the number of samples, and q is the number of measured metabolites (that is, the number of data items). The above equation (1) can record, for example, the measured values of q metabolites measured in the sample corresponding to the line number per line as metabolome data. Various calculated values may be recorded instead of the measured values (eg, isotopomer ratio, etc.).

The analysis of metabolome data is performed by the following procedure using principal component analysis. That is, first, the data distribution of the sample is visualized in the score obtained by the principal component analysis of the metabolome data, and the principal component related to the desired phenotype, group information, time series information, etc. is found. After that, by selecting significant metabolites based on the loading hypothesis test corresponding to the main component, the relationship between the selected metabolite group and the metabolic pathway can be investigated.

In the metabolome data analysis as described above, in addition to the metabolome data, additional information regarding the relationship between samples or groups may be given in advance. While conventional typical multivariate analysis is useful for analyzing metabolome data, such additional information is not considered in the analysis. Therefore, in a typical PCA or the like, additional information may not be reflected in the score used for visualizing the sample, and it may be difficult to proceed with the analysis. As an analysis method incorporating additional information in order to avoid such a problem, "smoothing PCA" has been previously proposed by the present inventors (Non-Patent Document 1).

Smoothed PCA is useful for analyzing metabolome data of samples taken over time. For example, in research on culturing and fermentation of microorganisms, metabolome data is analyzed in order to observe changes in the concentrations of various substances over time. According to the research by the present inventors, the effectiveness of smoothing PCA was applied to the metabolome data for the purpose of visualizing the fermentation process of yeast (Non-Patent Document 1). Here, the present inventor focuses on the problem that smoothed PCA cannot theoretically explain the statistical meaning of loading, and it is difficult to select biotransforms from loading on a statistical basis. did.

Therefore, the present inventor repeated diligent studies on the above problems, and obtained a calculation result equivalent to that of smoothed PCA, and made it possible to select a statistically significant metabolite by a loading hypothesis test. We devised one method of analysis, "Orthogonal Smoothed PCA (OS-PCA)".

2. 2. Theory The theory of OS-PCA according to this embodiment will be described below.

2-1. Smoothed PCA In various analysis methods such as OS-PCA and smoothed PCA, the statistical data to be analyzed is represented by, for example, the data matrix X of the equation (1). Hereinafter, the data in the p-th column in the data matrix X will be referred to as “x _p ”. The data matrix X is used, for example, by scaling the data x _p (p = 1 to q) of each column to an average of "0" and a variance of "1" between n components (that is, between samples).

For the score of the principal component analysis for the data matrix X, the explanatory variable t of the n-dimensional vector as in the following equation (2) can be used.
t = Xw _x (2)

In the above equation (2), the weight vector w _x is a q-dimensional vector and has q components. According to the above equation (2), each component of the weight vector w _x indicates the weight of the explanatory variable t for each data item in the data matrix X. The n values of the explanatory variables t indicate the scores of the corresponding samples.

In addition to the various variables described above, the OS-PCA and the smoothing PCA commonly use the smoothing parameter κ and the dummy matrix D, which will be described later. First, the smoothed PCA is formulated as the following equations (31) to (32) (Non-Patent Document 1).

In the above equations (31) to (32), "'" represents the transpose of a matrix or the like (the same applies hereinafter). The second term on the left side of the above equation (32) constitutes a smoothing term based on the smoothing parameter κ.

According to the above equations (31) to (32), the smoothed PCA results in a generalized eigenvalue problem as in the following equation (33). Note that I is an identity matrix and λ is an eigenvalue.

2-2. OS-PCA The OS-PCA according to the present embodiment introduces the auxiliary variable s as in the following equation (3) in order to incorporate the smoothing term by a formulation different from the smoothing PCA as described above.
s = _Xw y (3)

The auxiliary variable s is an auxiliary variable in which the constraint conditions described later are set (see Equation (6)). The auxiliary variable s is an n-dimensional vector like the explanatory variable t, and a score for each sample can be constructed. Further, in the above equation (3), the weight vector w _y, as well as the weight vector w _x explanatory variables t and q-dimensional vector. According to the above equation (3), each component of the weight vector w _y indicates the weighting of the auxiliary variables s for each data item in the data matrix X.

The smoothed PCA maximized the variance of the one variable t corresponding to the principal component score (see equation (31)). Instead, the OS-PCA of the present embodiment is formulated to obtain the principal component by maximizing the covariance of the two variables t and s. Specifically, this method is formulated as the following equations (4) to (6).

In the above equations (4) to (6), the smoothing parameter κ is set within the range of 0 <κ <1, and the matrix P is expressed as in the following equation (7).
P = (1-κ) I + κX'D'DX (7)

In the above equation (4), the objective variable is not included in the argument of the covariance cov (t, s). As described above, this method does not utilize the information of the objective variable as in PLS and the like, and is an unsupervised method. Further, in this method, the maximization of the above equation (4) may be local, and the covariance cov (t, s) is optimized within the range satisfying the above conditional equations (5) and (6). As described above, it is possible to calculate the eigenvectors for a plurality of eigenvalues.

The above conditional expression (5) represents a condition (that is, a normalization condition) for setting the magnitude of the weight vector w _x to “1”. Condition (6), the partial smoothing parameter kappa, representing the constraint condition of shifting the magnitude of the weight vector w _y "1". The second term on the left side of the equation (6) is a smoothing term that smoothes the data between the samples in the data matrix X by the dummy matrix D.

The dummy matrix D is a matrix for setting smoothing according to the order between samples. As the dummy matrix D, for example, as shown in FIG. 1 (A), a first-order difference matrix D ⁽¹⁾ or a second-order difference matrix D ⁽²⁾ can be adopted. Data smoothing can be realized between the samples in the order of taking the difference for each row of each difference matrix D ⁽¹⁾ and D ⁽²⁾ .

In FIGS. 1A and 1B, the number of rows and the number of columns of each difference matrix D ⁽¹⁾ and D ⁽²⁾ when the number of groups between samples is one are illustrated. When the number of groups is a plurality of G, the dummy matrix D is set diagonally (block) as shown in FIG. 1 (C) by using the dummy matrices D _{(1) to} D _(G) for each group. It is possible. For the dummy matrices D _{(1) to} D _(G) for each group, the same difference matrix as in FIGS. 1 (A) and 1 (B) can be adopted between the samples in the same group.

The OS-PCA formulated as in the above equations (4) to (11) can be described as the following optimization problem of the Lagrange function J by using the Lagrange multiplier method (λ _x and λ _y are the Lagrange multipliers). ).

By partially differentiating the above function J each vector _w x, in _{w y,} the following equation (8), obtained respectively (9).

Equation (8), (9), each vector _w x, for _{w y,} the following equation (10), can be summarized as (11).

In the above equations (10) and (11), the eigenvalue λ satisfies λ = 4λ _x λ _y . In the above equation (10), the right side is the product of the eigenvalue λ and the weight vector w _x , and the left side is the product of the symmetric matrix and the weight vector w _x .

According to the above equation (10), this method describes the weight vector w _x of the explanatory variable t as an eigenvalue problem. The smoothed PCA resulted in a generalized eigenvalue problem, so the eigenvectors were not orthogonal to each other. On the other hand, in the OS-PCA of the present embodiment, it can be seen from the above eigenvalue problem that the eigenvectors for different eigenvalues λ are orthogonal to each other with respect to the weight vector w _x of the explanatory variable t.

According to the above OS-PCA, equation (10), apart from the eigenvalues λ of (11), the weight vector _w x as eigenvectors, and _{w y} calculated equation (2), by substituting (3), each The score of the sample can be calculated as a component of the variables t and s. Hereinafter, the score with the largest eigenvalue λ may be referred to as the first principal component, and the score with the next largest eigenvalue λ may be referred to as the second principal component.

2-2-1. About loading hypothesis test According to the above OS-PCA, the order information between samples can be reflected in the score by the smoothing term, and the weight vector w _x has statistical properties that enable loading hypothesis test. Satisfy (Equation (13)). This point will be described below.

First, the data _{x p} data items p-th in the data matrix X (p = 1 to q) (metabolite), the score s and the correlation coefficient corr (s, _{x p)} is the following formula (12) It is represented by.

According to the variance Var (x _p ) = 1 by scaling the data matrix X and the equations (3), (8), and (12), the correlation coefficient corr (s, x _p ) is as in the following equation (13). Can be expressed in.

In the above equation (13), w _{x and p} are the p-th components of the weight vector w _x . The denominator on the right side of the above equation (13) does not affect the p-th variable. Therefore, it can be seen that the weight vector w _x finally has a statistical property that it is proportional to the correlation coefficient corr (s, x _p ) between the p-th data x _p and the score s.

If R = corr (s, x _p ), the t-statistic of the following equation (14) follows the t distribution with n-2 degrees of freedom.

From the above, according to this method, it is possible to obtain a p-value or the like based on the above t-statistic for each data item such as a metabolite by using each component of the weight vector w _x . That is, according to the OS-PCA of the present embodiment, a statistical hypothesis test of loading can be performed in the same manner as the PCA and the like.

2-2-2. About the averaging operation The OD-PCA of the present embodiment is repeatedly measured for one sample, and when a plurality of data from the repeated samples are in the data matrix X, the same sample is used to handle such data. An averaging operation can be introduced for the derived data. The OS-PCA into which the averaging operation is introduced is expressed by the following equations (15) to (17).

In the above equations (15) to (17), the dummy matrix M for averaging is represented by an n-by-g matrix as in the following equation (18). In addition, g is the number of samples after the elimination of the repetition, and can be considered as the number of groups (by repeating the data) in the n samples before the elimination.

In the above equation (18), each vector m _{1 to mg} has a dimension corresponding to the number of repeated data for the corresponding sample. For example, the vector m ₁ for averaging the first sample is expressed by the following equation (19) based on the number n1 of repeated data.
m ₁ '= [1 / n1, 1 / n1, 1 / n1, ..., 1 / n1] (19)

Further, the matrix Q in the equation (17) corresponds to the matrix P when the averaging operation is not performed, and is expressed as in the following equation (20).
Q = (1-κ) I + X'M'D'DMX (20)

According to the above equations (15) to (17), the averaging operation can be realized for each repeated sample by the averaging matrix M. The OS-PCA in this case can also be described by the eigenvalue problem as in the case described above. Specifically, it is described as the following equations (21) to (22).

3. 3. Verification example The above OS-PCA theory was verified using actual metabolome data. As two verification cases, OS-PCA was applied to the turnover analysis and the metabolome data of green tea, and the usefulness of OS-PCA was confirmed by comparing with the analysis result of the usual principal component analysis. Each case will be described below.

3-1. Case 1
In Case 1, a typical PCA and OS-PCA were applied for the same turnover analysis as in Non-Patent Document 2.

In this case, samples of yeast Saccharomyces cerevisiae BY4742 (amino acid cocktail) and X2180 strain (minimum medium and amino acid cocktail) areotope-labeled with ¹³ C glucose were used. Sampling was performed in a time series of 0 seconds, 10 seconds, 20 seconds, 40 seconds, 80 seconds, 160 seconds, 320 seconds, 640 seconds, 1280 seconds, and 2560 seconds (that is, the order between samples). The value obtained by calculating the isotopomer ratio from the measured value (metabolomics data) of the metabolome by GC / MS for each sampling result was used as the statistical data to be analyzed (that is, the data matrix X).

FIG. 2 shows the results of performing normal PCA (that is, κ = 0) with respect to the above statistical data. In FIG. 2, the horizontal axis represents the score of the first principal component, and the vertical axis represents the score of the second principal component (PC2). According to FIG. 2, in a normal PCA, although the state of the time series can be confirmed with the first principal component, the difference between the strains cannot be confirmed.

In Non-Patent Document 2, the principal component analysis is performed using the data obtained by subtracting the average of all the samples for the above isotopomer ratio, so that the difference between the strains appears in the principal component score. From this result, Lysine's 4TMS and Isoleucine's 2TMS are cited as notable metabolites. However, in the method of Non-Patent Document 2, time-series information is lost. Furthermore, since the isotopomer ratio itself is not directly used as data, it becomes necessary to visually confirm it when selecting related metabolites.

Next, the results of OS-PCA according to this embodiment are shown in FIGS. 3 (A) and 3 (B). In this example, OS-PCA was applied to the above statistical data with a smoothing parameter κ = 0.999.

In FIG. 3A, the score (PC1t) of the first principal component of the explanatory variable t in OS-PCA is shown on the horizontal axis, and the score (PC2t) of the second component of the variable t is shown on the vertical axis. In FIG. 3B, the score (PC1s) of the first principal component of the auxiliary variable s in OS-PCA is shown on the horizontal axis, and the score (PC2s) of the second component of the variable s is shown on the vertical axis.

From the results shown in FIGS. 3 (A) and 3 (B), in OS-PCA, the time series can be confirmed for each variable t and s with the first principal component, and the difference between strains, that is, the difference between groups can be confirmed with the second principal component. I was able to confirm. Regarding the score PC2s of the second principal component, the corresponding loading was focused on because the difference appeared depending on the medium. FIG. 4 shows the results of the loading hypothesis test in this case.

As shown in FIG. 4, there is a significant negative correlation with the above score PC2s for the four peaks (biotransformers) of Lysine_3TMS_Minor :: C00047, Lysine_4TMS_Major :: C00047, Histidine :: C00135 + 0, and Peak-63 as loading. confirmed. It can be seen that this result includes Lysine's 4TMS, which is listed as a notable metabolite in Non-Patent Document 2, and is consistent with existing reports.

As described above, by using the OS-PCA according to the present embodiment, time-series information and differences between groups were confirmed, and valid and results were obtained for the biotransformers selected by using the statistical hypothesis test of loading. Was done.

3-2. Case 2
In this case, the metabolic syndrome data of green tea leaves ranked at the green tea fair was used as the analysis target (Non-Patent Document 3). This data was measured three times for each green tea having the order of 1st, 6th, 11th, 16th, 21st, 31st, 36th, 41st, 46th, and 51st. It is data. As a result, a group of 3 samples can be formed.

Regarding the above statistical data, first, the result of PCA is shown in FIG. FIG. 5 shows the scores of the first and second principal components as in FIG. According to FIG. 5, PCA can confirm the tendency of some groups, but cannot confirm the relevance to the ranking of the competition.

Next, the result of OS-PCA according to this embodiment is shown in FIG. In this example, OS-PCA was applied to the above statistical data with a smoothing parameter κ = 0.1. In FIG. 6A, the score (PC1os) of the first principal component of the auxiliary variable s in OS-PCA is shown on the horizontal axis, and the score (PC2os) of the second component of the variable s is shown on the vertical axis.

From the results shown in FIG. 6, it can be confirmed that the score PC1os of the first principal component in OS-PCA generally matches the order of rank (although the score is relatively low for the 21st-ranked sample). Therefore, a statistical hypothesis test of loading was performed for the score PC1os of the first principal component.

As a result of the above hypothesis test, among 225 substances including unknown peaks (metabolites), 73 were significant when p <0.05, and 57 were significant when q <0.05. It was. Among them, the following five substances had a correlation coefficient higher than 0.7 and a known name in particular with the above score PC1os.
Raffinose (R = -0.8600, p = 1.133 × 10 ^-9 , q = 2.550 × 10 ^-7 )
threo-3-Hydroxy-L-aspartic acid (R = -0.7912, p = 1.941 × 10 ^-7 , q = 1.674 × 10 ^-5 )
Arabinose (R = -0.7880, p = 2.352 × 10 ^-7 , q = 1.764 × 10 ^-5 )
Shikimic acid (R = -0.7334, p = 4.023 × 10 ^-6 , q = 2.073 × 10 ^-4 )
Galactose (R = -0.7228, p = 6.450 × 10 ^-6 , q = 2.073 × 10 ^-4 )

Existing reports list sugars, amino acids, and quinic acid as substances associated with their rank at the show. In the above analysis results by OS-PCA, it was confirmed that Raffinose, Arabinose, and Galactose had a high negative correlation with the score PC1os, and that high-ranked green tea contained a large amount of these sugars. Regarding amino acids, although the correlation is smaller than that of the above saccharides, Serine (R = 0.5427, p = 1.945 × 10 ^-3 , q = 1.287 × 10 ^-2 , Glycine (R = 0.5385, p = 2.140 ×) 10 ^-3 , q = 1.338 × 10 ^-2 ) has a significant positive correlation with the score PC1os, and these two amino acids tend to be less in high-ranked green tea, as well as some other amino acids. A statistically significant correlation was confirmed. For Quinic acid, no statistically significant correlation with the score PC1os was confirmed.

As described above, we proposed an OS-PCA that improved the problems of the smoothed PCA, and theoretically showed the statistical properties of loading. By applying it to the actual metabolome analysis, we were able to confirm a pattern that should be noted for the OS-PC score, and selected biotransformers using the statistical hypothesis test, and confirmed the agreement with the conventional findings.

4. Data analysis device The data analysis device that realizes the above OS-PCA will be described below.

4-1. Configuration The configuration of the data analysis device 5 according to the present embodiment will be described with reference to FIG. FIG. 7 is a block diagram showing the configuration of the data analysis device 5.

The data analysis device 5 is composed of an information processing device such as a PC (personal computer). As shown in FIG. 7, the data analysis device 5 includes a control unit 51, a storage unit 52, an operation unit 53, a display unit 54, an equipment interface 55, and a network interface 56.

The control unit 51 includes, for example, a CPU, an MPU, or the like that realizes a predetermined function in cooperation with software, and controls the overall operation of the data analysis device 5. The control unit 51 reads data and programs stored in the storage unit 52 and performs various arithmetic processes to realize various functions. For example, the control unit 51 executes a program including a group of instructions for causing the data analysis device 5 to perform the data analysis method according to the present embodiment. The above program may be provided from a communication network such as the Internet, or may be stored in a portable recording medium.

Further, the control unit 51 may be a hardware circuit such as a dedicated electronic circuit or a reconfigurable electronic circuit designed to realize a predetermined function. The control unit 51 may be composed of various semiconductor integrated circuits such as a CPU, MPU, GPU, microcomputer, DSP, FPGA, and ASIC.

The storage unit 52 is a recording medium that stores programs and data necessary for realizing the functions of the data analysis device 5, and includes, for example, a hard disk (HDD) or a semiconductor storage device (SSD). Further, the storage unit 52 may be provided with a semiconductor device such as a DRAM or SRAM, and temporarily stores data and also functions as a work area of the control unit 51.

The operation unit 53 is a user interface on which the user operates. The operation unit 53 is composed of, for example, a keyboard, a touch pad, a touch panel, buttons, switches, and a combination thereof. The operation unit 53 is an example of an acquisition unit that acquires various information input by the user.

The display unit 54 is composed of, for example, a liquid crystal display or an organic EL display. The display unit 54 displays various information such as information input from the operation unit 53.

The device interface 55 is a circuit (module) for connecting another device to the data analysis device 5. The device interface 55 is an example of an acquisition unit that performs communication according to a predetermined communication standard. Predetermined standards include USB, HDMI®, IEEE1395, WiFi, Bluetooth® and the like.

The network interface 56 is a circuit (module) for connecting the data analysis device 5 to the network via a wireless or wired communication line. The network interface 56 is an example of an acquisition unit that performs communication conforming to a predetermined communication standard. Predetermined communication standards include communication standards such as IEEE802.3 and IEEE802.11a / 11b / 11g / 11ac.

In the above description, an example of the data analysis device 5 composed of a PC or the like has been described. The data analysis device 5 is not limited to this, and may be various information processing devices (that is, a computer). For example, the data analysis device 5 may be one or more server devices such as an ASP server. Further, the data analysis method according to the present disclosure may be realized in a computer cluster, cloud computing, or the like.

For example, the data analysis device 5 may acquire the metabolome data input from the outside via the communication network by the network interface 56 and execute the data analysis method of the present embodiment. The data analysis device 5 may transmit the analysis result of the data analysis method to the outside from the network interface 56.

4-2. Operation The operation of the data analysis device 5 according to the present embodiment will be described with reference to FIGS. 8 to 9. FIG. 8 is a flowchart showing a data analysis process by the data analysis device 5. FIG. 9 is a flowchart showing an OS-PCA calculation process in the data analysis process.

Each process of the flowchart shown in FIG. 8 is executed by the control unit 51 of the data analysis device 5.

First, the control unit 51 acquires the data matrix X as an example of the statistical data to be analyzed (S1). For example, as statistical data to be analyzed for metabolomics, a data matrix X showing metabolome data is acquired in step S1. The data in the data matrix X may be a measured value of the metabolite or various calculated values (for example, isotopomer ratio) based on the measurement result.

In step S1, the control unit 51 reads, for example, the data stored in advance in the storage unit 52 into the work area to acquire the data matrix X. The control unit 51 may input data by the operation of the user in the operation unit 53, or the control unit 51 may acquire the data matrix X from the outside using various interfaces 55 and 56.

Further, the control unit 51 acquires a dummy matrix D, which is an example of order information regarding the order between samples in the data matrix X (S2). For example, information on the order between samples is set when metabolome data is input by a user operation.

In step S2, the control unit 51 acquires the dummy matrix D by referring to the information stored in the storage unit 52, for example. For example, the control unit 51 determines the value of the matrix element so as to take the difference between the data of two or more samples adjacent to each other in the order set between the samples, generates the dummy matrix D, and generates the dummy matrix D of the storage unit 51. Hold in the work area. The control unit 51 may acquire the dummy matrix D by using various interfaces 55 and 56 or the operation unit 53.

Further, the control unit 41 determines whether or not there is data to be averaged, that is, a repeating sample in the acquired data matrix X (S3). When the control unit 51 determines that there is no repeated sample (NO in S3), the control unit 51 proceeds to step S5 without performing the process of step S4 in particular. The processes of steps S3 and S4 are executed, for example, in response to a user operation.

When the control unit 51 determines that there are repeated samples in the data matrix X (YES in S3), the control unit 51 acquires a dummy matrix M for performing an averaging operation between the repeated samples (S4). The processes of steps S3 and S4 may be executed, for example, by referring to the information of the data items recorded in the row direction in the data matrix X acquired by the control unit 51. For example, the control unit 51 generates a dummy matrix M according to the number of repeated samples in the data matrix X (see equation (18)).

Next, the control unit 51 performs an OS-PCA calculation process, which is a process of calculating a score by applying the above-mentioned OS-PCA theory, based on the acquired data matrix X and dummy matrices D and M (S5). ). An example of the OS-PCA arithmetic processing (S5) will be described with reference to the flowchart of FIG.

In the example of FIG. 9, first, the control unit 51 scales the data (standard) so that the average between the samples is "0" and the variance is "1" for each data item such as a biotransform in the data matrix X. (S10). The data scaling (S10) may be performed at the time of acquisition of the data matrix X (S1). Further, when the acquired data matrix X has been scaled, the process of step S10 can be omitted.

Next, the control unit 51 substitutes the scaled data matrix X and the dummy matrices D and M into the arithmetic expression in the theory of OS-PCA (S11). When there is no repeating sample (NO in S3), the control unit 51 uses the equation (10) or the like as the arithmetic expression in step S11 based on the matrices X and D. When there is a repeating sample (YES in S3), the control unit 51 uses the equation (21) or the like as an arithmetic expression based on the respective matrices X, D, and M. Each calculation formula is stored in advance in, for example, a storage unit 52.

Next, the control unit 51 calculates one or more eigenvalues λ and eigenvectors in the eigenvalue problem by the substituted arithmetic expression (S12). Accordingly, the covariance cov (t, s) for optimizing such that each weight vector _w x, _{w y} is calculated.

In step S12, for example, the control unit 51 calculates each eigenvalue λ of the equation (10), and calculates one or more (n-1) or less weight vectors w _x as eigenvectors in descending order of the calculated eigenvalues λ. .. Further, the control unit 51, the eigenvalues λ of the calculated weight vector w _x into Equation (11), calculates the corresponding weight vector w _y. Incidentally, the calculation of the weight vector _{w y} the formula (8) may be employed (9).

Next, the control unit 51 calculates the corresponding score based on the calculation results of the eigenvalue λ and the eigenvector (S13). The control unit 51 ends the OS-PCA calculation process (S5 in FIG. 8) by calculating the score (S13), and proceeds to step S5.

In step S13, for example, the control unit 51 calculates n values of the explanatory variables t as scores of each sample based on the weight vector w _x and the equation (2) for each eigenvector with different eigenvalues λ. Also, Similarly, the auxiliary variable s, the control unit 51 calculates the value of the auxiliary variable s based on the weight vector w _y and equation (3) as a score. In step S13, the score based on only one of the two variables t and s may be calculated. The score may be calculated by limiting the first principal component, the first and second principal components, and the like in descending order of the eigenvalues λ, for example.

Returning to FIG. 8, the control unit 51 controls the display unit 54 so as to display the calculated score based on the calculation result of the OS-PCA calculation process (S5) (S6). For example, the control unit 51 displays each of the scores of the first and second principal components as a plot for each sample for each of the two variables t and s, for example, as shown in FIGS. 3A and 3B. To display.

Next, the control unit 51 accepts the user's operation in the operation unit 53, and whether or not the user has selected one of the displayed score types (first or second principal component, etc.) for further data analysis. Is determined (S7). For example, the user can select the type of score that reflects the order between the samples from the plot image of the score displayed on the display unit 54 (see FIGS. 3A and 3B). The selection of step S7 is accepted, for example, for the type of score by the auxiliary variable s.

When the control unit 51 determines that the user has not selected the score type (NO in S6), the control unit 51 ends this process.

On the other hand, when it is determined that the user has selected one of the score types (YES in S6), the control unit 51 performs a loading hypothesis test based on the weight vector w _x corresponding to the selected principal component. (S8 to S9).

For example, the control unit 51 calculates the correlation coefficient corr (s, x _p ) between the auxiliary variable s of the selected score and the data x _p for each data item such as a metabolite in the data matrix X (S8). Further, the control unit 51 acquires the p-value of each data item based on, for example, the t-statistic of the equation (14).

Further, the control unit 51 compares the p-value of each data item with a predetermined threshold value (referred to as “α”), and selects a data item having a p-value less than the threshold value α (S9). .. The threshold value α indicates a statistically significant level, for example, α = 0.05. In step S9, for example, if the data item relates to a metabolite, the metabolite that meets the statistical significance level is automatically selected. The control unit 51 may generate a list or the like (for example, FIG. 4) showing the calculation results of steps S8 and S9.

When the control unit 51 executes the loading hypothesis testing process (S8, S9) as described above, the data analysis process shown in FIG. 8 ends.

According to the above data analysis process, a data analysis method based on the theory of OS-PCA is carried out, and a score reflecting the order between the samples is obtained. Furthermore, a loading hypothesis test can be realized in which a metabolite or the like whose correlation with the score is statistically significant is selected.

In the above description, an example in which statistically significant data items are automatically selected in step S9 has been described, but the selection does not have to be performed automatically. For example, the user may appropriately calculate the hypothesis test and select statistically significant data items by using the processing result of step S5.

5. Summary As described above, the data analysis device 5 of the present embodiment performs multivariate analysis on a plurality of data items on a plurality of statistical samples. The data analysis device 5 includes a storage unit 52 and a control unit 51. The storage unit 52 records a data matrix X, which is an example of statistical data that manages a plurality of data items for each statistical sample, and a dummy matrix D, which is an example of order information indicating the order between the plurality of statistical samples. The control unit 51 performs a predetermined arithmetic process (S5) based on the statistical data and the order information. The control unit 51 optimizes the covariance between the explanatory variable t in the principal component analysis of the statistical data and the auxiliary variable s in which the constraint conditions (equations (6) and (17)) according to the order information are set. to be calculated as the weight vector _{w x} corresponding to the explanatory variable t (first vector), the weight vector corresponding to the auxiliary variable s _{w y} (second vector) (S12). The control unit 51 calculates a score for a plurality of statistical samples based on at least one of the first vector and the second vector (S13).

According to the above data analysis device 5, a score reflecting the order between samples is obtained based on the weight vector w _x that enables hypothesis testing of loading according to the theory of OS-PCA, and the order between statistical samples is taken into consideration. However, it is possible to analyze various data.

In the present embodiment, the constraint condition is defined by a smoothing term (the second term on the left side of equations (6) and (17)) that smoothes the data for each statistical sample in the order indicated by the order information. The smoothing term relates weight vector w _y of such auxiliary variables s, the score reflects the order between samples, it is possible to achieve both the possible weights hypothesis test loading vector w _x.

In the present embodiment, the score increases or decreases in the order indicated by the order information such as the dummy matrix D, for example, as shown in FIG. 3C. According to the data analysis device 5 of the present embodiment, the order between the samples can be reflected in the score in this way.

The order information in the present embodiment may indicate the order between the statistical samples for each group formed by a plurality of statistical samples, for example, as in the dummy matrix D shown in FIG. 1C. This makes it possible to reflect the group information between the samples in the score.

In this embodiment, the weight vector _{w x} includes data _{x p} for each data item in statistical data, the correlation coefficient corr (s, _{x p)} between the score s based on the weight vector _{w y} plurality proportional to q It has individual components. The control unit 51 may select a data item satisfying the statistical significance level from a plurality of data items based on each component of the weight vector w _x (S9). This also makes it possible to automate the loading hypothesis test.

In the present embodiment, the data matrix X of an example of statistical data includes a plurality of biotransformers in a living body as a plurality of data items, and includes at least one of a measured value and a calculated value relating to the corresponding biotransformer for each data item. By applying OS-PCA to the data matrix X for biotransforms, it is possible to analyze various data in metabolomics while considering the order between statistical samples.

The data analysis method of the present embodiment is a method in which a computer such as the data analysis device 5 performs multivariate analysis on a plurality of data items on a plurality of statistical samples. In the storage unit 52 of the computer, statistical data for managing a plurality of data items for each statistical sample and order information indicating the order among the plurality of statistical samples are recorded. The method corresponds to the explanatory variable t so that the computer optimizes the covariance between the explanatory variable t in the principal component analysis of the statistical data and the auxiliary variable s in which the constraints according to the order information are set. For a plurality of statistical samples based on the step (S12) of calculating the first vector and the second vector corresponding to the auxiliary variable s, and at least one of the first vector and the second vector. It includes a step (S13) of calculating a score.

In this embodiment, a program for causing a computer to execute the above data analysis method is provided. This program can be provided by storing it on various computer-readable, non-temporary recording media. According to the above data analysis method and program, by applying the theoretical OS-PCA that optimizes the covariance cov (t, s) between the explanatory variable t and the auxiliary variable s in which the constraint condition according to the order information is set. , It is possible to analyze various data while considering the order between statistical samples.

(Other embodiments)
In the first embodiment described above, an application example of this data analysis method to metabolomics has been described. This data analysis method is not limited to metabolomics, and may be applied to various omics analysis and multivariate analysis of chemometrics. In this case, the measurement data may be data obtained by omics analysis or chemometrics in the same living body.

5 Data analysis device 51 Control unit 52 Storage unit

Claims (8)

A data analysis device that performs multivariate analysis on multiple data items for multiple statistical samples.
A storage unit that records statistical data that manages the plurality of data items for each statistical sample, and order information that indicates the order between the plurality of statistical samples.
It is provided with a control unit that performs predetermined arithmetic processing based on the statistical data and the order information.
The control unit
The first vector corresponding to the explanatory variable and the first vector corresponding to the explanatory variable so as to optimize the covariance between the explanatory variable in the principal component analysis of the statistical data and the auxiliary variable for which the constraint condition according to the order information is set. Calculate with the second vector corresponding to the auxiliary variable,
A data analysis device that calculates scores for the plurality of statistical samples based on at least one of the first vector and the second vector. The data analysis apparatus according to claim 1, wherein the constraint condition is defined by a smoothing term that smoothes data for each statistical sample in the order indicated by the order information. The data analysis apparatus according to claim 1 or 2, wherein the score increases or decreases in the order indicated by the order information. The data analysis apparatus according to any one of claims 1 to 3, wherein the order information indicates the order between the statistical samples for each group formed by a plurality of statistical samples. The first vector has a plurality of components proportional to the correlation coefficient between the data for each data item in the statistical data and the score based on the second vector.
The control unit according to any one of claims 1 to 4, which selects a data item satisfying a statistical significance level from the plurality of data items based on each component of the first vector. Data analyzer. The statistical data is any one of claims 1 to 5, which comprises at least one of a measured value and a calculated value relating to the corresponding biotransformer for each of the data items, with the plurality of biotransformers in the living body as the plurality of data items. The data analysis apparatus described in 1. A data analysis method in which a computer performs multivariate analysis on multiple data items on multiple statistical samples.
In the storage unit of the computer, statistical data for managing the plurality of data items for each statistical sample, and order information indicating the order between the plurality of statistical samples are recorded.
The computer
The first vector corresponding to the explanatory variable and the first vector corresponding to the explanatory variable so as to optimize the covariance between the explanatory variable in the principal component analysis of the statistical data and the auxiliary variable for which the constraint condition according to the order information is set. Steps to calculate the second vector corresponding to the auxiliary variable,
A data analysis method comprising the step of calculating a score for the plurality of statistical samples based on at least one of the first vector and the second vector. A program for causing a computer to execute the data analysis method according to claim 7.

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