Computing system, learning method of fitting algorithm, and computer

Abstract

To separate a spectrum into a plurality of peaks by using an arbitrary fitting function without a local solution.SOLUTION: A system for learning a fitting algorithm for calculating a model function approximating a spectrum repeatedly performs fitting processing that includes addition processing which adds to the model function a new peak function and optimizes a parameter on the basis of a parameter of the peak function calculated by an additional algorithm and deletion processing which deletes the peak function from the model function and optimizes the parameter on the basis of a deletion condition calculated by a deletion algorithm, generates an additional algorithm by performing machine learning using first history data to be an execution history of the addition processing, and generates the deletion algorithm by performing the machine learning that uses second history data to be a performance history of the deletion processing.SELECTED DRAWING: Figure 3

Description

[Technical field]

[0001] The present invention relates to a technique for calculating a model function that approximates a spectrum. [Background technology]

[0002] X-ray diffraction equipment is used to measure the physical properties of samples. The measurement results are obtained as a diffraction pattern (spectrum). A spectrum contains waveforms derived from multiple physical phenomena. Therefore, it is necessary to separate the spectrum into multiple peaks.

[0003] As a technique for separating a spectrum into a plurality of peaks, for example, the technique described in Patent Document 1 is known.

[0004] Patent Document 1 describes that "an EM algorithm of a mixed Gaussian distribution is applied to separate overlapping peaks on a chromatogram. However, since the number of models, i.e., the number of overlapping components itself, is unknown here, the number of models is appropriately set (S1), and model parameters are fitted while appropriately distributing the measured signal to each model using the EM algorithm (S2, S3). Then, if the solution converges (Yes in S4), it is determined whether or not there is a peak-like waveform in the undistributed residual signal (S5), and if there is a peak-like waveform, a peak model is added (S6) and the EM algorithm is executed again. In the M step, optimization is performed using not only a simple Gaussian function, but also a modified Gaussian function that assumes tailing. Also, in the M step, optimization of both the chromatogram waveform and the spectral waveform is performed by repeatedly estimating the spectrum assuming a chromatogram and estimating the chromatogram assuming a spectrum." [Prior art documents] [Patent documents]

[0005] [Patent Document 1] International Publication No. 2016 / 35167 Summary of the Invention [Problem to be solved by the invention]

[0006] In the EM algorithm described in Patent Document 1, the fitting function is limited to a Gaussian function, and there is a possibility that the algorithm may fall into a local solution.

[0007] The present invention aims to provide a system, method and apparatus for separating a spectrum into multiple peaks using an arbitrary fitting function without getting stuck in a local minimum. [Means for solving the problem]

[0008] A representative example of the invention disclosed in the present application is as follows: That is, a computer system for learning a fitting algorithm for calculating a model function approximating a spectrum obtained by plotting observed values ​​corresponding to values ​​of variables characterizing an observation target, the computer system includes a processor, a storage device connected to the processor, and a communication device connected to the processor, the model function is a function obtained by superimposing peak functions having different parameters characterizing a peak, the fitting algorithm includes an addition algorithm for calculating the parameters of the peak function to be added, and a deletion algorithm for calculating deletion conditions for selecting the peak function to be deleted from the model function, the computer system receives an input of the spectrum, generates an initial model function, and performs the following steps based on the parameters calculated by the addition algorithm: a fitting process including an addition process of adding a new peak function to a model function and optimizing the parameters of the peak function included in the model function so as to approximate the spectrum, and a deletion process of deleting the peak function from the model function based on the deletion condition calculated by the deletion algorithm and optimizing the parameters of the peak function included in the model function so as to approximate the spectrum, is repeatedly performed until a convergence condition for an index for evaluating the degree of fitting of the model function to the spectrum is satisfied, and the addition algorithm is generated by performing machine learning using first history data which is an execution history of the addition process, and the deletion algorithm is generated by performing machine learning using second history data which is an execution history of the deletion process. Effect of the Invention

[0009] According to the present invention, the system can separate a spectrum into multiple peaks using any fitting function without falling into a local optimum. Problems, configurations and effects other than those described above will become apparent from the following description of the embodiments. [Brief description of the drawings]

[0010] [Figure 1] FIG. 1 illustrates an example of a system configuration according to a first embodiment. [Diagram 2] FIG. 2 is a diagram illustrating an example of a hardware configuration of a computer that configures the system of the first embodiment. [Diagram 3] FIG. 2 is a diagram illustrating an example of a functional configuration of the algorithm learning system according to the first embodiment. [Figure 4A] FIG. 13 is a diagram showing an example of adding and deleting peaks in the fitting algorithm of the first embodiment. [Figure 4B] FIG. 13 is a diagram showing an example of adding and deleting peaks in the fitting algorithm of the first embodiment. [Diagram 5] FIG. 2 illustrates an example of a functional configuration of a spectrum analysis system according to a first embodiment. [Figure 6] 1 is a flowchart illustrating an example of a process executed by the algorithm learning system according to the first embodiment. [Figure 7] FIG. 2 is a diagram showing an example of a data structure of data generated by the algorithm learning system of the first embodiment. [Figure 8] 4 is a flowchart illustrating an example of a process executed by the spectrum analysis system according to the first embodiment. [Figure 9] FIG. 2 is a diagram illustrating an example of a data structure of data generated by the spectrum analysis system according to the first embodiment. [Figure 10] 4 is a flowchart illustrating an example of a process executed by the feature estimation system according to the first embodiment. [Figure 11] 4 is a flowchart illustrating an example of a process executed by the feature estimation system according to the first embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0011] Hereinafter, an embodiment of the present invention will be described with reference to the drawings. However, the present invention is not to be interpreted as being limited to the description of the embodiment shown below. It will be easily understood by those skilled in the art that the specific configuration can be changed without departing from the concept or purpose of the present invention.

[0012] In the configurations of the invention described below, the same or similar configurations or functions are given the same reference numerals, and duplicated explanations are omitted.

[0013] In this specification, the terms "first," "second," "third," and the like are used to identify components and do not necessarily limit the number or order. EXAMPLES

[0014] Fig. 1 is a diagram illustrating an example of a system configuration of the first embodiment. Fig. 2 is a diagram illustrating an example of a hardware configuration of a computer that constitutes the system of the first embodiment.

[0015] The system includes an algorithm learning system 100, a spectrum analysis system 101, a feature estimation system 102, and a terminal 103. Each system is connected via a network 104 such as a wide area network (WAN) or a local area network (LAN).

[0016] The algorithm learning system 100 learns the fitting algorithm used by the spectrum analysis system 101 .

[0017] The fitting algorithm is an algorithm for separating a spectrum into multiple peaks. More specifically, the fitting algorithm is an algorithm for outputting a model function that approximates the spectrum. The model function is a function obtained by superimposing multiple fitting functions (peak functions). The peak function is, for example, a Gaussian function, a Lorentz function, a Voigt function, or the like. Note that the present invention is not limited to the type of peak function.

[0018] The spectrum analysis system 101 separates the spectrum into multiple peaks using a fitting algorithm, that is, a model function that approximates the spectrum is calculated.

[0019] The feature estimation system 102 separates a spectrum into multiple peaks using a prediction model generated by machine learning, and extracts features of the spectrum, such as the position and width of the peaks, and the integrated intensity.

[0020] The terminal 103 is a terminal operated by a user who uses each system.

[0021] Each system is configured, for example, with a computer 200 shown in Fig. 2. The computer 200 has a processor 201, a main memory device 202, a secondary memory device 203, a communication device 204, an input device 205, and an output device 206. Each hardware element is connected via a bus 207.

[0022] The processor 201 executes a program stored in the main memory device 202. The processor 201 executes processing according to the program, thereby operating as a functional unit (module) that realizes a specific function. In the following explanation, when a process is explained with a functional unit as the subject, it indicates that the processor 201 is executing a program that realizes the functional unit.

[0023] The main memory 202 is a storage device that stores the programs executed by the processor 201 and the information executed by the programs, and is, for example, a volatile or non-volatile memory. The main memory 202 is also used as a work area. The secondary memory 203 is a storage device that permanently stores the programs and information, and is, for example, a hard disk drive (HDD) and a solid state drive (SSD).

[0024] The programs and information stored in the primary storage device 202 may be stored in the secondary storage device 203. In this case, the processor 201 reads the programs and information from the secondary storage device 203 and loads them into the primary storage device 202.

[0025] The communication device 204 is a device for communicating with an external device or system, such as a NIC. The input device 205 is a device for inputting data and instructions, such as a keyboard, a mouse, a touch panel, etc. The output device 206 is a device for outputting various information, such as a display, etc.

[0026] The algorithm learning system 100, the spectrum analysis system 101, and the feature estimation system 102 may be realized as a single system. Also, any combination of the algorithm learning system 100, the spectrum analysis system 101, and the feature estimation system 102 may be realized as a single system.

[0027] Fig. 3 is a diagram illustrating an example of a functional configuration of the algorithm learning system 100 according to the first embodiment. Fig. 4A and Fig. 4B are diagrams illustrating an example of adding and deleting peaks in the fitting algorithm according to the first embodiment.

[0028] The algorithm learning system 100 includes an optimization unit 300, a peak addition unit 301, a peak deletion unit 302, a change amount calculation unit 303, a residual curve calculation unit 304, a residual feature amount calculation unit 305, an initial parameter calculation unit 306, a deletion condition calculation unit 307, and an algorithm update unit 308. Arrows indicate the flow of processing. Solid lines indicate the flow of processing related to adding peaks, dotted lines indicate the flow of processing related to deleting peaks, and dashed dotted lines indicate the flow of processing related to updating the algorithm.

[0029] In this embodiment, the fitting process is repeatedly performed based on the fitting algorithm until the convergence condition is satisfied. The fitting process includes a process (addition process) of adding a peak function to a model function expressing a spectrum and optimizing a parameter of the peak function included in the model function, and a process (deletion process) of deleting a peak function from the model function and optimizing a parameter of the peak function included in the model function. The parameter is a parameter that characterizes a peak represented by the peak function.

[0030] The fitting algorithm is composed of an algorithm for calculating initial parameters of a peak function to be added, and an algorithm for calculating a deletion condition for selecting a peak function to be deleted. In the following description, these algorithms are referred to as an adding algorithm and a deleting algorithm, respectively.

[0031] The adding algorithm is an algorithm for calculating initial parameters of a peak function to be added using the change in an index for evaluating the degree of approximation between the spectrum and the model function, the feature of the residual curve which is the difference between the spectrum and the model function, and the parameters of the deleted peak function. The adding algorithm is implemented as, for example, a neural network. The neural network receives the change in the index, the feature of the residual curve, and the parameters of the deleted peak function as inputs, and outputs the initial parameters of the peak function to be added.

[0032] The deletion algorithm is an algorithm for calculating the deletion condition of the peak function by using the change amount of the index and the feature amount of the residual curve. The deletion algorithm is implemented as, for example, a neural network. The neural network receives the change amount of the index and the feature amount of the residual curve as input, and outputs the deletion condition of the peak function.

[0033] The peak adding unit 301 adds a peak function defined by the initial parameters calculated by the initial parameter calculating unit 306 to the model function, and outputs the model function to the optimization unit 300. In this embodiment, the initial parameters are calculated so that a peak function is added to a position where the residual in the residual curve is maximized, as shown in Fig. 4A. The spectra shown in Fig. 4A and Fig. 4B represent X-ray diffraction patterns.

[0034] The peak deletion unit 302 deletes peak functions from the model function to which the peak functions have been added and optimized, based on the peak deletion conditions calculated by the deletion condition calculation unit 307, and outputs the model function to the optimization unit 300. In this embodiment, as shown in Fig. 4B, peak functions that meet the peak deletion conditions are deleted.

[0035] The optimization unit 300 optimizes the parameters of the peak function included in the model function. Specifically, the parameters are optimized so that the residual representing the difference between the spectrum and the model function is minimized. The optimization may be performed using a known method such as the Levenberg-Marquardt method, the least squares method, or the differential evolution method.

[0036] The change amount calculation unit 303 calculates the amount of change in the index of the model function before and after the execution of the addition process or the deletion process, and outputs it to the initial parameter calculation unit 306 or the deletion condition calculation unit 307. The index is, for example, the Bayes Information Criterion.

[0037] The residual curve calculation unit 304 calculates a residual curve and outputs it to the residual feature calculation unit 305. The residual feature calculation unit 305 calculates the feature of the residual curve and outputs it to the initial parameter calculation unit 306 or the deletion condition calculation unit 307. The feature of the residual curve can be calculated using, for example, a variational autoencoder.

[0038] The initial parameter calculation unit 306 uses an adding algorithm to calculate initial parameters of a peak function to be added, and outputs the initial parameters to the peak adding unit 301. The deletion condition calculation unit 307 uses a deletion algorithm to calculate deletion conditions for the peak function, and outputs the deletion conditions to the peak deleting unit 302.

[0039] The algorithm update unit 308 updates the adding algorithm based on the history regarding the adding process, and updates the deleting algorithm based on the history regarding the deleting process.

[0040] In this embodiment, the addition algorithm and the deletion algorithm are learned in a reinforcement learning framework. An agent is used in which the addition algorithm and the deletion algorithm are set as a policy. The optimized model function is set as the environment, and the index is set as the reward. The change in the index, the residual feature, and the parameters of the deleted peak function are set as values ​​representing the state of the environment.

[0041] Regarding each functional unit of the algorithm learning system 100, multiple functional units may be combined into one functional unit, or one functional unit may be divided into multiple functional units for each function.

[0042] FIG. 5 is a diagram illustrating an example of a functional configuration of the spectrum analysis system 101 according to the first embodiment.

[0043] The spectrum analysis system 101 includes an optimization unit 500, a peak addition unit 501, a peak deletion unit 502, a change amount calculation unit 503, a residual curve calculation unit 504, a residual feature amount calculation unit 505, an initial parameter calculation unit 506, and a deletion condition calculation unit 507. Arrows indicate the flow of processing. Solid lines indicate the flow of processing related to adding peaks, and dotted lines indicate the flow of processing related to deleting peaks.

[0044] The optimization unit 500, the peak addition unit 501, the peak deletion unit 502, the change amount calculation unit 503, the residual curve calculation unit 504, the residual feature calculation unit 505, the initial parameter calculation unit 506, and the deletion condition calculation unit 507 are the same as the optimization unit 300, the peak addition unit 301, the peak deletion unit 302, the change amount calculation unit 303, the residual curve calculation unit 304, the residual feature calculation unit 305, the initial parameter calculation unit 306, and the deletion condition calculation unit 307.

[0045] The initial parameter calculation unit 506 uses the addition algorithm learned by the algorithm learning system 100. The deletion condition calculation unit 507 uses the deletion algorithm learned by the algorithm learning system 100.

[0046] Regarding each functional unit included in the spectrum analysis system 101, multiple functional units may be integrated into one functional unit, or one functional unit may be divided into multiple functional units for each function.

[0047] Fig. 6 is a flowchart illustrating an example of processing executed by the algorithm learning system 100 of the embodiment 1. Fig. 7 is a diagram illustrating an example of a data structure of data generated by the algorithm learning system 100 of the embodiment 1.

[0048] When the algorithm learning system 100 receives an execution instruction together with a plurality of spectra for learning, it starts the process described below.

[0049] The learning spectrum may be stored in advance in the algorithm learning system 100. It is assumed that the spectrum type and the like are set for the spectrum. It is assumed that the initial addition algorithm and deletion algorithm are set in advance. It is assumed that the type of model function to be used is set in advance.

[0050] The algorithm learning system 100 selects one spectrum (step S101). The fitting process is repeatedly performed on the selected spectrum.

[0051] The algorithm learning system 100 performs initial settings for the selected spectrum (step S102).

[0052] Specifically, the algorithm learning system 100 sets an initial model function. The initial model function may be generated based on any algorithm, or may be set manually. The algorithm learning system 100 calculates initial parameters of a peak function to be added based on an addition algorithm, and calculates a deletion condition of a peak function to be deleted based on a deletion algorithm. Here, only the feature values ​​of the model function and the residual curve representing the difference between the spectra are used, and other values ​​are treated as zero values.

[0053] The peak adding unit 301 of the algorithm learning system 100 adds a peak function to the model function based on the parameters calculated by the initial parameter calculating unit 306 (step S103).

[0054] The optimization unit 300 of the algorithm learning system 100 executes an optimization process for the parameters of the peak functions included in the model function to which the peak function has been added (step S104).

[0055] The algorithm learning system 100 calculates the change amount of the index and the residual feature amount (step S105).

[0056] Specifically, the change amount calculation unit 303 calculates the index of the model function before the peak function is added and the index of the model function optimized in step S104, and calculates the difference between the two indexes as the change amount of the index. The change amount of the index is output to the initial parameter calculation unit 306. The residual curve calculation unit 304 calculates a residual curve for the model function and spectrum optimized in step S104, and the residual feature amount calculation unit 305 calculates the residual feature amount using the residual curve. The residual feature amount is output to the initial parameter calculation unit 306.

[0057] The peak deletion unit 302 of the algorithm learning system 100 deletes the peak function from the optimized model function based on the deletion condition calculated by the deletion condition calculation unit 307 (step S106). The peak deletion unit 302 outputs the parameters of the deleted model function to the initial parameter calculation unit 306.

[0058] The optimization unit 300 of the algorithm learning system 100 executes an optimization process for the parameters of the model function from which the peak function has been deleted (step S107).

[0059] The algorithm learning system 100 calculates the change amount of the index and the residual feature amount (step S108).

[0060] Specifically, the change amount calculation unit 303 calculates the index of the model function before the peak function is deleted and the index of the model function optimized in step S107, and calculates the difference between the two indexes as the change amount of the index. The change amount of the index is output to the deletion condition calculation unit 307. The residual curve calculation unit 304 calculates a residual curve for the model function and spectrum optimized in step S107, and the residual feature amount calculation unit 305 calculates the residual feature amount using the residual curve. The residual feature amount is output to the deletion condition calculation unit 307.

[0061] The index of the model function optimized in step S107 is saved as the index of the current fitting process.

[0062] The initial parameter calculation unit 306 of the algorithm learning system 100 calculates the initial parameters of the peak function to be used in the next fitting process (step S109), and outputs the parameters to the peak adding unit 301.

[0063] Specifically, the initial parameter calculation unit 306 receives as input the change in index and the residual feature calculated in step S105 and the parameters of the deleted model function, and calculates initial parameters of the peak function to be used in the next fitting process based on the addition algorithm.

[0064] At this time, the initial parameter calculation unit 306 generates and stores first history data in which the change amount of the index and the residual feature amount calculated in step S105, the parameters of the model function deleted in step S106, and the initial parameters of the peak function calculated in step S109 are associated with each other.

[0065] The deletion condition calculation unit 307 of the algorithm learning system 100 calculates the deletion condition of the peak function to be used in the next fitting process (step S110), and outputs the calculated condition to the peak deletion unit 302.

[0066] Specifically, the deletion condition calculation unit 307 receives the change in index and the residual feature calculated in step S108 as input, and calculates the deletion condition of the peak function to be used in the next fitting process based on the deletion algorithm. The deletion condition of the peak function is calculated as, for example, an inequality related to the parameters of the peak function.

[0067] At this time, the deletion condition calculation unit 307 generates and stores second history data in which the change amount of the index and the residual feature amount calculated in step S108 correspond to the deletion condition of the peak function calculated in step S110.

[0068] The algorithm learning system 100 determines whether or not a termination condition is satisfied (step S111).

[0069] For example, the algorithm learning system 100 determines whether the model function is sufficiently approximate to the spectrum based on the index. For example, if the amount of change in the index is smaller than a threshold, the algorithm learning system 100 determines that the model function is sufficiently approximate to the spectrum. The algorithm learning system 100 may also determine that the termination condition is satisfied if the number of times the processes from step S103 to step S110 have been executed is greater than a threshold.

[0070] If the termination condition is not satisfied, the algorithm learning system 100 returns to step S103 and executes the fitting process again.

[0071] If the termination condition is met, the algorithm update unit 308 of the algorithm learning system 100 updates the added algorithm and the deleted algorithm (step S112).

[0072] Specifically, the algorithm update unit 308 updates the addition algorithm by performing machine learning using the first history data, and updates the deletion algorithm by performing machine learning processing using the second history data.

[0073] The algorithm learning system 100 determines whether the processing has been completed for all spectra (step S113).

[0074] If the processing has not been completed for all spectra, the algorithm learning system 100 returns to step S101 and executes fitting processing for a new spectrum. If the processing has been completed for all spectra, the algorithm learning system 100 ends the processing.

[0075] After all spectra have been processed, the adding algorithm and the deleting algorithm may be updated. In this case, the adding algorithm is updated by performing machine learning using the first history data of the processing of each spectrum, and the deleting algorithm is updated by performing machine learning using the second history data of the processing of each spectrum.

[0076] 7 from the learning result, and transmits it to the spectrum analysis system 101. The data 700 includes an ID 701, a spectrum type 702, an addition algorithm 703, a deletion algorithm 704, and a selection count 705.

[0077] ID 701 is a field that stores an ID for identifying data 700. Spectrum type 702 is a field that stores the type of spectrum used for learning. Addition algorithm 703 is a field that stores an added rhythm. Deletion algorithm 704 is a field that stores a deletion algorithm. Number of selections 705 is a field that stores the number of times the addition algorithm and deletion algorithm corresponding to data 700 have been used.

[0078] The data 700 may include other fields, such as a field for storing information about the user who performed the learning.

[0079] Fig. 8 is a flowchart illustrating an example of a process executed by the spectrum analysis system 101 according to the first embodiment. Fig. 9 is a diagram illustrating an example of a data structure of data generated by the spectrum analysis system 101 according to the first embodiment.

[0080] The spectrum analysis system 101 displays fitting algorithms (addition algorithm and deletion algorithm) on the screen based on the data 700. The user refers to the screen and selects the fitting algorithm to be used. The spectrum analysis system 101 adds 1 to the value of the selection count 705 of the data corresponding to the selected fitting algorithm.

[0081] Alternatively, the spectrum analysis system 101 may sort the data 700 in descending order of frequency of selection and present the sorted data 700.

[0082] When a spectrum is input, the spectrum analysis system 101 starts processing. The processing from step S201 to step S210 is the same as the processing from step S102 to step S111, and therefore a description thereof will be omitted.

[0083] 9 from the processing result, and transmits it to the feature estimation system 102. The data 900 includes a spectrum 901 and a model function 902.

[0084] Spectrum 901 is a field for storing an input spectrum. Model function 902 is a field for storing a model function.

[0085] 10 and 11 are flowcharts illustrating an example of processing executed by the feature estimation system 102 according to the first embodiment.

[0086] The feature estimation system 102 starts the process shown in FIG. 10 when an execution instruction is received via the terminal 103, or when the accumulated amount of the data 900 is greater than the threshold value.

[0087] The feature estimation system 102 uses the data 900 to learn a prediction model that outputs a model function from a spectrum (step S301).

[0088] A spectrum 901 of data 900 is used as an input to the prediction model, and a model function 902 of the data 900 is used as the correct answer to the output of the prediction model, and the prediction model is trained. A known method may be used for the training, and therefore a description thereof will be omitted.

[0089] When the feature estimation system 102 receives an input of a spectrum, it starts the process shown in FIG.

[0090] The feature estimation system 102 calculates a model function by inputting the spectrum into a prediction model (step S401).

[0091] The feature estimation system 102 executes a process of optimizing the parameters of the model function (step S402). The process of step S401 is the same as the process of step S104.

[0092] If the model function is sufficiently approximate to the spectrum, the process of step S402 does not need to be executed.

[0093] The feature estimation system 102 generates data 900 from the processing result of step S402.

[0094] According to the first embodiment, the spectrum analysis system 101 can automatically generate a model function in which complex peak functions are superimposed. In addition, by constructing an algorithm for controlling the addition and deletion of peak functions based on machine learning, a model function with high approximation accuracy can be generated. The peak function can be set arbitrarily and is not limited to the peak function. In addition, by constructing an algorithm based on machine learning, the possibility of falling into a local solution can be sufficiently reduced.

[0095] The present invention is not limited to the above-mentioned embodiment, but includes various modified examples. For example, the above-mentioned embodiment describes the configuration in detail to easily explain the present invention, and the present invention is not necessarily limited to the configuration including all the described configurations. Also, it is possible to add, delete, or replace a part of the configuration of each embodiment with another configuration.

[0096] In addition, each of the above configurations, functions, processing units, processing means, etc. may be realized in part or in whole by hardware, for example, by designing them as integrated circuits. The present invention can also be realized by software program code that realizes the functions of the embodiments. In this case, a storage medium on which the program code is recorded is provided to a computer, and a processor included in the computer reads the program code stored in the storage medium. In this case, the program code itself read from the storage medium realizes the functions of the above-mentioned embodiments, and the program code itself and the storage medium storing it constitute the present invention. Examples of storage media for supplying such program code include flexible disks, CD-ROMs, DVD-ROMs, hard disks, SSDs (Solid State Drives), optical disks, magneto-optical disks, CD-Rs, magnetic tapes, non-volatile memory cards, ROMs, etc.

[0097] Furthermore, the program code for realizing the functions described in this embodiment can be implemented in a wide range of program or script languages, such as assembler, C / C++, perl, Shell, PHP, Python, Java (registered trademark), etc.

[0098] Furthermore, the program code of the software that realizes the functions of the embodiments may be distributed over a network and stored in a storage means such as a computer's hard disk or memory, or in a storage medium such as a CD-RW or CD-R, and the processor of the computer may read out and execute the program code stored in the storage means or storage medium.

[0099] In the above-mentioned embodiment, the control lines and information lines are shown as those considered necessary for the explanation, and not all the control lines and information lines are shown in the product. All the components may be connected to each other. [Explanation of symbols]

[0100] 100 Algorithm Learning System 101 Spectral Analysis System 102 Feature Estimation System 103 Terminal 104 Network 200 calculator 201 Processor 202 Main storage 203 Secondary storage device 204 Communication Equipment 205 Input Device 206 Output Device 207 Bus 300, 500 Optimization Section 301, 501 Peak Addition 302, 502 Peak deletion section 303, 503 Change amount calculation unit 304, 504 Residual curve calculation section 305, 505 Residual feature calculation unit 306, 506 Initial parameter calculation unit 307, 507 Deletion condition calculation unit 308 Algorithm Update Division

Claims

1. A computer system that learns a fitting algorithm for calculating a model function that approximates a spectrum obtained by plotting observed values ​​corresponding to values ​​of variables that characterize an observation object, comprising: a computer having a processor, a storage device connected to the processor, and a communication device connected to the processor; The model function is a function obtained by superposing peak functions having different parameters characterizing the peaks, the fitting algorithm includes an adding algorithm for calculating the parameters of the peak functions to be added, and a deleting algorithm for calculating a deleting condition for selecting the peak functions to be deleted from the model function; The computer system comprises: Accepting an input of the spectrum; generating an initial said model function; a fitting process including an adding process of adding a new peak function to the model function based on the parameters calculated by the adding algorithm, and optimizing the parameters of the peak function included in the model function so as to approximate the spectrum, and a removing process of removing the peak function from the model function based on the removing condition calculated by the removing algorithm, and optimizing the parameters of the peak function included in the model function so as to approximate the spectrum, is repeatedly performed until a convergence condition for an index for evaluating a degree of fitting of the model function to the spectrum is satisfied; generating the additional algorithm by executing machine learning using first history data which is an execution history of the additional process; A computer system that generates the deletion algorithm by performing machine learning using second history data, which is an execution history of the deletion process.

2. The computer system according to claim 1, In the fitting process, after the adding process and the deleting process are executed, the first history data including a first change amount which is a difference between the index calculated in the previous fitting process and the index for the model function for which the current adding process has been executed, a feature amount of a first residual curve which represents a residual of the model function for which the current adding process has been executed and the spectrum, the parameters of the model function deleted in the current deletion process, and the parameters of the model function to be added in the next fitting process; the second history data including a second change amount which is a difference between the index calculated in the previous fitting process and the index for the model function on which the current deletion process has been executed, a feature amount of a second residual curve which represents a residual of the model function and the spectrum on which the current deletion process has been executed, and the deletion condition to be used in the next fitting process; Generate If the convergence condition is met, a neural network that receives, as the addition algorithm, the first change amount, a feature amount of the first residual curve, and the parameters of the model function deleted in the current deletion process as inputs, and outputs the parameters of the model function to be added in a next fitting process; a neural network that receives, as the deletion algorithm, the second change amount and the feature amount of the second residual curve as input and outputs the deletion condition to be used in a next fitting process; 23. A computer system for generating a time series of a plurality of time series.

3. 3. The computer system of claim 2, In the additional processing, the first change amount and a feature amount of the first residual curve are calculated; In the deletion process, the second change amount and a feature amount of the second residual curve are calculated; In the fitting process, after the adding process and the deleting process are executed, calculating the parameters of the model function to be added in a next fitting process based on the first change amount, the feature amount of the first residual curve, the parameters of the model function deleted in the deletion process, and the adding algorithm; generating the first historical data; calculating the deletion condition to be used in a next fitting process based on the second change amount, the feature amount of the second residual curve, and the deletion algorithm; A computer system for generating the second history data.

4. 3. The computer system of claim 2, A computer system that generates data for displaying information about the adding algorithm and the deleting algorithm.

5. 3. The computer system of claim 2, When the spectrum to be analyzed is received, the model function is calculated based on the fitting algorithm, and learning data in which the spectrum and the model function are associated with each other is stored; A computer system comprising: a computer that generates a prediction model for outputting the model function from the spectrum by executing machine learning using the training data.

6. A method for learning a fitting algorithm executed by a computer system to calculate a model function approximating a spectrum obtained by plotting observed values ​​corresponding to values ​​of variables characterizing an observation target, comprising the steps of: The computer system includes a computer having a processor, a storage device connected to the processor, and a communication device connected to the processor; The model function is a function obtained by superposing peak functions having different parameters characterizing the peaks, the fitting algorithm includes an adding algorithm for calculating the parameters of the peak functions to be added, and a deleting algorithm for calculating a deleting condition for selecting the peak functions to be deleted from the model function; The method for learning the fitting algorithm includes: a first step in which the computer system receives an input of the spectrum; a second step in which the computer system generates an initial model function; a third step in which the computer system repeatedly executes a fitting process including an addition process of adding a new peak function to the model function based on the parameters calculated by the addition algorithm and optimizing the parameters of the peak function included in the model function so as to approximate the spectrum, and a deletion process of deleting the peak function from the model function based on the deletion condition calculated by the deletion algorithm and optimizing the parameters of the peak function included in the model function so as to approximate the spectrum, until a convergence condition for an index for evaluating the degree of fitting of the model function to the spectrum is satisfied; a fourth step of generating the additional algorithm by executing machine learning using first history data, which is an execution history of the additional process, by the computer system; a fifth step of generating the deletion algorithm by the computer system executing machine learning using second history data which is an execution history of the deletion process; A method for learning a fitting algorithm, comprising:

7. A method for learning a fitting algorithm according to claim 6, The third step includes: After the addition process and the deletion process are executed, the first history data including a first change amount which is a difference between the index calculated in the previous fitting process and the index for the model function for which the current adding process has been executed, a feature amount of a first residual curve which represents a residual of the model function for which the current adding process has been executed and the spectrum, the parameters of the model function deleted in the current deletion process, and the parameters of the model function to be added in the next fitting process; the second history data including a second change amount which is a difference between the index calculated in the previous fitting process and the index for the model function on which the current deletion process has been executed, a feature amount of a second residual curve which represents a residual of the model function and the spectrum on which the current deletion process has been executed, and the deletion condition to be used in the next fitting process; generating the fourth step includes a step of generating, as the addition algorithm, a neural network that receives as input the first change amount, the feature amount of the first residual curve, and the parameters of the model function deleted in the current deletion process, and outputs the parameters of the model function to be added in a next fitting process, by the computer system; The fifth step is a method for learning a fitting algorithm, characterized in that it includes a step in which the computer system generates, as the deletion algorithm, a neural network that receives the second change amount and the feature amount of the second residual curve as input and outputs the deletion condition to be used in a next fitting process.

8. A method for training a fitting algorithm according to claim 7, comprising: The third step includes: a step of the computer system calculating, in the additional processing, the first change amount and a feature amount of the first residual curve; the computer system includes a step of calculating, in the deletion process, the second change amount and a feature amount of the second residual curve; The third step further comprises the step of: after the addition process and the deletion process are executed, the computer system: calculating the parameters of the model function to be added in a next fitting process based on the first change amount, the feature amount of the first residual curve, the parameters of the model function deleted in the deletion process, and the adding algorithm; generating the first historical data; calculating the deletion condition to be used in a next fitting process based on the second change amount, the feature amount of the second residual curve, and the deletion algorithm; generating the second history data.

9. A method for training a fitting algorithm according to claim 7, comprising: The method for learning a fitting algorithm, further comprising a step of generating data for displaying information relating to the adding algorithm and the deleting algorithm by the computer system.

10. A method for training a fitting algorithm according to claim 7, comprising: a step of, when the computer system receives the spectrum to be analyzed, calculating the model function based on the fitting algorithm, and storing learning data in which the spectrum and the model function are associated with each other; and generating a predictive model for outputting the model function from the spectrum by executing machine learning using the training data by the computer system.

11. A computer that learns a fitting algorithm for calculating a model function that approximates a spectrum obtained by plotting observed values ​​corresponding to values ​​of variables that characterize an observation object, comprising: A processor, a storage device connected to the processor, and a communication device connected to the processor, The model function is a function obtained by superposing peak functions having different parameters characterizing the peaks, the fitting algorithm includes an adding algorithm for calculating the parameters of the peak functions to be added, and a deleting algorithm for calculating a deleting condition for selecting the peak functions to be deleted from the model function; The computer includes: Accepting an input of the spectrum; generating an initial said model function; a fitting process including an adding process of adding a new peak function to the model function based on the parameters calculated by the adding algorithm, and optimizing the parameters of the peak function included in the model function so as to approximate the spectrum, and a removing process of removing the peak function from the model function based on the removing condition calculated by the removing algorithm, and optimizing the parameters of the peak function included in the model function so as to approximate the spectrum, is repeatedly performed until a convergence condition for an index for evaluating a degree of fitting of the model function to the spectrum is satisfied; generating the additional algorithm by executing machine learning using first history data which is an execution history of the additional process; A computer that generates the deletion algorithm by performing machine learning using second history data, which is an execution history of the deletion process.

12. The computer according to claim 11, In the fitting process, after the adding process and the deleting process are executed, the first history data including a first change amount which is a difference between the index calculated in the previous fitting process and the index for the model function for which the current adding process has been executed, a feature amount of a first residual curve which represents a residual of the model function for which the current adding process has been executed and the spectrum, the parameters of the model function deleted in the current deletion process, and the parameters of the model function to be added in the next fitting process; the second history data including a second change amount which is a difference between the index calculated in the previous fitting process and the index for the model function on which the current deletion process has been executed, a feature amount of a second residual curve which represents a residual of the model function and the spectrum on which the current deletion process has been executed, and the deletion condition to be used in the next fitting process; Generate If the convergence condition is met, a neural network that receives, as the addition algorithm, the first change amount, a feature amount of the first residual curve, and the parameters of the model function deleted in the current deletion process as inputs, and outputs the parameters of the model function to be added in a next fitting process; a neural network that receives, as the deletion algorithm, the second change amount and the feature amount of the second residual curve as input and outputs the deletion condition to be used in a next fitting process; A computer that generates a

13. 13. The computer of claim 12, In the additional processing, the first change amount and a feature amount of the first residual curve are calculated; In the deletion process, the second change amount and a feature amount of the second residual curve are calculated; In the fitting process, after the adding process and the deleting process are executed, calculating the parameters of the model function to be added in a next fitting process based on the first change amount, the feature amount of the first residual curve, the parameters of the model function deleted in the deletion process, and the adding algorithm; generating the first historical data; calculating the deletion condition to be used in a next fitting process based on the second change amount, the feature amount of the second residual curve, and the deletion algorithm; A computer that generates the second history data.

14. 13. The computer of claim 12, A computer that generates data for displaying information about the adding algorithm and the deleting algorithm.

15. 13. The computer of claim 12, When the spectrum to be analyzed is received, the model function is calculated based on the fitting algorithm, and learning data in which the spectrum and the model function are associated with each other is stored; A computer that generates a prediction model for outputting the model function from the spectrum by executing machine learning using the training data.

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