Computer-readable recording medium storing arithmetic program, arithmetic method, and information processing device

Abstract

The invention discloses a non-transitory computer-readable recording medium storing an arithmetic program, an arithmetic method, and an information processing apparatus. An arithmetic program for causing a computer to execute a process including: generating a first vector by extracting each element of a matrix of a plurality of pieces of analysis data represented as two-dimensional data; creating a first normalized vector by normalizing each element of the first vector; generating a second vector by extracting each element of a matrix of characteristic data corresponding to the plurality of pieces of analysis data; creating a second normalized vector by normalizing each element of the second vector; and specifying a correspondence relationship between elements included in the first vector and elements included in the second vector according to a similarity between the first normalization vector and the second normalization vector.

Description

Technical Field

[0001] The present application relates to a non-transitory computer-readable recording medium storing an arithmetic program, an arithmetic method, and an information processing device. Background Art

[0002] There has been disclosed a technique for analyzing analysis data obtained by analyzing a substance to be analyzed.

[0003] As related technologies, Japanese Laid-Open Patent Publication No. 2005-010931, Japanese Laid-Open Patent Publication No. 2007-164772, and Japanese Laid-Open Patent Publication No. 2018-119897 are disclosed. Summary of the invention

[0004] Technical issues

[0005] It is necessary to predict the material composition, material structure, chemical state, etc. that exhibits desired physical properties and functions by correlating the obtained analysis data with characteristic data including physical properties, etc. In view of the above, techniques using mathematics and statistical sciences have been proposed. The mathematics and statistical science techniques mainly used are regression analysis. However, in regression analysis, despite the complex processing of selecting an appropriate hyperparameter λ, the obtained results include inaccurate results.

[0006] In one aspect, an object of the present application is to provide an arithmetic program, an arithmetic method, and an information processing apparatus capable of obtaining highly accurate results.

[0007] Solution to the problem

[0008] According to one aspect of the embodiment, a non-transitory computer-readable recording medium storing an arithmetic program is provided, the arithmetic program being used to cause a computer to perform processing including: generating a first vector by extracting each element of a matrix of multiple pieces of analysis data represented as two-dimensional data; creating a first normalized vector by normalizing each element of the first vector; generating a second vector by extracting each element of a matrix of characteristic data corresponding to the multiple pieces of analysis data; creating a second normalized vector by normalizing each element of the second vector; and specifying a correspondence between elements included in the first vector and elements included in the second vector based on a similarity between the first normalized vector and the second normalized vector.

[0009] Beneficial effects of the present invention

[0010] Highly accurate results can be obtained. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 is a diagram illustrating an X-ray diffraction spectrum;

[0012] Figure 2 is a diagram illustrating the setting of target variables and explanatory variables;

[0013] Figure 3 is a diagram illustrating the analysis results;

[0014] Figure 4 is a graph illustrating the results of the changes in regression coefficients;

[0015] Figure 5 It is used to check Figure 4 A diagram showing whether the results shown are correct;

[0016] Fig. 6A is a functional block diagram illustrating the overall configuration of an information processing apparatus, and Figure 6B is a block diagram illustrating a hardware configuration of an information processing apparatus;

[0017] Figure 7 is a flowchart illustrating an exemplary operation of an information processing apparatus;

[0018] Figure 8 is a flowchart illustrating an exemplary operation of an information processing apparatus;

[0019] Fig. 9 is a flowchart illustrating an exemplary operation of an information processing apparatus;

[0020] Fig.10 is a diagram illustrating calculation results; and

[0021] Fig.11 is a diagram illustrating calculation results. DETAILED DESCRIPTION

[0022] In order to develop new materials and new substances with new physical properties and functions or to improve the physical properties and functions of existing materials and existing substances, physical analysis and chemical analysis are performed on materials and substances. In this physical and chemical analysis, the mass-to-charge ratio (m / z) in the case of mass analysis, the wave number (1 / cm) in the case of infrared spectroscopy analysis, and the diffraction angle (2θ) in the case of X-ray diffraction analysis are used as parameters. The analytical data obtained by the analysis are obtained as two-dimensional data, such as a spectrum, in which the signal intensity (detection signal value) on the vertical axis obtained by each detector is recorded for a change parameter with the horizontal axis as a parameter. Alternatively, in the case of electron microscopy observation, two-dimensional data, such as an image, is obtained, in which the grayscale obtained by the accompanying detector is recorded as a detection signal value for a change parameter with the scanning position of the electron beam as a parameter.

[0023] These analysis data are correlated with characteristic data including physical properties to predict material composition, material structure, chemical state, etc. that exhibit desired physical properties and functions. In this correlation, it is very important to find out which part of the two-dimensional data is closely related to the characteristics. For example, correlation is performed by repeated construction and verification of temporary structures based on physical principles and chemical principles, which requires high expertise and extensive experience, and in addition, it usually takes a lot of time.

[0024] In view of the above, in order to improve efficiency, techniques using mathematics and statistical science have been proposed. The main mathematics and statistical science technique used is regression analysis. In regression analysis, characteristic values ​​are used as target variables, and two-dimensional data are used as explanatory variables. Then, the explanatory variable with the maximum regression coefficient obtained as a result of regression analysis is considered to be the part most closely related to the target variable. In recent years, in order to suppress overtraining, regression analysis using regularization has been used to improve analysis accuracy. Regression analysis using regularization is the following technique.

[0025] As in the following formula (1), it is assumed that there are m+1 explanatory variables y for n+1 target variables s. Both the target variable s and the explanatory variable y are represented by vectors.

[0026] [Mathematical formula 1]

[0027] s=(s0,s1,…,s n ), y=(y0,y1,…,y m ) (1)

[0028] Each of the predicted value and the regression coefficient is expressed as the following formula (2): Both the predicted value and the regression coefficient are expressed by vectors.

[0029] [Mathematical formula 2]

[0030]

[0031] In this case, the linear regression equation can be expressed by the following equation (3): Note that w0y0 represents the intercept.

[0032] [Mathematical formula 3]

[0033]

[0034] When the above equation (3) is expressed by a vector, the following equation (4) is obtained.

[0035] [Formula 4]

[0036]

[0037] In multiple regression analysis, the number of predicted values ​​is not one, and the regression coefficients are obtained from a large number of training data. Therefore, the number of predicted values ​​is equal to the number of training data. The sample size is n+1, which is the number of target variables, and is expressed as the following formula (5).

[0038] [Formula 5]

[0039]

[0040] The weight w (regression coefficient) is specified so that there is no separation between the predicted value and the actual s as the target variable. In the multiple regression analysis, the least squares method is used to determine the parameters so that the loss function L represented by the following equation (6) is minimized.

[0041] [Mathematical formula 6]

[0042]

[0043] In regularization, a function obtained by adding a regularization term to the loss function L is set as a new minimization target. Examples of representative regularization terms include the L2 regularization term of the following equation (7) and the L1 regularization term of the following equation (8). Note that λ represents a hyperparameter that can be freely determined.

[0044] [Formula 7]

[0045] L2 Regularization:

[0046] [Mathematical formula 8]

[0047] L1 Regularization:

[0048] When minimizing the loss function with the regularization term added, the coefficients of the variables that do not contribute to the target variable are reduced compared to the case where the regularization term is not added, and the substantial number of explanatory variables is reduced, and the effect of suppressing overtraining can be obtained. By manipulating the λ of the regularization term, the influence of regularization can be manipulated. As the value of λ increases, the influence of the regularization term increases, and the number of items with coefficient values ​​of 0 in the explanatory variable group increases. Specifically, an optimization problem of the regression function represented by the following formula (9) is obtained, and the regression coefficient w is optimized (L1 regularization) as in the following formula (10).

[0049] [Mathematical formula 9]

[0050]

[0051] [Formula 10]

[0052]

[0053] An example of regression analysis using regularization is described below. For example, suppose that Figure 1 The X-ray diffraction spectrum of a material is shown. Assume Figure 1 The X-ray diffraction spectrum in is represented as the sum of eight spectra containing different proportions of a substance. Figure 1 Each intensity value of the X-ray diffraction spectrum in contains eight spectra as components. When the eight spectra (data 7, data 8, data 9, data 10, data 17, data 19, data 21 and data 22) and their corresponding characteristics (abundance ratio of a certain element: 0%, 0.25%, 0.5%, 0.75%, 0.11%, 0.14%, 0.06%, 0.46%) are compared with the above formulas (5) to (8) and as shown in Figure 2 When we set the target variable and explanatory variables in this way to perform regularized regression analysis, we get Figure 3 result.

[0054] Figure 3 It is shown that only two diffraction angles, 23.3 degrees and 29.5 degrees, among a set of 4,350 explanatory variables (diffraction angles) have regression coefficients, and the regression coefficients associated with the other diffraction angles are 0. However, 23.3 degrees indicates a negative value, and 29.5 degrees indicates a positive value. In the X-ray diffraction spectrum, a negative value indicates that the intensity at 23.3 degrees is inversely proportional to a characteristic (abundance ratio of a certain element), and a positive value indicates a proportional relationship.

[0055] As mentioned above, although Figure 3 Although the results are easy to understand, it is necessary to set the hyperparameter λ to an appropriate value in the regularization process. As a method for setting λ, a technique of sweeping the value of λ within a certain range is adopted. As described above, as the value of λ increases, the number of items with coefficient values ​​of 0 in the explanatory variable group increases, and the regression coefficient gradually shrinks.

[0056] Then, the appropriate term is selected from the reduced regression coefficients and the value of the explanatory variable associated with it is set to the target value, that is, the part of the spectrum that shows the strongest relationship with the characteristic. For example, when λ is swept from 0.01 to 100 and the change in the regression coefficient associated with it is examined, we obtain Figure 4 As the value of λ increases, the remaining two are 23.3 degrees and 29.5 degrees. Figure 3 It is assumed that when λ = 50, the remaining regression coefficient is based on Figure 3 The graph is obtained by taking appropriate values ​​of . Figure 5 It is used to check Figure 4The results shown in the figure are correct. The diffraction X-ray intensity at 29.5 degrees increases as the abundance ratio increases, and it is found that this part is closely related to the abundance ratio. On the other hand, the diffraction X-ray intensity at 23.3 degrees tends to decrease slightly as the abundance ratio increases, and is considered to be related to the abundance ratio to a certain extent, but it is difficult to see a close relationship.

[0057] In view of these results, it can be said that according to the above technology, despite the complex processing of selecting an appropriate hyperparameter λ, the obtained results include inaccurate results. Therefore, in the following embodiments, an exemplary case in which highly accurate results can be obtained without undergoing a complex processing will be described.

[0058] [First embodiment]

[0059] First, the principle of the first embodiment will be described.

[0060] For two-dimensional data such as spectra, images, etc. obtained as a result of physical and chemical analysis, when m+1 vertical axis values ​​y corresponding to each x are obtained as analysis data relative to m+1 horizontal axis values ​​x, each of them is expressed as the following formula (11). The horizontal axis value x and the vertical axis value y are represented by vectors.

[0061] [Mathematical formula 11]

[0062] x=(x0,x1,·····,x m ), y=(y0, y1,·····,y m ) (11)

[0063] In addition, when there are n+1 pieces of analysis data (e.g., spectra) represented by the above formula (11) and there are n+1 characteristic values ​​s corresponding to each piece of analysis data as in the following formula (12), the analysis data can be expressed as a matrix Y and characteristic value s as in the following formula (13).

[0064] [Mathematical formula 12]

[0065] s=(s0,s1,……,s n ) (12)

[0066] [Mathematical formula 13]

[0067]

[0068] Here, each column of Y is expressed as the following equation (14) to be extracted as the first vector. Note that the vector of the above equation (12) is the second vector.

[0069] [Formula 14]

[0070] yi =(y i0 ,y i1 , ..., y in ), i=0, 1, ..., m (14)

[0071] Next, yi is normalized to create a first normalized vector, and s is normalized to create a second normalized vector. p The norm performs normalization, the L p The norm is the length of each vector represented by the following equations (15) and (16). Therefore, normalization is performed so that the sum of the detection signal values ​​becomes constant.

[0072] [Mathematical formula 15]

[0073]

[0074] [Formula 16]

[0075]

[0076] The normalized values ​​are expressed by the following equations (17) and (18).

[0077] [Mathematical formula 17]

[0078]

[0079] [Mathematical formula 18]

[0080]

[0081] Next, calculate z s With z yi For example, as z s With z yi The similarity between them is calculated as the cosine similarity as shown in the following formula (19). Next, the z closest to 1 in the following formula (19) is extracted. yi and the z closest to -1 yi .

[0082] [Mathematical formula 19]

[0083]

[0084] As the cosine similarity approaches 1, the similarity increases, and as the cosine similarity approaches -1, the direction of the vector approaches the opposite direction. Therefore, the z vector with the cosine similarity closest to 1 yi With z s The z with the strongest positive relationship and cosine similarity closest to -1 yihas the strongest negative relationship. Here, positive and negative represent proportional and inversely proportional, respectively. It can be said that given this z yi x i It is the part of the two-dimensional data that shows the strongest relationship with the feature.

[0085] Next, a specific device configuration and the like of the present embodiment will be described. Fig. 6A 1 is a functional block diagram illustrating the overall configuration of the information processing apparatus 100 according to the first embodiment. Fig. 6A As illustrated, the information processing apparatus 100 functions as an acquisition unit 10 , a vector creation unit 20 , a normalization unit 30 , a similarity calculation unit 40 , a specification unit 50 , an output unit 60 , and the like.

[0086] Figure 6B is a block diagram illustrating the hardware configuration of the information processing apparatus 100. Figure 6B As illustrated, the information processing apparatus 100 includes a central processing unit (CPU) 101 , a random access memory (RAM) 102 , a storage device 103 , an input device 104 , a display device 105 , and the like.

[0087] CPU 101 is a central processing unit. CPU 101 includes one or more cores. RAM 102 is a volatile memory that temporarily stores programs to be executed by CPU 101, data to be processed by CPU 101, etc. Storage device 103 is a non-volatile storage device. As storage device 103, for example, read-only memory (ROM), solid-state drive (SSD) such as flash memory, hard disk to be driven by hard disk drive, etc. can be used. Storage device 103 stores arithmetic programs. Input device 104 is an input device such as a keyboard or a mouse. Display device 105 is a display device such as a liquid crystal display (LCD). CPU 101 executes arithmetic programs to implement acquisition unit 10, vector creation unit 20, normalization unit 30, similarity calculation unit 40, designation unit 50 and output unit 60, etc. Note that hardware such as dedicated circuits can be used as acquisition unit 10, vector creation unit 20, normalization unit 30, similarity calculation unit 40, designation unit 50 and output unit 60, etc.

[0088] Figures 7 to 9 is a flowchart showing an exemplary operation of the information processing apparatus 100. Figure 7 As illustrated, the acquisition unit 10 acquires analysis data of samples 1 to n (step S1). The analysis data is two-dimensional data that records the signal intensity (detection signal value) on the vertical axis obtained by the detector for a variation parameter with the horizontal axis as a parameter.

[0089] Next, the vector creation unit 20 represents each piece of analysis data obtained in step S1 with a vector as in the above equation (13) (step S2) However, it is assumed that for each piece of analysis data, for m+1 x coordinates, there are m+1 y coordinates.

[0090] Then, the normalization unit 30 extracts each column of the matrix obtained in step S2 as a vector and uses L p The norm normalizes the elements as in the above equation (18) (step S3).

[0091] In parallel with steps S1 to S3, Figure 8 As illustrated, the acquisition unit 10 obtains characteristic data of samples 1 to n (step S11 ).

[0092] Next, the vector creation unit 20 expresses each piece of characteristic data obtained in step S11 by a vector as in the above-mentioned equation (13) (step S12).

[0093] Next, the normalization unit 30 uses L p The norm normalizes the elements of the matrix obtained in step S12 as in the above equation (17) (step S13).

[0094] After executing step S3 and after executing step S13, as Fig. 9 As shown in the example, the similarity calculation unit 40 calculates z as shown in the above equation (19). s With z yi The cosine similarity cos(x, y) between them (step S21).

[0095] Next, the designation unit 50 extracts the z whose cosine similarity is closest to 1. yi and the z closest to -1 yi , and specify that z yi x i As the part of the analysis data that shows the strongest relationship with the characteristic (step S22). The output unit 60 outputs the result specified by the specifying unit 50. The output result is displayed, for example, by the display device 105. For example, the display device 105 graphically displays the relationship between the detection signal value (y coordinate value) and the characteristic value in the extracted parameter value (x coordinate value).

[0096] As described above, according to the present embodiment, each element of the matrix of multiple analysis data represented as two-dimensional data is extracted as a first vector, and a first normalized vector normalized for each element is obtained. In addition, each element of the matrix of characteristic data corresponding to the multiple analysis data is extracted as a second vector, and a second normalized vector normalized for each element is obtained. The correspondence between the elements included in the first vector and the elements included in the second vector is obtained based on the similarity between the first normalized vector and the second normalized vector. In this way, highly accurate results can be obtained without going through a complex processing process of selecting appropriate hyperparameters.

[0097] Next, the usefulness of the present embodiment will be described with respect to the above eight X-ray diffraction spectra (Data 7, Data 8, Data 9, Data 10, Data 17, Data 19, Data 21, and Data 22). The characteristic value s represents the abundance ratio of a certain element, and yi represents the y coordinate of each of the eight spectra having 4,351 x coordinates. The characteristic value s, x coordinate, and y i It can be expressed by the following equations (20) to (22).

[0098] [Mathematical formula 20]

[0099] s=(0, 0.25, 0.5, 0.75, 0.11, 0.14, 0.06, 0.46) (20)

[0100] [Mathematical formula 21]

[0101] x=(x0,x1,…,y 4350 ) (twenty one)

[0102] [Mathematical formula 22]

[0103] yi=(y i0 ,y i1 ,·····,y i7 ), i=0, 1,·····,4350 (22)

[0104] Based on the above equations (14) to (19), the cosine similarity of the above equations (20) and (22) is calculated to obtain Fig.10 Note that L for p = 1 1 The norm is used as the norm.

[0105] exist Fig.10 In the example, the diffraction X-ray intensity at the diffraction angle of 38.48 degrees, where the similarity is closest to 1, is plotted against the abundance ratio to obtain Fig.11 .like Fig.11 As shown, a favorable proportional relationship is obtained. Note that Fig.10It can be seen that there is no negative result indicating similarity in the results according to the present embodiment. Therefore, in the spectrum, the abundance ratio does not appear inversely proportional.

[0106] Although Fig.10 and Fig.11 Shows the use of L 1 norm, but using L 2 Norm, L 3 Norm or L 4 Similar results can be obtained with the norm. In addition, Fig.11 The results can also be used as a highly accurate calibration curve when searching analytical data for unknown properties.

[0107] As described above, according to this embodiment, using L p After norm normalization, similarity evaluation is performed using cosine similarity, which allows the extraction of the portion of two-dimensional data such as spectra, images, etc. that exhibits the strongest relationship with the characteristics. Fig.11 The result indicates that the result is appropriate. In addition, although searching for appropriate hyperparameters involves complicated work, favorable results can be obtained by simple calculation according to the present embodiment. In addition, the accuracy is clearly indicated by the numerical value of the similarity. On the other hand, although information about negative relationships is extracted according to the technique using regularized regression analysis, Figure 4 Indicates that the information is inaccurate. As described above, it can be said that this embodiment is a more useful technology.

[0108] Although the embodiment has been described in detail above, the present embodiment is not limited to such specific embodiment, and various modifications and changes may be made within the scope of the gist of the present embodiment described in the claims.

Claims

1. A non-transitory computer-readable recording medium storing an arithmetic program for causing a computer to execute a process comprising: generating a first vector by extracting each element of a matrix of a plurality of pieces of analysis data represented as two-dimensional data; creating a first normalized vector by normalizing each element of the first vector; generating a second vector by extracting each element of a matrix of characteristic data corresponding to the plurality of pieces of analysis data; creating a second normalized vector by normalizing each element of the second vector; and A correspondence relationship between elements included in the first vector and elements included in the second vector is specified according to a similarity between the first normalized vector and the second normalized vector.

2. The non-transitory computer-readable recording medium according to claim 1, wherein When normalizing the first vector and the second vector, a norm is used for the normalization.

3. The non-transitory computer-readable recording medium according to claim 1, wherein: When the parameter is set as the horizontal axis of the plurality of analysis data, the vertical axis coordinate is extracted as a matrix of the plurality of analysis data, The cosine similarity is calculated as the similarity between the first normalized vector and the second normalized vector, and A vector whose cosine similarity is closest to 1 and a vector whose cosine similarity is closest to -1 are extracted from the first normalized vectors, and the coordinates of each of the extracted vectors are assigned from the horizontal axis coordinates of the plurality of analysis data.

4. The non-transitory computer-readable recording medium according to claim 1, wherein: The analysis data includes spectral data or image data.

5. An arithmetic method implemented by a computer, the arithmetic method comprising: generating a first vector by extracting each element of a matrix of a plurality of pieces of analysis data represented as two-dimensional data; creating a first normalized vector by normalizing each element of the first vector; generating a second vector by extracting each element of a matrix of characteristic data corresponding to the plurality of pieces of analysis data; creating a second normalized vector by normalizing each element of the second vector; and A correspondence relationship between elements included in the first vector and elements included in the second vector is specified according to a similarity between the first normalized vector and the second normalized vector.

6. An information processing device, comprising: a vector creation unit configured to generate a first vector by extracting each element of a matrix of a plurality of pieces of analysis data represented as two-dimensional data, and to generate a second vector by extracting each element of a matrix of characteristic data corresponding to the plurality of pieces of analysis data; a normalization unit configured to: create a first normalized vector by normalizing each element of the first vector, and create a second normalized vector by normalizing each element of the second vector; as well as A specifying unit configured to specify a correspondence relationship between elements included in the first vector and elements included in the second vector according to a similarity between the first normalized vector and the second normalized vector.

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