Method for estimating content ratio of components contained in a sample, composition estimation device, and program

Abstract

The method of the present invention is a method for estimating the content ratio of components in a sample containing components selected from among K types, and is capable of estimating the composition of the components of an unknown mixture, even from mass spectra obtained under ambient conditions, the method including: heating a sample set, sequentially ionizing the resulting gas components, and continuously observing a mass spectrum; obtaining a two-dimensional mass spectrum for each sample from the mass spectrum, and combining a plurality thereof to obtain a data matrix; performing nonnegative matrix factorization of the data matrix; correcting an intensity distribution matrix by means of a canonical correlation analysis between a basal spectral matrix and the data matrix; obtaining a feature vector from the corrected intensity distribution matrix and representing the same in a vector space; setting a K-1 dimensional simple substance and determining an end member; and estimating the content ratio of the components in the sample from the end member and the feature vector.

Description

[Technical field]

[0001] The present invention relates to a method for estimating a content ratio of components contained in a sample, a composition estimation device, and a program. [Background technology]

[0002] Conventionally, methods for estimating the component composition of a sample, which is a mixture of multiple components, have been known, for example, to separate each component in the sample by some method and identify and quantify each fractionated component. As one of such identification methods, mass spectra obtained by a mass spectrometer have been used.

[0003] However, since the information obtained from the mass spectrum is a huge amount of multidimensional data having many correlations, it is difficult to intuitively or empirically extract characteristic signals that lead to the identification of components. In recent years, as described in Non-Patent Document 1, a method has been used in which the dimensions of these multidimensional data are reduced by principal component analysis to search for features. However, even if these known data analysis methods are used, it is essentially difficult to perform quantification using mass spectra in which the peak intensity is influenced by the ionization efficiency. In order to perform quantitative analysis, it is necessary to first determine the ionization efficiency, which is an unknown variable that each compound has, and for this purpose, it is necessary to use an isotopic specimen with a known specimen amount and the same ionization efficiency as a standard substance. [Prior art documents] [Non-patent literature]

[0004] [Non-Patent Document 1] Analytical chemistry,2020,vol.92,issue2,P.1925-1933 Summary of the Invention [Problem to be solved by the invention]

[0005] In the method described in Non-Patent Document 1, much of the information contained in the original multidimensional data is lost during the dimensionality reduction process, and although qualitative analysis of components is possible, quantitative analysis is not possible.

[0006] In addition, since the ionization efficiency of each component varies depending on the type of component and the test environment, the ratio of the sizes (areas) of the obtained mass spectra does not reflect the ratio of the contents of each component in the mixture, which is one of the factors that hinders quantitative analysis using mass spectrometry.

[0007] In recent years, ambient desorption ionization (ADI), which performs mass spectrometry on samples under ambient conditions (in an open space at atmospheric pressure) without pretreatment, has become widely used as a mass spectrometry method. While this method has the advantage of being able to analyze untreated samples and samples from open systems in their solid state, it has been considered difficult to perform quantitative analysis due to discrepancies in the ionization rates of each component and the effects of the measurement environment.

[0008] In consideration of the above circumstances, an object of the present invention is to provide a method for estimating the content ratio of components, which is capable of estimating the composition of components in an unknown mixture even from a mass spectrum obtained under ambient conditions. Another object of the present invention is to provide a composition estimation device and a program. [Means for solving the problem]

[0009] As a result of extensive investigations aimed at achieving the above object, the present inventors have found that the above object can be achieved by the following configuration.

[0010] [1] A method for estimating a content ratio of at least one component selected from K components, where K is an integer of 1 or more, in a suspected sample containing at least one component selected from the K components, the method comprising: preparing K or more training samples each containing at least one component selected from the K components and differing in composition from one another, and a background sample not containing the component; heating each of the samples in a sample set including the suspected sample, the training samples, and the background sample, sequentially ionizing gas components generated by thermal desorption and / or pyrolysis, and continuously observing mass spectra; storing the mass spectra obtained for each heating temperature in each row, obtaining a two-dimensional mass spectrum for each sample, and converting at least two or more of the two-dimensional mass spectra into a data matrix; performing non-negative matrix factorization of the data matrix and NMF processing to decompose the data matrix into a product of a normalized basis spectrum matrix and an intensity distribution matrix thereof; extracting noise components contained in an intensity distribution matrix by canonical correlation analysis between a matrix and the data matrix, and correcting the intensity distribution matrix to reduce the influence of the noise components to obtain a corrected intensity distribution matrix; dividing the corrected intensity distribution matrix into sub-matrices corresponding to each of the samples, and expressing each of the samples in a vector space using the sub-matrices as feature vectors; setting a K-1 dimensional simplex containing all of the feature vectors, and determining K end-members in the K-1 dimensional simplex; calculating Euclidean distances between the K end-members and the feature vectors of the estimated sample to be estimated, and estimating a content ratio of the components in the estimated sample to be estimated based on a ratio of the Euclidean distances, wherein when K is 3 or more, at least one of the feature vectors of the training sample is located in each of the outer regions of a hypersphere inscribing the K-1 dimensional simplex, or the training sample includes at least one of the end-members. [2] The method according to [1], wherein K is an integer of 2 or more, and the suspected target specimen is a mixture of the components. [3] The method according to [1] or [2], wherein the training sample comprises the end member. [4] The method according to [3], wherein the end members are determined based on discriminant labels attached to the training samples. [5] The method according to [3], wherein the end members are determined by vertex component analysis of the feature vectors of the training samples. [6] The method according to [1], wherein the determination of the end members is performed by an algorithm that determines vertices so that the K-1 dimensional simplex has the smallest volume. [7] The method according to [6], in which the end members are determined by a second NMF process that decomposes the corrected intensity distribution matrix into a non-negative matrix factorization, and decomposes the matrix into a product of a matrix representing the weight fraction of the K types of the above components in the sample and a matrix representing the fragment presence intensities of each of the K types of the above components. [8] The method according to [6] or [7], wherein the training sample does not contain the end member. [9] The method according to any one of [1] to [8], wherein obtaining the corrected intensity distribution matrix further includes performing intensity correction of the intensity distribution matrix.

[10] The method according to [9], wherein the sample set further includes a calibration sample, the calibration sample contains all of the K types of components and has a known composition, and the intensity correction includes normalizing the intensity distribution matrix.

[11] The intensity correction includes assigning at least a portion of the intensity distribution matrix by a product of masses of corresponding analytes in the analyte set and environmental variables; The method according to [9], wherein the environmental variables are variables representing the effect of the component on ionization efficiency during the observation.

[12] The method according to

[11] , wherein the environmental variable is a sum of the peaks of the mass spectrum of a compound having a molecular weight of 50 to 1,500 contained in a predetermined amount in the atmosphere during the observation, or of an organic low molecular weight compound having a molecular weight of 50 to 500 contained in a predetermined amount in each of the sample sets.

[13] A composition estimation device for estimating a content ratio of at least one component selected from K components in a suspected sample containing at least one component selected from the K components, where K is an integer of 1 or more, the composition estimation device comprising: a mass spectrometer for heating K or more learning samples each containing at least one component selected from the K components and differing in composition from one another, a background sample not containing the component, and each sample included in a sample set including the suspected sample, sequentially ionizing gas components generated by thermal desorption and / or pyrolysis, and continuously observing mass spectra; and an information processing device for processing the observed mass spectra, the information processing device comprising: a data matrix creation unit for storing the mass spectra obtained for each heating temperature in each row, obtaining a two-dimensional mass spectrum for each sample, and converting at least two or more of the two-dimensional mass spectra into a data matrix together; an NMF processing unit for performing non-negative matrix factorization of the data matrix and performing NMF processing to decompose the data matrix into a product of a normalized basis spectrum matrix and an intensity distribution matrix thereof; a vector processing unit that divides the corrected intensity distribution matrix into sub-matrices corresponding to each of the sample sets and expresses each of the samples in a vector space using the sub-matrices as feature vectors; an endmember determination unit that sets a K-1 dimensional simplex containing all of the feature vectors and determines K endmembers in the K-1 dimensional simplex; and a content ratio calculation unit that calculates Euclidean distances between the K endmembers and the feature vectors of the estimation target sample and estimates a content ratio of the components in the estimation target sample based on a ratio of the Euclidean distances, wherein when K is 3 or more, at least one of the feature vectors of the training sample is located in each of the outer regions of a hypersphere inscribing the K-1 dimensional simplex, or the training sample includes at least one of the endmembers.

[14] The composition estimation device described in

[13] , wherein the end member determination unit determines the end members based on discriminant labels attached to the training samples.

[15] The composition estimation device according to

[13] , wherein the end member determination unit determines the end members using an algorithm that determines vertices so that the K-1-dimensional simplex has a minimum volume.

[16] The composition estimation device described in

[15] , wherein the end member determination unit determines the end members by a second NMF process that decomposes the corrected intensity distribution matrix into a non-negative matrix factorization, and decomposes the matrix into a product of a matrix representing the weight fraction of the K types of the above components in the sample and a matrix representing the fragment presence intensities for each of the K types of the above components.

[17] The composition estimation device according to

[15] , wherein the correction processing unit further performs intensity correction of the intensity distribution matrix.

[18] The composition estimation device described in

[17] , wherein the sample set further includes a calibration sample, the calibration sample contains all of the K types of components and has a known composition, and the intensity correction includes normalizing the intensity distribution matrix.

[19] The intensity correction includes assigning at least a portion of the intensity distribution matrix by a product of masses of corresponding analytes in the analyte set and environmental variables; The composition estimation device described in

[17] , wherein the environmental variables are variables representing the influence of the components on ionization efficiency during the observation.

[20] The composition estimation apparatus according to

[19] , further comprising a pressure reducing pump, wherein the environmental variable is a sum of peaks in the mass spectrum of a substance produced by operation of the pressure reducing pump.

[21] A program used in a composition estimation device that estimates a content ratio of at least one component selected from K components in a target sample containing at least one component selected from the K components, where K is an integer of 1 or more. The program includes a mass spectrometer that sequentially ionizes gas components generated by thermal desorption and / or pyrolysis while heating each of K or more learning samples that contain at least one component selected from the K components and have different compositions, a background sample that does not contain the component, and a sample set including the target sample, and continuously observes mass spectra; and an information processing device that processes the observed mass spectra. The program includes a data matrix creation function that stores the mass spectra acquired for each heating temperature by the mass spectrometer in each row, obtains a two-dimensional mass spectrum for each sample, and converts at least two or more of the two-dimensional mass spectra into a data matrix together; and an NMF processing function that performs NMF processing to perform non-negative matrix factorization of the data matrix and decompose it into a product of a normalized basis spectrum matrix and an intensity distribution matrix thereof. a correction processing function for extracting noise components contained in an intensity distribution matrix by canonical correlation analysis between the basis spectral matrix and the data matrix, and correcting the intensity distribution matrix to reduce the influence of the noise components to create a corrected intensity distribution matrix; a vector processing function for dividing the corrected intensity distribution matrix into sub-matrices corresponding to each of the specimens and expressing each of the specimens in a vector space using the sub-matrices as feature vectors; an endmember determination function for setting a K-1 dimensional simplex containing all of the feature vectors and determining K endmembers in the K-1 dimensional simplex; and a content ratio calculation function for calculating Euclidean distances between the K endmembers and the feature vectors of the estimation target specimen, and estimating a content ratio of the components in the estimation target specimen based on a ratio of the Euclidean distances, wherein when K is 3 or more, at least one of the feature vectors of the training specimen is located in each of the outer regions of a hypersphere inscribing the K-1 dimensional simplex, or the training specimen includes at least one of the endmembers. Effect of the Invention

[0011] The method of the present invention (hereinafter also referred to as "this method") has one of its features in that it heats each sample in a sample set, sequentially ionizes gas components generated by thermal desorption and / or pyrolysis, and continuously observes mass spectra to obtain a two-dimensional mass spectrum for each sample in which the mass spectra obtained for each heating temperature are stored in each row. The data matrix obtained by compiling these is decomposed by nonnegative matrix factorization (NMF) into the product of a normalized basis spectrum matrix and its intensity distribution matrix, and noise components contained in the intensity distribution matrix are extracted and corrected by canonical correlation analysis to obtain a corrected intensity distribution matrix containing the feature vectors of each sample, and then quantitative calculations are performed.

[0012] By performing a process to correct the intensity distribution matrix using this canonical correlation analysis, it has become possible to perform quantitative analysis more easily and with higher accuracy (details will be described later).

[0013] Furthermore, when K is an integer of 2 or more and the sample to be estimated (estimated sample) is a mixture of K components, the mixture ratio (composition) of the K components in the estimated sample can be estimated by this method.

[0014] Furthermore, when the training sample contains endmembers, the composition of the sample can be estimated more accurately and more easily.

[0015] Furthermore, if a discrimination label for discriminating the endmember is attached to the learning sample, the endmember can be determined from the information on the label, making it easier to estimate the composition of the sample.

[0016] In addition, when no discriminant label is attached and the training sample contains endmembers, the endmembers can be determined by vertex component analysis of the feature vector of the training sample, and the composition of the sample can be estimated.

[0017] In addition, even if the training sample does not contain endmembers, the composition of the sample can be estimated by determining the endmembers using an algorithm that determines the vertices so that the K-1-dimensional simplex has the smallest volume. This method is advantageous in that it does not require endmembers in the training sample.

[0018] Furthermore, if the corrected intensity distribution matrix is ​​obtained after intensity correction of the intensity distribution matrix, the accuracy of the estimation is further improved.

[0019] Furthermore, when the sample set further includes a calibration sample, and the intensity correction includes normalizing the intensity distribution matrix, the composition of the sample can be estimated with a simpler procedure and with a higher accuracy.

[0020] Furthermore, by assigning the portion of the intensity distribution matrix corresponding to each sample to the product of the sample's mass and environmental variables, the influence of the ionization efficiency of each component during observation is corrected, and the composition of the sample can be estimated with high accuracy even if the sample set does not include a calibration sample.

[0021] Furthermore, when the environmental variables used in the above allocation are the sum of the mass spectrum peaks of a compound with a molecular weight of 50 to 1500 contained in a predetermined amount in the atmosphere during observation, or a low molecular weight organic compound with a molecular weight of 50 to 500 contained in a predetermined amount in each sample in the sample set, more accurate composition estimation results can be obtained with simpler operations even if the sample set does not include a calibration sample. [Brief description of the drawings]

[0022] [Figure 1] 1 is a flowchart of a composition estimation method according to an embodiment of the present invention. [Diagram 2] This is an image showing a K-1-dimensional simplex (a two-dimensional simplex, a triangle) when K is 3. [Diagram 3] FIG. 1 is a hardware configuration diagram of a composition estimation device according to an embodiment of the present invention. [Figure 4]FIG. 1 is a functional block diagram of a composition estimation device according to an embodiment of the present invention. [Diagram 5] This shows the original spectrum for "MSE_calib" (A) and the reconstructed spectrum after processing (B). [Figure 6] This shows Cδ(MSE_Calib), a part of the C matrix after NMF decomposition, and ST after removing the background and impurity spectra using the CCA filter. [Figure 7] This is the result of composition analysis of a three-component system of M (polymethyl methacrylate), S (polystyrene), and E (polyethyl methacrylate). [Figure 8] This is the composition estimation result when the orthogonal constraint is lifted from the NMF conditions. [Figure 9] This is the composition estimation result when only merging S is removed from the NMF optimization conditions. [Figure 10] This shows the composition estimation results when the CCA filter was turned off (Comparative Example). [Figure 11] This figure shows the original spectrum for "MSE_calib" (top, raw of MSE_calib) and the reconstructed spectrum after the above processing with the CCA filter removed. [Figure 12] This is the composition estimation result without correction by environmental variables. [Figure 13] This is an image showing a K-1-dimensional simplex (a two-dimensional simplex, a triangle) when K is 3. [Figure 14] FIG. 11 is an explanatory diagram of the mechanism of an end member determination method in the second embodiment of the present invention. [Figure 15] FIG. 13 is a diagram showing the estimation results of the second embodiment. [Figure 16] FIG. 13 is a diagram showing the estimation results of the third embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0023] The present invention will be described in detail below. The following description of the components may be based on a representative embodiment of the present invention, but the present invention is not limited to such an embodiment. In this specification, a numerical range expressed using "to" means a range that includes the numerical values ​​before and after "to" as the lower and upper limits.

[0024] [Terminology definition] The terms used in this specification are explained below. Note that terms not explained below are used with the meaning commonly understood by those skilled in the art.

[0025] In this specification, the term "component" refers to a substance that constitutes each sample, and the suspected sample, training sample, and calibration sample refer to a mixture constituted by a combination of components.

[0026] A "specimen to be estimated" is a specimen whose composition is to be estimated, and the number of components contained and the amount of each component may both be unknown.

[0027] The term "training sample" refers to samples required for determining K end members of a K-1 dimensional simplex, which will be described later. These samples contain at least one component selected from K types of components, and each has a different composition. The number of components contained is not particularly limited and may be 1 to K types. The training sample may contain a sample with the same composition as the estimation target sample. In other words, the estimation target sample and the training sample may be the same, but the training samples are different from each other.

[0028] An "end member" refers to a vector corresponding to a vertex of a K-1 dimensional simplex, and this end member corresponds to the feature vector of a sample (a training sample or a virtual sample) consisting of only one component out of K types.

[0029] The term "background sample" refers to a sample that is different from the suspected sample and the learning sample, and does not contain any of the above components.

[0030] The term "calibration sample" refers to a sample that is different from the estimation target sample, the learning sample, and the background sample, that contains all K types of components, and whose composition is known.

[0031] [First embodiment of the present method] FIG. 1 is a flowchart of a composition estimation method according to an embodiment of the present invention (hereinafter, also referred to as "the method").

[0032] First, a sample to be estimated, K or more learning samples having different compositions, and a background sample (collectively referred to as a "sample set") are prepared (step S101). The sample set may further include a calibration sample.

[0033] The suspected specimen contains at least one of the K components. When the suspected specimen contains one component, the purity of the component can be estimated by this method. In this case, the suspected specimen contains the above-mentioned "component" and other impurities.

[0034] When K is 2 or more, the suspected specimen is a mixture of components. In the present method, there is no particular upper limit to K, so long as it is 1 or more. Typically, K is preferably 1000 or less. The number of training samples must be K or more, depending on the number of components K. There is no particular limit to the number of training samples as long as it is K or more, but if the number is greater, the accuracy of determining the vertices of the K-1-dimensional simplex (described later) tends to be higher, and as a result, more accurate composition estimation results are likely to be obtained. That is, the ratio of the number of training samples to the number of components K (number of training samples / number of components) is 1 or more, preferably 2 or more, more preferably 3 or more, even more preferably 5 or more, and particularly preferably 10 or more. On the other hand, the upper limit is not particularly limited, but generally, it is preferably 1000 or less.

[0035] The learning samples have different compositions. The composition is determined by the type and number of components contained, and the amount of each component. The same composition means that the type, number, and amount of each component contained are the same. If any one of the components is different, the samples are in a "different composition."

[0036] In this method, as long as the learning samples have different compositions, other information, i.e., the types of components contained, the number of components, and the amounts of each component, is not necessary for estimating the composition of the estimation target sample. In other words, the composition of the learning samples may be unknown. The difference between the suspected target specimen and the training specimen is that the training specimens must have different compositions, although the training specimens may include specimens having the same composition as the suspected target specimen.

[0037] The training sample may include an end member. That is, the training sample may include a sample (single component, pure sample) consisting of one component selected from K components. When the training sample includes an end member, it is possible to more easily estimate the composition with high accuracy.

[0038] In this case, the training samples that are end members may contain a discrimination label. When the training samples contain a discrimination label, this is preferable because it makes it easier to determine the end members.

[0039] Next, the suspected target specimens are each heated, and gases generated by thermal desorption and / or pyrolysis are sequentially ionized to obtain mass spectra (step S102).

[0040] Although there is no particular limitation on the method for obtaining a mass spectrum, a method of performing mass analysis of a sample under ambient conditions without pretreatment is preferred. As a method for such ionization and mass analysis, a mass spectrometer called DART-MS, which combines an ion source called a DART (Direct Analysis in Real Time) ion source with a mass spectrometer, is known. The mass spectrometer is not particularly limited, and is preferably one capable of performing accurate mass analysis, and may be any of a quadrupole type, a time-of-flight (TOF) type, or the like.

[0041] There are no particular limitations on the specific conditions for obtaining a mass spectrum, but one non-limiting example is a procedure in which each sample in a sample set is heated sequentially at a heating rate of 50°C / min, and helium ions are injected at intervals of 50 shots / min into the pyrolysis gas generated in the temperature range of 50 to 550°C to ionize the gas, thereby obtaining a two-dimensional MS spectrum with m / z on the horizontal axis and temperature on the vertical axis.

[0042] Next, the mass spectrum obtained for each heating temperature is stored in each row, a two-dimensional mass spectrum is obtained for each specimen, and at least two of these two-dimensional mass spectra are collectively converted into a data matrix (step S103).

[0043] A method for acquiring the data matrix will now be specifically described.

[0044] In step S102, mass spectra are continuously acquired at predetermined intervals of temperature rise. These mass spectra may be used directly to create a data matrix, or may be averaged for each predetermined temperature rise range. By averaging the mass spectra for each predetermined temperature rise range into one, the amount of data can be compressed. An example of such a temperature rise range is about 10 to 30°C.

[0045] In addition, the peak intensities in each spectrum may be normalized, for example, by a method in which the sum of squares of the peak intensities is 1.

[0046] In this way, a predetermined number of mass spectra (which may vary depending on the grouping method, e.g., 20) can be obtained for each heating temperature (or for each heating temperature grouped into a predetermined range) for a given sample by performing a single measurement. When this mass spectrum is stored in each row and the heating temperature is stored in each column, a two-dimensional mass spectrum for each specimen is obtained.

[0047] Once two-dimensional mass spectra for each sample are obtained in this way, at least two of these are combined and converted into a data matrix X. The number of two-dimensional mass spectra used to create the data matrix X is not particularly limited as long as it is two or more, but it is preferable to use the two-dimensional mass spectra of all samples included in the sample set. When measurements are performed two or more times for one sample, some or all of the two-dimensional mass spectra obtained in the two or more measurements may be used to create the data matrix X.

[0048] Next, the obtained data matrix is ​​subjected to nonnegative matrix factorization (NMF) and is decomposed into the product of a normalized basis spectrum matrix and its intensity distribution matrix (step S104).

[0049] We now explain non-negative matrix factorization.

[0050] Under the assumption of linear additivity between the spectral intensities and the sample composition, the spectral data matrix is ​​generally written as:

[0051]

number

[0052] Here, the data matrix X is an N×M data matrix made by stacking N spectra with M channels, S is the basis spectrum matrix, and C is its intensity distribution matrix. If the total number of components included in the data set is K1, then C is an N×K1 matrix, and S is an M×K1 matrix. Since actual measurements contain noise,

[0053]

number

[0054] Taking into account the error matrix N, we determine the C and S matrices to minimize N. The T on the right side of the matrix means the transpose matrix. If we assume Gaussian noise,

[0055]

number

[0056] This is formulated as an optimization problem for C and S such that

[0057]

number

[0058] is the Frobenius norm of the matrix,

[0059]

number

[0060] is the L1 norm of the vector,

[0061]

number

[0062] Let denote the L2 norm of a vector.

[0063] In addition, since there is no unique solution for C and S in the above equation, we impose constraints that the spectrum will satisfy based on physical requirements. NMF requires that the composition ratio and spectral intensity have non-negative values, so

[0064]

number

[0065] However, since a unique solution cannot be determined by the non-negative condition alone, it is necessary to apply further constraints according to the measurement device. The constraints of NMF in this step are explained below.

[0066] (About the NMF update formula) In the NMF process in this step, it is preferable to solve the above equation (7) as a convex optimization problem for each column of C and S by alternating column-vector-wise updates of C and S using Hierarchical alternating least squares (HALS), which is easy to incorporate constraints as described below.

[0067] In this method, mass analysis is performed on the gas generated by thermal desorption and / or pyrolysis while heating each sample, so it is difficult to obtain the number of components K1 after pyrolysis as prior information and it is necessary to estimate it from the data. A preferred estimation method is automatic relevance determination (ARD). This assumes sparsity in the intensity distribution matrix C, which is a natural assumption considering that the pyrolysis of a certain component occurs only at a specific temperature for a sample containing that component. This balances the efforts to reduce the number of components as much as possible with the efforts to minimize the above formula (7), making it possible to determine the optimal number of components.

[0068] (orthogonal constraints) Mass spectrometers generally have a resolution of about 0.1 to 0.001 m / z. Therefore, it is rare that the m / z of different gas components match to the decimal point and occupy the same channel. Therefore, it is reasonable to assume a certain degree of orthogonality between the column vectors of the basis spectrum matrix S.

[0069] This is expected to not only lead to a good local solution, but also to prevent fitting from concentrating only on peaks with strong intensity. On the other hand, since complete orthogonality and non-negativeness are too strong constraints, it is preferable to impose the orthogonal constraint softly by adding a penalty term with an undetermined Lagrange multiplier (soft orthogonal constraint).

[0070] (Merging of Components) During the update of C and S, when multiple almost identical base spectra are obtained, the correct number of components n can be obtained by combining them into one spectrum. When applying the spectral image of EALS to NMF, the k-th column vector of S is denoted as S :k and S T :k S :m >threshold, there exists a k < m such that

[0071]

Number

[0072] can be merged by (Merging C). Here, Threshold is a hyperparameter given in the range of 0.9 to 0.99. Similarly, perform the merging of similar S. Furthermore, when multiple column vectors of C are parallel, it is preferable to superimpose the corresponding column vectors of S according to the weights of C. That is,

[0073]

Number

[0074] when there exists a k ≠ m such that

[0075]

Number

[0076] merge them into (Merging S). It is considered that this has the effect of combining isotope peaks and oligomer peaks into one base spectrum.

[0077] (Derivation of Update Equations) The update equations obtained as above will be described. The overall simultaneous distribution of the model is

[0078]

number

[0079] Here, σ 2 is the dispersion parameter,

[0080]

number

[0081] Element λ of k is a parameter that follows the inverse gamma distribution and represents the importance of component k in the data. Since we assume a Gaussian distribution for the noise,

[0082]

number

[0083] The exponential distribution that C follows is given by K, an arbitrary number of components large enough (about 50) as the initial value.

[0084]

number

[0085] λ k follows the inverse gamma distribution,

[0086]

number

[0087] Here, a is a hyperparameter such that a-1 is an extremely small positive number, and b is the mean value of the data matrix μ X By

[0088]

number

[0089] The expected value of the elements of C is

[0090]

number

[0091] The negative log-likelihood of p(X,C,S) is

[0092]

number

[0093] Here, the variance parameter σ when assuming a Gaussian distribution is 2 teeth,

[0094]

number

[0095] Since it is a convex function with respect to λ,

[0096]

number

[0097] can be obtained. Next, we explain the update formula for S. First, we use the negative log-likelihood function to :k The term J(S :k ) is the contribution of the kth component to X.

[0098]

number

[0099] Using

[0100]

number

[0101] Therefore, excluding the constant term,

[0102]

number

[0103] The above is derived based on Shiga, M. et al. Sparse modeling of EELS and EDX spectral imaging data by nonnegative matrix factorization. Ultramicroscopy 170, 43-59 (2016). Here, we add a penalty term due to the orthogonal constraint added to S mentioned above.

[0104]

number

[0105] Here, ξ k is the Lagrange multiplier,

number

[0106] s :k Differentiate with

[0107]

number

[0108]

number

[0109] So, s :k The update formula for

[0110]

number

[0111] We obtain the complete orthogonal condition ξ k teeth,

[0112]

number

[0113] twist,

[0114]

number

[0115] The soft orthogonal condition is ξ k By multiplying by the hyperparameter w in [0,1], the degree of orthogonality can be freely adjusted between perfect orthogonality and no orthogonal constraint. The final update formula is

[0116]

number

[0117] Next, we explain the update formula for C. From the negative log-likelihood function, :k The term J(C :k Consider extracting only

[0118]

number

[0119]

number

[0120] If we standardize it as follows, the update formula becomes

[0121]

number

[0122] twist,

[0123]

number

[0124] The specific algorithm is as follows:

[0125]

number

[0126] Returning to FIG. 1, next, the basis spectrum matrix and the data matrix are subjected to canonical correlation analysis to obtain a corrected intensity distribution matrix (step S105). Specifically, noise components contained in the intensity distribution matrix are extracted by canonical correlation analysis between the basis spectrum matrix and the data matrix, and the intensity distribution matrix is ​​corrected to reduce the influence of the noise components, thereby obtaining a corrected intensity distribution matrix.

[0127] Since NMF is a low-rank approximation of a data matrix, even if a component k does not actually exist in the i-th spectrum, if the approximation improves in the least squares sense by assuming that it exists, then C ik >0. In many cases, such a C ik is very small and is often not an issue in NMF analysis.

[0128] However, in the case of trace component detection, the trace amount of C jk >0 and the NMF artifact C ik >0 and ghost peak C ik It is preferable to substitute 0 for , because this will allow for more accurate estimation results by removing false peaks resulting from artifacts in the NMF algorithm as part of the noise.

[0129] In this step, in order to solve the above problem, Canonical Correlation Analysis is used. This step is one of the features of the present method, and the inventors have named this step Canonical Correlation Analysis (CCA) Filter.

[0130] Conceptually, the CCA filter is a filter that extracts the basis spectrum S output from NMF. T The method is to scan sample-wise to see whether each component of was actually included in the original data, and if no similar peak pattern is found in the original data, to remove it from the spectrum of that sample. If the spectrum generated from the Lth sample is stored in rows l to l′ of the data matrix X, the submatrix extracted from that portion is called X. δ(L) That is, δ(L) = {l, l+1, ..., l'-2, l'-1}.

[0131] CCA is conventionally known as a method for examining the correlation between two sets of data, and is formulated as follows: A matrix consisting of N p-dimensional vectors is

[0132]

number

[0133] A matrix consisting of N q-dimensional vector data

[0134]

number

[0135] As,

[0136]

number

[0137] Where:

[0138]

number

[0139] It is.

[0140] That is, project Y and Z onto a certain axis and find the solution (a T ,b T ) T The problem formulation of CCA is to find

[0141] (a T ,b T ) T and the correlation coefficient ρ are given as the eigenvectors and eigenvalues ​​of the generalized eigenvalue problem of the following equation, and all eigenvectors (a T ,b T ) T Putting it all together (A T ,B T ) T If we write

number

[0142] Now, the basis spectrum S of a certain component k :k Suppose we want to determine whether or not a certain part of sample L is included in the data matrix X. First, we extract the corresponding partial data matrix X from the data matrix X. δ(L) On the other hand, S T is S :k T Let S be the set of all spectra similar to sim T , and a group of spectra that is significantly different from them are called S out T And, divide it into two matrices,

[0143]

number

[0144] Here, for a given value t ∈ (0,1], all eigenvalues ​​with ρ>t1 are taken out, and the first component of the corresponding eigenvector b is b1>t2b for its maximum component. max If this is satisfied, then the basis spectrum S of component k is :k is included in sample L. Otherwise, the corresponding C δ(L)k =0. Here, t1 and t2 are hyperparameters that are strongly affected by the fitting accuracy of NMF, i.e., the NMF hyperparameter threshold, so they must be carefully considered. Empirically, t1 = 0.9threshold, t2 ∈ [0.1, 0.3] gives good results.

[0145] The above describes an example of applying the CCA filter to NMF artifacts (noise), but the above noise removal can be applied to removing not only NMF artifacts, but also background and contamination.

[0146] That is, examples of noise that can be removed using a CCA filter include: (1) NMF artifacts (so-called false peaks); (2) peaks (background) derived from trace chemical substances that are mixed in from the environment surrounding the device; and (3) peaks (contamination) derived from substances contained in the sample that may distort its true nature if included in the analysis.

[0147] The sample set used in this method includes background samples.

[0148]

number

[0149] Then, the basis spectrum S :k It can be determined whether or not was included in the background file. If it was included, it is system noise from the environment, so C :kSetting =0 will remove the spectrum from the sample.

[0150] Furthermore, if the background sample contains a contaminant, the noise due to the contamination can also be removed by the same procedure as above. The contaminant is not particularly limited, but examples thereof include the solvent used for preparing or loading the sample.

[0151] This step may further include performing an intensity correction of the intensity distribution matrix.

[0152] For example, DART-MS primarily ionizes water and ammonia in the air with helium ions, which then secondarily ionizes the sample. Therefore, the peak intensity may change depending on atmospheric conditions such as humidity. In addition, the sample mass loaded is usually different for each sample, which also affects the peak intensity. In addition, the ionization efficiency of each component in the sample generally differs, which also affects the peak intensity. Intensity correction of the intensity distribution matrix can reduce the above effects and provide more accurate quantitative results.

[0153] When all samples contain all K components and include a calibration sample whose composition is known, the intensity correction can be performed by normalizing the intensity distribution matrix.

[0154] Normalizing the intensity distribution matrix means normalizing the C matrix for each sample, and more specifically, means an operation of adding up all elements for each sample to 1. Split the C matrix sample-wise and denote the C matrix derived from sample L as C δ(L) In short,

[0155]

number

[0156] Since decomposition temperature information is not necessary for composition analysis,

[0157]

number

[0158] The vector obtained by adding vertically

[0159]

number

[0160] is the feature vector of sample L. Next, we arrange the feature vectors of p single-component samples measured as endmembers to obtain the endmember matrix

[0161]

number

[0162] Create a feature vector of the mixed samples.

[0163]

number

[0164] Since can be written as a linear sum of the feature vectors of the end members, the coefficient vector

[0165]

number

[0166] Using

[0167]

number

[0168] It can be written as follows. Since one calibration sample always gives one or more pyrolysis samples, the number of components after pyrolysis is a full-rank matrix, P. Therefore, it is generally impossible to solve, and an approximate solution in the least-squares sense can be solved by quadratic programming.

[0169] In the mass spectrum obtained by this method, the ionization efficiency differs for each compound, and the pyrolysis efficiency also differs, so that the amount of compound is not proportional to the peak intensity. However, the peak intensity ratio including the ionization efficiency of component k by NMF is S :k T The intensity ratio between the spectra is already reflected in :k This is reflected in The hierarchical data structure formed by this NMF enables more accurate quantitative composition analysis without the need for unknown ionization efficiencies, as long as the peak intensity ratios in the endmembers are taken into account.

[0170] On the other hand, if the sample set does not include a calibration sample, more accurate quantitative analysis can be achieved by assigning at least a portion (preferably the entirety) of the intensity distribution matrix by the product of the mass of the corresponding sample and environmental variables. Here, the environmental variables are variables that represent the effect of each component on the ionization efficiency during observation.

[0171] If the component has a high ionization efficiency, the peak intensity will be large, and if the component has a low ionization efficiency, the peak intensity will be small. Furthermore, as for the mass of the specimen, generally, if the mass is large, the peak intensity will be large, and if the mass is small, the peak intensity will be small.

[0172] When the sample set does not include a calibration sample, the intensity distribution matrix is ​​not normalized, and the C matrix is ​​corrected as follows so that the intensity information between samples held in the intensity distribution matrix can be used.

[0173]

number

[0174] where m L is the mass of sample L, I L is the peak intensity of (poly)dimethylsiloxane generated by the oil pump attached to the DART-MS, observed at 610 m / z over the entire temperature range. L reflects the standby state at the time of measurement, and the peak intensity actually differs by about three times between rainy days and sunny days.

[0175]

number

[0176] Vector obtained by adding vertically

[0177]

number

[0178] is the feature vector of sample L. Similarly, we can obtain the endmember matrix

[0179]

number

[0180] Create

[0181]

number

[0182] From L Request.

[0183] In addition, in the above, I Lis set to 610 m / z derived from (poly)dimethylsiloxane, but is not limited to the above, and is preferably derived from a compound having a molecular weight of 50 to 1500 contained in a predetermined amount in the atmosphere at the time of observation, and / or derived from an organic low molecular weight compound having a molecular weight of 50 to 500 contained in a predetermined amount in each of all samples.

[0184] Returning to FIG. 1, next, the corrected intensity distribution matrix is ​​divided into sub-matrices corresponding to each sample included in the sample set, and each sample is represented in vector space as a feature vector (step S106). Furthermore, a K-1 dimensional simplex that includes all of these feature vectors (each corresponding to each specimen) is set, and K end members in the K-1 dimensional simplex are determined (step S107).

[0185] When the training sample contains an endmember and a discrimination label (a label for discriminating that the training sample is an "endmember") is attached to the training sample, the endmember is determined based on the label.

[0186] If the training samples contain end members but are not labeled with discriminant labels, i.e., the training samples contain end members but it is unclear which training samples are end members, then the end members are determined by vertex component analysis of the feature vectors.

[0187] If the training sample does not contain endmembers, the endmembers are determined by an algorithm that determines the vertices so that the K-1-dimensional simplex has the smallest volume, which in the case of a 2-dimensional simplex (triangle) means the smallest area.

[0188] In one embodiment of the method, even if the training sample does not contain endmembers, at least one of the feature vectors of the training sample is located in each of the outer regions of the hypersphere inscribed in the K-1-dimensional simplex (when K is 3 or more), so that the endmembers can be determined with high accuracy.

[0189] 2 is an image diagram showing a K-1-dimensional simplex (two-dimensional simplex, triangle) when K is 3. The K-1-dimensional simplex 10 is a triangle with end members 13, 14, and 15 determined by learning samples 16, 17, and 18 as vertices.

[0190] As shown in FIG. 2, when the learning samples 16, 17, and 18 are located in the outer regions 19 (hatched) of the inscribed hypersphere 12 (in this case, a circle) of the K-1 dimensional simplex, highly accurate quantitative analysis results can be obtained. The above method is based on Robust Volume Minimization-Based Matrix Factorization for Remote Sensing and Document Clustering, IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 64, NO. 23, DECEMBER 1, 2016.

[0191] The algorithm for determining the vertices so that the K-1-dimensional simplex has the minimum volume is not particularly limited, and any known algorithm can be applied. Examples of such algorithms include the Minimum volume constraint-NMF method, the Minimum Distance Constraint-NMF method, the Simplex identification via split augmented Lagrangian method, and the Simplex volume minimization method.

[0192] Next, the Euclidean distance between each of the K endmembers and the feature vector of the sample to be estimated is calculated, and the content ratio of each component in the sample is estimated (step S108).

[0193] In another embodiment of the method, when a training sample includes at least one end member (at least one of the training samples is an end member), the feature vectors of the other training samples may be located in the inner region of a hypersphere inscribed in the K-1-dimensional simplex. FIG. 13 is an image diagram showing a K-1-dimensional simplex (two-dimensional simplex, triangle) when K is 3, similar to FIG. 2. A K-1-dimensional simplex 60 is a triangle with vertices of a training sample 61, which is an end member, a training sample 62 other than the training sample, and end members 64 and 65 determined by a training sample 63. The difference from FIG. 2 is that the training samples 62 and 63 are located in the inner region of a hypersphere inscribed in the K-1-dimensional simplex.

[0194] Even if at least one of the training specimens is an end member, the other training specimens may be located on a hypersphere inscribed in the K-1-dimensional simplex or may be located in an outer region. In other words, in this case, the positions of the other training specimens may be arbitrary. In particular, in terms of obtaining better effects of the present invention, it is preferable that the other learning specimen contains 20% by mass or more, and more preferably 40% by mass or more, of components of end members different from the learning specimen which is an end member (components of other end members).

[0195] According to this method, even solid samples that are difficult to dissolve in a solvent and difficult to analyze using conventional composition analysis can be analyzed without any special pretreatment, and accurate quantitative analysis is possible. This method can significantly reduce the time required to obtain results, particularly when applied to quality control of samples that are mixtures of multiple components and investigation of the cause of defects.

[0196] [Second embodiment of the method] The second embodiment of the present method includes a method for determining an end member (vertex) in the case where the training sample does not include an end member in step S107 in the first embodiment already described, i.e., where there is no training sample located at a K-1-dimensional simplex vertex.

[0197] One of the features of the method according to this embodiment is that the endmembers are determined by a second NMF process in which a matrix representing the fragment abundance intensities for each sample is subjected to nonnegative matrix factorization and decomposed into a product of a matrix representing the weight fractions of K components in the sample and a matrix representing the fragment abundance intensities for each of the K components.

[0198] FIG. 14 is a schematic diagram for explaining this mechanism. Each sample is a mixture of K components (hereinafter, described as a mixture of “polymers”), but what is actually observed is an appropriate linear sum of the spectra S of M fragment gases produced by the thermal decomposition of each polymer.

[0199] The above feature of this embodiment is that the coefficient matrix is

number

number

number

number

[0200] In addition, here

number

[0201] In the following description, the symbols used in the description of the first embodiment will be replaced as shown in the table below.

[0202] [Table 1]

[0203] In the following description, we will follow many of the notations commonly used in signal processing.

number

[0204] represents a non-negative or real N × M matrix. A matrix

number

number

number

number

number

[0205] (1st NMF)

number

[0206] Input: Data matrix

number

[0207] Output: distribution matrix

number

number

[0208] The first NMF was developed to better suit the interpretation of MS (mass spectrometry) data by making the following three major changes to the ARD-SO-NMF proposed by Shiga et al.

[0209] 1) Variance-covariance matrix of Gaussian noise for each channel

number

[0210] 2) Applying soft orthogonal constraints between the base fragment spectra

[0211] 3) Merging fragment spectra with similar intensity distributions (extension of merging conditions)

[0212] Regarding 1), for the time being, we will use the variance σ 2 We assume that the noise is independent and uniformly distributed (iid) Gaussian, and introduce the variance-covariance matrix R along the way. If we assume that the noise is iid, the probability generation model for the data matrix X is

number

[0213] That is,

number

number

number

number

number

number

number

number

number

number

number

number

[0214] It is known that the assumption of an iid Gaussian distribution for noise does not hold for MS data, and larger signals tend to have larger noise.

number

number

number

number

number

number

number

number

number

number

number

number

number

number

number

number

number

number

number

number

number

number

[0215]

number

[0216] Here, similar components are merged each time A and S are updated. Shiga et al. proposed merging components with similar spectra, but here we also decided to merge components with similar intensity distributions. This allows isotope peaks, fragment series ionized by different ion additions, and oligomer peak series with different monomer numbers to be treated as a single component, providing results with greater interpretability.

[0217] (Derivation of Canonical correlation analysis filter (CCA-filter))

[0218] Input: 1st NMF output

number

number

[0219] Output: List of component numbers determined to be background origin

[0220] The M-components obtained in the first NMF include those derived from background and contaminants, which may distort the composition analysis results, so it is preferable to remove them from A and S. If the M′-component is determined to be a component derived from the background by the CCA-filter,

number

number

number

number

number

number

number

number

number

number

number

number

[0221] and

number

number

number

number

number

number

number

number

number

number

number

number

number

number

number

[0222] After the background components were identified, they were removed from the system by deleting the corresponding column vectors of A and row vectors of S. The output from the CCA filter is the M′-component from the background removed.

number

number

number

number

number

[0223] In the following sections, we frequently use non-negative least squares (NNLS) fitting. This problem is solved by finding optimal non-negative coefficients.

number

number

number

number

number

number

number

number

number

number

[0224] (2nd NMF)

[0225] Input: Represents the FA for each sample

number

number

[0226] Output: Polymer weight fraction per sample

number

number

[0227] Second NMF:

number

number

number

number

number

number

number

number

number

number

number

number

number

number

number

number

number

number

number

number

number

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number

number

number

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number

number

number

number

number

number

number

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number

number

number

number

number

number

number

number

number

number

[0228] Objective function

number

number

number

number

number

number

number

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number

number

number

number

number

[0229] (Projection of test data onto the hyperplane spanned by S and B) After estimating S and B from the dataset, we use data that was not used to estimate S and B (here called test data).

number

number

number

number

number

number

[0230] The dataset and hyperparameters are as follows.

[0231] [Table 2]

[0232] In addition, the cited references are as follows: [Table 3]

[0233] (Composition estimation device) Next, a composition estimation device according to an embodiment of the present invention will be described with reference to the drawings. Fig. 3 is a hardware configuration diagram of the composition estimation device according to an embodiment of the present invention.

[0234] The composition estimation apparatus 30 includes a mass spectrometer 31 and an information processing apparatus 33, and the mass spectrometer 31 includes a pressure reducing pump 32. The information processing apparatus 33 includes a processor 34, a storage device 35, a display device 36, and an input device 37, and the mass spectrometer 31 and the information processing apparatus 33 are configured to be able to transmit and receive data to and from each other.

[0235] The processor 34 may be, for example, a microprocessor, a processor core, a multiprocessor, an application-specific integrated circuit (ASIC), a field programmable gate array (FPGA), or a general-purpose computing on graphics processing units (GPGPU).

[0236] The storage device 35 has a function of temporarily and / or non-temporarily storing various programs and data, and provides a working area for the processor 34. The storage device 35 is, for example, a Read Only Memory (ROM), a Random Access Memory (RAM), a Hard Disk Drive (HDD), a flash memory, and a Solid State Drive (SSD).

[0237] The input device 37 can receive various types of information input, and can also receive input of instructions to the composition estimation apparatus 30. The input device 37 may be a keyboard, a mouse, a scanner, a touch panel, or the like.

[0238] The display device 36 can display the status of the composition estimation apparatus 30, the progress of the analysis, the composition estimation results, etc. The display device 36 may be a liquid crystal display, an organic EL (Electro Luminescence) display, or the like. Moreover, the display device 36 may be configured integrally with the input device 37. In this case, the display device 36 may be a touch panel display that provides a GUI (Graphical User Interface).

[0239] The information processing device 33, which includes a processor 34, a storage device 35, an input device 37, and a display device 36 that are capable of communicating data with each other via a data bus, is typically a computer.

[0240] Mass spectrometer 31 includes a pressure reducing pump 32, and is typically a mass spectrometer including a DART ion source, a specimen heating device, and a time-of-flight mass spectrometer. The ion source and mass spectrometer included in mass spectrometer 31 are both non-limiting examples, and the configuration of the mass spectrometer included in the composition estimation device is not limited to the above.

[0241] 4 is a functional block diagram of a composition estimation apparatus 30 according to an embodiment of the present invention. Composition estimation apparatus 30 has a mass analysis unit 41 that performs mass analysis of all samples, and an information processing unit 42 that processes the mass spectra obtained by mass analysis unit 41.

[0242] The mass analysis section 41 includes the mass analyzer 31, and is a function realized by the mass analyzer 31 being controlled by a control section 43, which will be described later. The mass analysis unit 41 heats the loaded sample set (sample, learning sample, and background sample, symbol a in FIG. 4 ) and ionizes the gas components produced by thermal desorption and / or pyrolysis, sequentially performs mass analysis, and outputs a mass spectrum (symbol c in FIG. 4 ). At this time, environmental factors arising from the environment in which the mass spectrometer 31 is installed (symbol b in FIG. 4, for example, (poly)dimethylsiloxane generated from the pressure reducing pump 32) are also loaded into the mass spectrometer 31 at the same time, affecting the mass spectrum.

[0243] Next, the function of each part of the information processing section 42 including the information processing device 33 will be described. The control unit 43 includes a processor 34. The control unit 43 realizes each function of the composition estimation device 30 by controlling each part.

[0244] The storage unit 44 includes the storage device 35. The storage unit 44 stores programs for controlling each unit in advance, and also provides a temporary or non-temporary storage area for data input and output by each unit. The storage unit 44 is controlled by the control unit 43, and can read and write data.

[0245] The input unit 45 is configured to include an input device 37. Moreover, the output unit 46 is configured to include a display device 36. By controlling these, the control unit 43 can receive input from a user of the composition estimation device 30, store this in the memory unit 44, transmit the information stored in the memory unit 44 to each unit, and display it to the user of the composition estimation device 30 via the output unit 46.

[0246] The data matrix creation unit 47 is a function that is realized when the control unit 43 executes a program stored in the storage unit 44 . The data matrix creation unit 47 creates a data matrix X from the two-dimensional mass spectrum in which the mass spectra (symbol c in FIG. 4) acquired for each heating temperature by the mass analysis unit 41 are stored in each row, and passes the data matrix X to the NMF processing unit 48 (symbol d in FIG. 4), which will be described later. Details of the data matrix X have already been described.

[0247] The NMF processing unit 48 is a function that is realized when a program stored in the storage unit 44 is executed by the control unit 43. The NMF processing unit 48 performs nonnegative matrix factorization (NMF) on the data matrix X (symbol d in FIG. 4) created by the data matrix creation unit 47, and calculates the product (X=C×S T The result is passed to the correction processing unit 49 (reference symbol e in FIG. 4). The details of the NMF processing have already been described.

[0248] The correction processing unit 49 is a function realized when the control unit 43 executes a program stored in the storage unit 44 . The correction processing unit 49 has a function of correcting the intensity distribution matrix by canonical correlation analysis between the basis spectrum matrix and the data matrix created by the NMF processing unit 48, and creating a corrected intensity distribution matrix. The created corrected intensity distribution matrix is ​​passed to the vector processing unit 50 (symbol f in FIG. 4).

[0249] In addition to the above-mentioned correction by canonical correlation analysis, the correction processing unit 49 may further perform the intensity correction already described. At this time, if there is a calibration sample composition (calibration sample composition) used for the intensity correction, it is passed to the correction processing unit 49 via the input unit 45 (symbol k in FIG. 4). The details of the correction by canonical correlation analysis (CCA filter) and the intensity correction have already been described.

[0250] The vector processing unit 50 is a function that is realized when the control unit 43 executes a program stored in the storage unit 44 . The vector processing unit 50 divides the corrected intensity distribution matrix created by the correction processing unit 49 into sub-matrices corresponding to each of all specimens, and expresses all specimens in vector space as feature vectors. This result is passed to the endmember determination unit 51 (symbol g in FIG. 4).

[0251] The end member determination unit 51 is a function that is realized when a program stored in the storage unit 44 is executed by the control unit 43 . The end member determination unit 51 sets a K-1 dimensional simplex that includes all of the feature vectors created by the vector processing unit 50, and determines K end members in the K-1 dimensional simplex. The result is passed to the content ratio calculation unit 52 (symbol h in FIG. 4).

[0252] At this time, when the learning sample contains an endmember and has a discrimination label, the discrimination label information is passed from the input unit 45 to the endmember determination unit 51 (symbol j in FIG. 4). However, as already explained, the discrimination label is not essential for determining the end members (the processing of the end member determination unit 51).

[0253] The content ratio calculation unit 52 is a function realized by the control unit 43 executing a program stored in the storage unit 44 . The content ratio calculation unit 52 calculates the Euclidean distance between the K endmembers determined by the endmember determination unit 51 and the characteristic vector of the estimation target specimen created by the vector processing unit 50, and estimates the content ratio of the K components in the estimation target specimen from the ratio of the Euclidean distances between the K endmembers and the characteristic vector of the specimen. The estimation result of the content ratio (symbol i in FIG. 4) is output from the output unit 46. At this time, the composition estimation results of the learning samples may also be output.

[0254] With this composition estimation device, even solid samples that are difficult to dissolve in solvents and difficult to perform conventional composition analysis can be analyzed without any special pretreatment, and accurate quantitative analysis results can be obtained. In particular, when this composition estimation device is applied to the quality control of samples that are mixtures of multiple components and to investigations of the causes of defects, it can significantly reduce the time required to obtain results. EXAMPLES

[0255] The composition analysis method of the present invention will be described in detail below with reference to examples. Note that the composition analysis method of the present invention should not be construed as being limited to the specific examples described below.

[0256] [Example 1] (Sample preparation) A dioxane solution (approximately 4% by mass, approximately 0.4 mg of polymer solid content) of three types of polymers, poly(methyl methacrylate) (symbol "M"), polystyrene (symbol "S"), and poly(ethyl methacrylate) (symbol "E"), was cast onto a sample pot and then air-dried overnight to obtain a specimen. Table 4 shows the composition of each specimen. Mass spectrometry was performed using a Shimadzu LCMS-2020 as a detector, an IonSense DART ion source, and a Biochromato ion rocket as a sample heater.

[0257] [Table 4]

[0258] The obtained mass spectrum was analyzed using an algorithm that implemented the following (i) to (iv).

[0259] (i) Soft orthogonal constraints on the C matrix ARD and the S matrix (ii) Merging conditions during NMF optimization (iii) Removal of NMF artifacts, background, and contamination using CCA-filter (iv) Quantitative analysis without the need for calibration by including environmental variables as correction terms

[0260] The hyperparameters used in the analysis are as follows: NMF: orthogonal constraint weight w=0.2, initial component number K=50, small positive number a=1+0.1 -15 , iteration number L=2000, threshold=0.9 CCA-Filter: t1=0.8,t2=0.2,

[0261] Figure 5 shows the original spectrum (A) for "MSE_calib" and the reconstructed spectrum (B) after the above processing. It can be seen that the waveforms of the two are similar. In other words, it was shown that the above processing preserved the characteristics of the original spectrum, making it easier to use for composition analysis.

[0262] In addition, in the original data, background signals such as phthalate esters emitted from air conditioners, etc., were observed at 390 m / z (in Figure 5 (A) marked "BG"), but this was removed in the reconstructed peak (B). Dioxane, the solvent used to prepare the sample (in Figure 5 (A) marked "DOX"), was also removed. All of these correspond to noise, and it was demonstrated that this method effectively removed noise.

[0263] Figure 6 shows a part of the C matrix after NMF decomposition, C δ(MSE_Calib) and S after removing the background and impurity spectra using the CCA-Filter. T It is.

[0264] Figure 7 shows the composition analysis results for the three-component system of M, S, and E. In Figure 7, the hollow circles and "Calibrated" in the legend indicate the composition estimation results for the sample when MSE_calib is used as the calibration sample, that is, when the composition information of MSE_calib is given as known and the intensity distribution matrix is ​​intensity corrected.

[0265] In addition, in Figure 7, the solid circles and the legend "Non-calibrated" indicate the composition estimation results of the specimen when the intensity distribution matrix was intensity-corrected using the product of the environmental variable (i.e., 610 m / z: peak intensity of polydimethylsiloxane) and the specimen mass.

[0266] In addition, in FIG. 7, the asterisks and the "Known" legend indicate the actual compositions (true values).

[0267] The results shown in Figure 7 show that excellent estimation results close to the true values ​​were obtained in both the “Calibrated” and “Non-calibrated” cases.

[0268] Next, Figure 8 shows the composition estimation results when the orthogonal constraint in (1) is released from the NMF conditions. The definition of each plot is the same as in Figure 7. The results in Figure 8 show that NMF with orthogonal constraints can produce better estimation results.

[0269] Next, Figure 9 shows NM This is the composition estimation result when only merging S is removed from the F optimization conditions. The definition of each plot is the same as in Figure 7. From the results in Figure 9, NM It was found that better estimation results were obtained when the F-optimization condition included merging S. Although the number of components can only be reduced to 36 by ARD, the importance of Merging S was demonstrated by the fact that the composition could be estimated more accurately with a component count of 9 when the Merging S conditions were maintained.

[0270] Figure 10 shows the composition estimation results when the CCA filter was turned off (comparative example). The definitions of each plot are the same as in Figure 7. In Figure 10, the calculation result for sample "SE" was that it contained about 1% M, even though the content of M was 0%. If 0% is estimated to be 1%, the estimation accuracy will be less than a few percent, which is not practical.

[0271] FIG. 11 shows the original spectrum for “MSE_calib” (top, raw of MSE_calib) and the reconstructed spectrum (bottom, reconstructed of MSE_calib) after the above processing with the CCA filter removed. These results show that when the CCA filter is removed, the noise of neither DOX nor BG (see the explanation of Figure 5) can be removed.

[0272] Figure 12 shows the composition estimation results when no correction by environmental variables was performed. In the results of Figure 12, "Non-calibrated" represented by a solid circle has a large deviation from Known, and it was found that the estimation results obtained are more accurate by correction by environmental variables.

[0273] [Example 2] (Estimated from samples that do not contain end members) In order to confirm that accurate estimation is possible even when the sample (group) including the learning sample does not contain end members, the samples shown in Table 5 were prepared and tests similar to those in Example 1 were performed. In the table, the symbols "M", "S", and "E" have the same meanings as in Table 4 (Example 1). In addition, each sample was adjusted so that the weight fraction of a single component (polymer) did not exceed 80%.

[0274] [Table 5]

[0275] For the above sample, a two-dimensional mass spectrum was obtained in the same manner as in Example 1, and converted into a data matrix. The obtained data matrix was subjected to the first NMF process already described, i.e.,

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[0276] Next, the CCA filter for A was applied, and the intensity was corrected by weight and standard peak. Note that, since temperature distribution information is not necessary for composition analysis, the sum was taken for each sample along the temperature axis,

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[0277] next,

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[0278] In addition, in the figure, BS shows the estimated spectra of the pure polymers E, M, and S superimposed on the actually measured spectra E, M, and S. There is no difference between the two, confirming that the spectra are well estimated, including the absolute intensities.

[0279] Thus, it was confirmed that the method of the present invention can accurately predict the spectra of the pure polymers E, M, and S, as well as the composition of the mixture, as shown in B-S of FIG. If there is test data, X test Project S and B continuously to C test get.

[0280] [Example 3] (Estimated based on a sample containing one end member) Next, we verified that when one of the (training) samples contains an endmember, the component contents in the other samples can be arbitrary (it does not have to be in the area outside the inscribed circle of the K-1-dimensional simplex).

[0281] Among the samples shown in Table 5, the samples containing 40% by mass or more of S were excluded, and the composition estimation was performed in the same manner as in Example 2, except that M pure polymer was added as a sample. Figure 16 shows the results.

[0282] In Fig. 16, the points represented by solid circles represent the estimation results of the samples used to estimate B and S, and the stars represent their actual compositions. From this result, it was confirmed that S could be estimated with high accuracy, even though there were no samples in the area outside the inscribed circle (hollow circles represent samples that were not used in the estimation). One of the reasons for the above is the non-orthogonal terms in the basis in the second NMF process (Eq.11) already explained.

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[0283] In many cases of material development, it is necessary to consider the performance of materials by reducing them to their constituent components. This requires identification and quantification of the components, but the more complex the system, the more difficult it becomes. High-resolution mass spectrometry, which has a low probability of overlapping peaks of different components, is the most powerful analytical method for identifying the chemical structures of components in complex mixtures. However, the problem with mass spectrometry is that it is not quantitative. In addition, although separation is not required in nature, the resulting spectra are complex and tend to be indecipherable in reality.

[0284] In this invention, we developed a method to directly pyrolyze the fragments of a material in air without pretreatment, analyze the resulting gas with DART-MS, and use unsupervised learning of the spectra to estimate the pure endmember spectra of each component and express the spectrum of the sample as a linear sum of the endmember spectra. This makes it possible to identify and quantify the components of a material with a complex composition without the need for separation.

[0285] Identification is relatively easy if a highly readable endmember spectrum from which all peaks derived from other components have been eliminated can be obtained. On the other hand, the fact that the ionization efficiency differs for each peak and the peak intensity and its abundance ratio are not proportional, which is an obstacle to quantitative analysis, is also true in the present invention. However, in the present invention, the peak intensity of each endmember spectrum can be estimated as an absolute intensity rather than a normalized relative value, so that when the specimen spectrum is expressed as a linear sum of the endmember spectra, the linear coefficient can be calculated as the composition ratio as it is.

[0286] This invention, which breaks down a sample into its components and determines the content ratios, will obviously be a valuable tool in material development, such as for identifying key components that are the factors that cause a material to exhibit its performance, but it is also expected to have an extremely wide range of applications, such as quality control, such as testing the content of degraded components, compliance testing for the content of hazardous materials, and testing to detect copyright infringement.It is also expected to accelerate technologies such as prediction of deterioration and lifespan of resins, detection of extremely small impurities in resins and organic materials, quantitative analysis of smell and taste, and tags to prevent food traceability and origin falsification.

[0287] In addition, the use of recycled materials is being promoted, with Plastics Europe proposing to the European Commission in September 2021 that plastic containers and packaging be required to contain 30% recycled plastic by 2030, but no general method has been established for measuring the content. This invention is also expected to be applied to quality control and compliance testing, as a technology that can accurately measure the ratio of virgin materials to recycled materials. [Explanation of symbols]

[0288] 10: K-1-dimensional simplex, 12: inscribed hypersphere, 13-15: endmember, 16-18: learning sample, 19: region, 30: composition estimation device, 31: mass spectrometer, 32: vacuum pump, 33: information processing device, 34: processor, 35: storage device, 36: display device, 37: input device, 41: mass analysis unit, 42: information processing unit, 43: control unit, 44: storage unit, 45: input unit, 46: output unit, 47: data matrix creation unit, 48: NMF processing unit, 49: correction processing unit, 50: vector processing unit, 51: endmember determination unit, 52: content ratio calculation unit

Claims

1. A method for estimating a content ratio of a component in a specimen to be estimated, the component including at least one component selected from K types of components, where K is an integer of 1 or more, the method comprising the steps of: Preparing K or more learning samples each containing at least one component selected from the K types of components and having a different composition from each other, and a background sample not containing the component; heating each of the samples in the sample set including the suspected sample, the learning sample, and the background sample, sequentially ionizing gas components generated by thermal desorption and / or pyrolysis, and continuously observing mass spectra; storing the mass spectrum obtained for each heating temperature in each row, obtaining a two-dimensional mass spectrum for each sample, and converting at least two of the two-dimensional mass spectra into a data matrix; performing an NMF process in which the data matrix is ​​decomposed into a non-negative matrix factorization and a product of a normalized basis spectrum matrix and its intensity distribution matrix; extracting noise components contained in an intensity distribution matrix by a canonical correlation analysis between the basis spectrum matrix and the data matrix, and correcting the intensity distribution matrix to reduce the influence of the noise components, thereby obtaining a corrected intensity distribution matrix; Dividing the corrected intensity distribution matrix into sub-matrices corresponding to each of the analytes, and expressing each of the analytes in a vector space using the sub-matrices as feature vectors; Setting a K-1 dimensional simplex that contains all of the feature vectors, and determining K end members in the K-1 dimensional simplex; calculating Euclidean distances between the K endmembers and the feature vector of the suspected target specimen, and estimating a content ratio of the components in the suspected target specimen based on a ratio of the Euclidean distances; When K is 3 or more, at least one of the feature vectors of the training sample is located in each of the outer regions of a hypersphere inscribed in the K-1-dimensional simplex, or the training sample includes at least one of the end members.

2. 2. The method of claim 1 , wherein K is an integer greater than or equal to 2, and the putative analyte of interest is a mixture of said components.

3. The method of claim 1 or 2, wherein the training sample comprises the end member.

4. The method of claim 3 , wherein the determination of the end members is based on discriminant labels attached to the training samples.

5. The method of claim 3 , wherein the determination of endmembers is performed by vertex component analysis of the feature vectors of the training exemplars.

6. The method of claim 1, wherein the determination of the endmembers is performed by an algorithm that determines vertices such that the K-1 dimensional simplex has a minimum volume.

7. The method of claim 6, wherein the endmembers are determined by a second NMF process that decomposes the corrected intensity distribution matrix into a non-negative matrix factorization, into a product of a matrix representing the weight fractions of K types of the components in the sample and a matrix representing the fragment presence intensities for each of the K types of individual components.

8. The method of claim 6 or 7, wherein the training sample does not include the end member.

9. The method of claim 1 , wherein obtaining the corrected intensity distribution matrix further comprises performing an intensity correction of the intensity distribution matrix.

10. the sample set further comprising a calibration sample; The calibration sample contains all of the K types of components and has a known composition; The method of claim 9 , wherein the intensity correction comprises normalizing the intensity distribution matrix.

11. the intensity correction includes assigning at least a portion of the intensity distribution matrix by a product of masses of corresponding analytes in the analyte set and environmental variables; The method of claim 9 , wherein the environmental variables are variables that represent an effect on ionization efficiency of the component during the observation.

12. The method according to claim 11, wherein the environmental variable is a sum of peaks of mass spectra of a compound having a molecular weight of 50 to 1500 contained in a predetermined amount in the atmosphere during the observation, or a mass spectrum of a low molecular weight organic compound having a molecular weight of 50 to 500 contained in a predetermined amount in each of the sample sets.

13. 1. A composition estimation device for estimating a content ratio of at least one component selected from K types of components, where K is an integer of 1 or more, in a estimation target specimen containing the component, the composition estimation device comprising: a mass spectrometer for heating each of K or more learning specimens, each of which contains at least one component selected from the K types of components and has a different composition from one another, a background specimen not containing the component, and the suspected target specimen, and sequentially ionizing gas components generated by thermal desorption and / or pyrolysis while heating each of the specimens, and continuously observing mass spectra; and an information processing device that processes the observed mass spectrum, The information processing device includes: a data matrix creation unit that stores the mass spectrum obtained for each heating temperature in each row, obtains a two-dimensional mass spectrum for each sample, and converts at least two of the two-dimensional mass spectra into a data matrix; an NMF processing unit that performs NMF processing to decompose the data matrix into a nonnegative matrix factorization and a product of a normalized basis spectrum matrix and its intensity distribution matrix; a correction processing unit that extracts noise components included in an intensity distribution matrix by a canonical correlation analysis between the basis spectral matrix and the data matrix, corrects the intensity distribution matrix to reduce the influence of the noise components, and creates a corrected intensity distribution matrix; a vector processing unit that divides the corrected intensity distribution matrix into sub-matrices corresponding to each of the sample sets, and represents each of the samples in a vector space using the sub-matrices as feature vectors; an end member determination unit that sets a K-1 dimensional simplex that includes all of the feature vectors and determines K end members in the K-1 dimensional simplex; a content ratio calculation unit that calculates the Euclidean distance between each of the K endmembers and a feature vector of the suspected target specimen, and estimates a content ratio of the components in the suspected target specimen based on a ratio of the Euclidean distances; When K is 3 or more, at least one of the feature vectors of the training sample is located in each of the outer regions of a hypersphere inscribed in the K-1 dimensional simplex, or the training sample includes at least one of the end members.

14. The composition estimation device according to claim 13 , wherein the endmember determination unit determines the endmembers based on discriminant labels attached to the training samples.

15. 14. The composition estimation device according to claim 13, wherein the end member determination unit determines the end members using an algorithm that determines vertices such that the K-1-dimensional simplex has a minimum volume.

16. The composition estimation device according to claim 15, wherein the endmember determination unit determines the endmembers by a second NMF process that performs non-negative matrix factorization on the corrected intensity distribution matrix and decomposes the matrix into a product of a matrix representing a weight fraction of the K types of components in the sample and a matrix representing fragment presence intensities for each of the K types of individual components.

17. The composition estimation device according to claim 15 , wherein the correction processing unit further performs intensity correction of the intensity distribution matrix.

18. the sample set further comprising a calibration sample; The calibration sample contains all of the K types of components and has a known composition; The composition estimation apparatus of claim 17 , wherein the intensity correction comprises normalizing the intensity distribution matrix.

19. the intensity correction includes assigning at least a portion of the intensity distribution matrix by a product of masses of corresponding analytes in the analyte set and environmental variables; The composition estimation device according to claim 17 , wherein the environmental variables are variables that represent the influence of the components on ionization efficiency during the observation.

20. The mass spectrometer further comprises a vacuum pump; 20. The composition estimation apparatus according to claim 19, wherein the environmental variable is a sum of peaks in a mass spectrum of a substance produced by operation of the pressure reducing pump.

21. A program used in a composition estimation device that estimates a content ratio of at least one component selected from K types of components, where K is an integer of 1 or more, in a estimation target specimen, the content ratio of the component being estimated, the program comprising: a mass spectrometer for heating each of K or more learning specimens, each of which contains at least one component selected from the K types of components and has a different composition from one another, a background specimen not containing the component, and the suspected target specimen, and sequentially ionizing gas components generated by thermal desorption and / or pyrolysis while heating each of the specimens, and continuously observing mass spectra; and an information processing device that processes the observed mass spectrum, a data matrix creation function that stores the mass spectra acquired for each heating temperature by the mass spectrometer in each row, obtains a two-dimensional mass spectrum for each sample, and converts at least two or more of the two-dimensional mass spectra into a data matrix; an NMF processing function for performing NMF processing to decompose the data matrix into a non-negative matrix factorization and a product of a normalized basis spectrum matrix and its intensity distribution matrix; a correction processing function for extracting noise components contained in an intensity distribution matrix by a canonical correlation analysis between the basis spectrum matrix and the data matrix, and correcting the intensity distribution matrix to reduce the influence of the noise components, thereby creating a corrected intensity distribution matrix; a vector processing function for dividing the corrected intensity distribution matrix into sub-matrices corresponding to each of the analytes, and expressing each of the analytes in a vector space using the sub-matrices as feature vectors; an end member determination function for setting a K-1 dimensional simplex that includes all of the feature vectors and determining K end members in the K-1 dimensional simplex; a content ratio calculation function for calculating the Euclidean distance between each of the K end members and the feature vector of the suspected target specimen, and estimating a content ratio of the components in the suspected target specimen based on a ratio of the Euclidean distances; When K is 3 or more, at least one of the feature vectors of the training sample is located in each of the outer regions of a hypersphere inscribed in the K-1-dimensional simplex, or the training sample includes at least one of the end members.

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