Learning device, learning method, and program

Abstract

To provide a learning device, a learning method, and a program for improving the accuracy of predicting future values from time series data.SOLUTION: The learning device is configured to generate, from time series data, a state vector including a first component including a difference between data at a target time and data at a time before the target time and a second component including a power of the data at the target time so as to be trained using the state vector.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] This disclosure relates to a learning device, a learning method, and a program. [Background technology]

[0002] Patent Document 1 discloses a technique for predicting future values ​​from time-series data using an RNN (Recurrent Neural Network). [Prior art documents] [Patent Documents]

[0003] [Patent Document 1] Japanese Patent Application Publication No. 9-245013 [Overview of the project] [Problems that the invention aims to solve]

[0004] There is a need to improve the accuracy of predicting future values ​​from time series data.

[0005] This disclosure is made to solve such problems and aims to provide a learning device, learning method, and program that improve the accuracy of predicting future values ​​from time series data. [Means for solving the problem]

[0006] The learning device in this embodiment is configured to generate a state vector from time-series data, which includes a first component containing the difference between the data at a target time and the data at a time prior to the target time, and a second component containing a power of the data at the target time, and to learn using the state vector.

[0007] The learning method in this embodiment generates a state vector from time-series data, which includes a first component containing the difference between the data at a target time and the data at a time prior to the target time, and a second component containing a power of the data at the target time, and then performs learning using the state vector.

[0008] The program in this embodiment causes the computer to generate a state vector from time-series data, which includes a first component containing the difference between the data at a target time and the data at a time prior to the target time, and a second component containing a power of the data at the target time, and to perform a learning process using the state vector. [Effects of the Invention]

[0009] This disclosure provides a learning device, learning method, and program that improve the accuracy of predicting future values ​​from time series data. [Brief explanation of the drawing]

[0010] [Figure 1] This diagram illustrates the flow of the learning method according to Embodiment 1. [Figure 2A] This figure illustrates the effectiveness of the learning method according to Embodiment 1. [Figure 2B] This figure illustrates the effectiveness of the learning method according to Embodiment 1. [Figure 2C] This figure illustrates the effectiveness of the learning method according to Embodiment 1. [Figure 2D] This figure illustrates the effectiveness of the learning method according to Embodiment 1. [Figure 2E] This figure illustrates the effectiveness of the learning method according to Embodiment 1. [Figure 2F] This figure illustrates the effectiveness of the learning method according to Embodiment 1. [Figure 3A] This figure illustrates the results of applying the learning method according to Embodiment 1 to the demand forecasting of service parts. [Figure 3B]This figure illustrates the results of applying the learning method according to Embodiment 1 to the demand forecasting of service parts. [Modes for carrying out the invention]

[0011] The present invention will be described below through embodiments, but the claims are not limited to the following embodiments. Furthermore, not all of the configurations described in the embodiments are necessarily essential for solving the problem.

[0012] Embodiment 1 The learning method according to Embodiment 1 will be described below with reference to the drawings. Figure 1 is a diagram illustrating the learning method according to Embodiment 1. The learning method includes steps S1 to S8. In the formulas in the following explanation, bold letters represent vectors. Since bold font cannot be used in this document, the normal formatting is used, and "(bold)" is added immediately after the corresponding letter.

[0013] In step S1, past order data Y for the target part (e.g., service parts for automobiles) is read as input to the program. Here, Y = {y1, y2, ..., y t} is. y i (1≦i≦t) represents the order history of the target component at past time i.

[0014] In step S2, as shown in equation (1), the order performance data Y is decomposed into a trend component T and a residual component R.

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[0015] In step S3, the maximum element T max and the minimum element T min are specified from the trend component T. Then, as shown in Equation (2), normalization using the maximum element T max and the minimum element T min is performed.

Equation

[0016] Similarly, the maximum element R max and the minimum element R min are specified from the residual component R. Then, as shown in Equation (3), normalization using the maximum element R max and the minimum element R min is performed.

Equation

[0017] In step S4, using T ~ normalized in step S3, the state vector at each time i, Ti ~ (Bold font) is generated. State vector T i ~ (Bold type) is defined by equation (4).

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[0018] Similarly, the normalized information R normalized in step S3 ~ Using this, the state vector R at each time step i i ~ (Bold font) is generated. State vector R i ~ (Bold type) is defined by equation (5).

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[0019] In equations (4) and (5), "T" represents the transpose. Referring to equation (4), the state vector T i ~ (Bold text) contains the first and second components. State vector T i ~ The first component (in bold) is the normalized information T at the target time i. i ~ And normalized information T at time im,...,i-1 prior to the target time i. i-m ~ ,···,T i-1 ~ Includes the difference from the state vector T. i ~ The second component (in bold) is the normalized information T at the target time i. i ~ Power T i ~ ,T i ~2 ,···,and T i ~m This includes the state order, where m is the state order. When forecasting demand for service parts, the state order is set to, for example, m=5 or m=6.

[0020] Referring to Equation (5), the state vector R i ~ (bold body) also includes a first component and a second component. The state vector R i ~ The first component of the (bold body) state vector R is the normalization information R at the target time i i ~ and the normalization information R at times i - m, ···, i - 1 before the target time i i-m ~ , ···, R i-1 ~ including the difference from. The state vector R i ~ The second component of the (bold body) state vector R is the normalization information R at the target time i i ~ to the power of R i ~ , R i ~2 , ···, R i ~m including.

[0021] And the state vector T i ~ (bold body) shown in Equation (4) is arranged in time order, and the state matrix Y of the normalization information of the trend component T is generated. The state matrix Y of the normalization information of the trend component T is defined by Equation (6).

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[0022] Similarly, the state vector R i ~ (bold body) shown in Equation (5) is arranged in time order, and the state matrix Y of the normalization information of the residual component R is generated. The state matrix Y of the normalization information of the residual component R is defined by Equation (7).

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[0023] In step S5, the state matrix Y T generated in step S4 is read as the input of the DMD (Dynamic Mode Decomposition) algorithm, and DMD analysis is performed. By the DMD analysis, the DMD eigenvalues λ T corresponding to the state matrix Y i and the DMD eigenvectors Uφ i (bold body) are calculated. Similarly, the state matrix Y R generated in step S4 is read as the input of the DMD algorithm, and the DMD eigenvalues λ R corresponding to the state matrix Y i and the DMD eigenvectors Uφ i (bold body) are calculated.

[0024] As described in Schmid, Peter J. 2010. “Dynamic Mode Decomposition of Numerical and Experimental Data.” Journal of Fluid Mechanics 656. Cambridge University Press:5-28., the DMD algorithm includes the following processes (1) to (4). (1) The state matrix Y = (y m+1 (bold body), ···, y t-1 (bold body), y t (bold body)) is divided into the matrix X￣ = (y m+1 (bold body), ···, y t-1 (bold body)) and the matrix Y￣ = (y m+2 (bold body), ···, y t (bold body)). (2) Singular value decomposition of X￣ is performed and X￣ = UΣW T is represented. U is a unitary matrix, and W Trepresents the transpose of the unitary matrix W, and Σ represents a matrix with diagonal elements. (3) Matrix S ~ =U T Y￣WΣ -1 This is composed of U T is the transpose of the unitary matrix U. W is a unitary matrix. Σ -1 is the inverse matrix of matrix Σ. And matrix S ~ Eigenvalue λ i and eigenvector φ i (Bold text) is calculated. (4) The i-th DMD eigenvalue is λ i It is said that the i-th DMD eigenvector is Uφ i (Bold font)

[0025] In DMD analysis, the state vector y at times m+1,···,t-1 m+1 (Bold font),···,y t-1 (Bold text) The state vector y at the following time points m+2,···,t m+2 (Bold font),···,y t The mapping map associated with (bold text) is approximated by a linear map. Then, the eigenvalues ​​and eigenvectors that define the eigenmodes of the linear map are calculated. The mapping map is represented using the information of the eigenmodes, and future states are predicted from past state vectors.

[0026] Specific demand forecast value y t+n ^ is the past state vector y, as shown in equation (8). t Function h in (bold font) n It is expressed as the value of .

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[0027] In step S6, based on Equation (10) calculated in step S5, the inner products of the state vector y j (bold) and the DMD eigenvector Uφ i (bold) (1 ≤ i ≤ m), <y j (bold), Uφ1 (bold)>, ···, <y j (bold), Uφ m (bold)> are used as inputs, and a regression model that outputs y j+n is learned. That is, <T ~ j (bold), Uφ1 (bold)>, ···, <T ~ j (bold), Uφ m (bold)> are used as inputs, and a first regression model that outputs the normalization information T of the trend component ~ j+n is learned. Then, <R ~ j (bold), Uφ1 (bold)>, ···, <R ~ j (bold), Uφ m (bold)> are used as inputs, and a second regression model that outputs the normalization information R of the residual component ~ j+n is learned. m + 1 ≤ j ≤ t - n, and as the machine learning algorithm of the regression model, SVR (Support Vector Regressor), GBR (Gradient Boosting Regressor), etc. are used.

[0028] In step S7, the regression model learned in step S6 is given <y t(Bold font), Uφ1 (Bold font)>,···, <y t (Bold font), Uφ m (Bold)> is entered, y^ t+n This is predicted. In other words, <T ~ t (Bold font), Uφ1 (Bold font)>,···, <T ~ t (Bold font), Uφ m (Bold text)> is input into the first regression model, and the normalized information T of the trend component is entered. ~ ^ t+n This is predicted. And, <R ~ t (Bold font), Uφ1 (Bold font)>,···, <R ~ t (Bold font), Uφ m (Bold text)> is input into the second regression model, and the normalized information of the residual component R ~ ^ t+n This is predicted. Time t+n (1≦n) represents the time when the data is predicted.

[0029] In step S8, as shown in equation (11), the T predicted in step S7 is ~ ^ t+n The biggest trending element is T max , and the smallest element T of the trend component min Using this, the trend prediction value T^ t+n This is calculated.

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[0030] Similarly, as shown in equation (12), the R predicted in step S7 is ~ ^ t+n , the largest element of the residual component R max , and the minimum element R of the residual component min Using this, the residual prediction value R^ t+n This is calculated.

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[0031] The learning method according to Embodiment 1 is not limited to the method shown in Figure 1. For example, in step S4, after generating state vectors at each time step, the first regression model may be trained to take the state vector at time j (m+1≦j≦tn) as input and output normalized information of the trend component at time j+n. Existing time series data models such as RNN (Recurrent Neural Network) or LSTM (Long Short Term Memory) can be used as the regression model.

[0032] The learning device according to Embodiment 1 comprises a processor, memory, and a storage device. The storage device stores a computer program in which the processes corresponding to steps S1 to S8 are implemented. The processor then loads the computer program from the storage device into the memory and executes the computer program.

[0033] Next, the effectiveness of the learning method according to Embodiment 1 will be explained with reference to Figures 2A to 2F. The 60 data points included in the time series data represented by each of equations (A) to (F) are divided into 48 training data points and 12 test data points. n represents the function value, and n represents the time. Figures 2A to 2F show the training data, the training results for the training data, the test data, and the prediction results for the test data.

[0034] Figure 2A shows periodic time-series data. The training data closely matches the training results, and the prediction results closely match the test data. This shows that the learning method according to Embodiment 1 is effective for periodic time-series data.

[0035] The time series data shown in Figures 2B, 2C, and 2D fluctuates periodically, increasing and decreasing, that is, exhibiting a trend component. The learning results closely match the training data, and the prediction results closely match the test data. This demonstrates that the learning method according to Embodiment 1 is effective for time series data that fluctuates periodically while increasing and decreasing.

[0036] Figures 2E and 2F show time series data that exhibits chaos and randomness and changes irregularly. Equation (E) represents the recurrence relation corresponding to the Hénon map, and equation (F) represents the recurrence relation corresponding to the logistic map. The learning results are sufficiently close to the training data, and the prediction results are sufficiently close to the test data. This shows that the learning method according to Embodiment 1 is also effective for time series data with irregularity.

[0037] The learning method according to Embodiment 1 can accurately reproduce various time-series data and accurately predict changes in various time-series data.

[0038] Next, with reference to Figures 3A and 3B, the results of applying the learning method according to Embodiment 1 to demand forecasting for automotive service parts will be described. Figures 3A and 3B show the order history for two different parts, Part 1 and Part 2, over a period of approximately five years.

[0039] Figures 3A and 3B show the results of predicting demand for the most recent year based on previous order data using the learning method according to Embodiment 1. The horizontal axis represents time (month), and the vertical axis represents the number of orders per month. For comparison, the results of predicting demand for the most recent year using the conventional technology are also shown. The conventional technology is a method of predicting demand using order data and associated information (e.g., manufacturing information, usage information, repair information) for groups of parts with many commonalities (e.g., a collection of multiple parts obtained by clustering). In the conventional technology, a database containing order data for approximately 9,000 parts was used to cluster the parts based on their features, extract the features, and then perform demand forecasting. The upper graph shows the prediction results when using the conventional technology. The lower graph shows the prediction results when using the learning method according to Embodiment 1.

[0040] Referring to Figures 3A and 3B, the prediction accuracy when using the learning method according to Embodiment 1 is higher than the prediction accuracy when using the conventional technology. Therefore, by using the learning method according to Embodiment 1, the demand for automotive service parts can be predicted with high accuracy.

[0041] Finally, the effects of the learning method according to Embodiment 1 will be explained. In order to improve production efficiency and logistics efficiency and to supply target parts in a timely manner, it is desirable to predict the demand for parts with high accuracy.

[0042] The patterns of change in demand for service parts are diverse. These patterns include not only trend components due to aging, but also periodic fluctuation components due to seasonal influences and irregular noise components. Therefore, conventional technologies create predictors using information on similar parts and supplementary information representing potential demand in order to forecast these complex characteristics. However, conventional technologies require the construction of a database that stores supplementary information and order records for multiple parts, but database construction is not easy and is time-consuming and costly. Furthermore, because the prediction results depend on the data stored in the database, accurate predictions may not be possible depending on the conditions under which the prediction is made (e.g., location, region, country).

[0043] The learning method according to Embodiment 1 reduces dependence on the database and can predict changes in time-series data from a small amount of data. Furthermore, the learning method according to Embodiment 1 can improve prediction accuracy by learning using the state vector described above.

[0044] It should be noted that the present invention is not limited to the embodiments described above, and can be modified as appropriate without departing from the spirit of the invention. [Explanation of symbols]

[0045] S1-S8 Steps

Claims

1. A learning device configured to generate a state vector from time-series data, the state vector comprising a first component including the difference between data at a target time and data at a time prior to the target time, and a second component including a power of the data at the target time, and to learn using the state vector, A state matrix is ​​generated by arranging multiple state vectors in time order. A regression model is trained that takes the dot product of the state vector at the target time and the DMD eigenvector calculated by performing a DMD (Dynamic Mode Decomposition) analysis on the state matrix as input, and outputs data at a time after the target time. Learning device.

2. The learning device decomposes the time series data into a trend component and a residual component, and generates the state vector from each of the trend component and the residual component. The learning device according to claim 1.

3. The aforementioned time-series data represents the order history of parts. The learning device according to claim 1.

4. A learning method in which a computer generates a state vector from time-series data, the state vector comprising a first component including the difference between data at a target time and data at a time prior to the target time, and a second component including a power of the data at the target time, and learns using the state vector, The aforementioned computer, A state matrix is ​​generated by arranging multiple state vectors in time order. A regression model is trained that takes the dot product of the state vector at the target time and the DMD eigenvector calculated by performing a DMD (Dynamic Mode Decomposition) analysis on the state matrix as input, and outputs data at a time after the target time. Learning methods.

5. A program that causes a computer to generate a state vector from time-series data, which includes a first component containing the difference between the data at a target time and the data at a time prior to the target time, and a second component containing a power of the data at the target time, and to perform a learning process using the state vector, The process of generating a state matrix by arranging multiple state vectors in chronological order, The process involves learning a regression model that takes the dot product of the state vector at the target time and the DMD eigenvector calculated by performing a DMD (Dynamic Mode Decomposition) analysis on the state matrix as input, and outputs data at a time after the target time. A program that causes the aforementioned computer to execute.

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