A method and system for interpolating missing values ​​of geographic time series data based on BI-Transformer model

Abstract

The present invention discloses a method and system for interpolating missing values ​​of geographic time series data based on a BI-Transformer model, including segmenting original continuous geographic time series data with missing values, constructing a sample set of geographic time series data with missing values, and dividing it into a training set, a validation set, and a test set; constructing a BI-Transformer model, using the training set, the validation set, and the test set to perform model training, hyperparameter adjustment, and generalization capability evaluation on BI-Transformer, respectively, and selecting the optimal interpolation sample length according to the set evaluation index; interpolating the original continuous geographic time series data with missing values ​​based on the trained BI-Transformer model and the selected optimal interpolation sample length to obtain complete geographic time series data. The present invention does not rely on other variables, makes full use of the time correlation characteristics of geographic time series data, and effectively realizes the improvement of the interpolation accuracy of geographic time series data under different sequence lengths, missing modes, and missing ratios.

Description

Technical Field

[0001] The present invention belongs to the field of computer science and technology, and in particular, relates to a method and system for interpolating missing values ​​of geographic time series data based on a BI-Transformer model. Background Art

[0002] In geographic time series data analysis, missing data is a common and unavoidable problem, especially in the field of environmental monitoring. During the long-term operation of ground environmental monitoring stations, data may be missing in some time periods due to equipment failure, maintenance downtime, data transmission interruption, extreme weather impact, etc. This missing data will not only weaken the integrity of the monitoring data, but also affect the accuracy of time series analysis, making it difficult to fully capture the long-term trends and seasonal changes of environmental variables. Missing data will lead to instability during model training, reduced prediction accuracy, and may aggravate the deviation of analysis results. Therefore, it is of great significance to develop a high-accuracy time series data missing value interpolation method to restore the continuity of ground environmental monitoring data and improve the accuracy and robustness of subsequent analysis.

[0003] Traditional interpolation methods based on statistics usually treat time series data as ordinary structured data, and mainly rely on local numerical relationships for interpolation. They pay insufficient attention to the dependencies and long-distance correlations in the time dimension, which makes it difficult for the interpolation results to truly reflect the dynamic patterns of time series data. In recent years, deep learning models such as recurrent neural networks and attention mechanisms have made breakthrough progress in time series analysis, providing new ideas for interpolation of missing values ​​in time series data. These models can capture long-term and short-term dependencies and complex patterns in time series, and have stronger adaptability and accuracy. Therefore, improvements and innovations based on deep learning frameworks to adapt to missing value interpolation tasks are a realistic and necessary research direction. Summary of the invention

[0004] In view of the deficiencies of the prior art, the present invention provides a method for interpolating missing values ​​of geographic time series data based on a BI-Transformer model, which can realize the reconstruction of missing data of ground environmental monitoring sites, comprising the following steps:

[0005] Step 1: Split the original continuous geographic time series data with missing values, extract geographic sub-time series data without missing values, and construct a sample set of geographic time series data without missing values;

[0006] Step 2, constructing the geographic time series data sample set without missing values ​​constructed in step 1 into a geographic time series data sample set with missing values;

[0007] Step 3, divide the geographic time series data sample set with missing values ​​constructed in step 2 into a training set, a validation set, and a test set;

[0008] Step 4: Build a BI-Transformer model to interpolate missing values ​​in geographic time series data with missing values;

[0009] Step 5: Use the training set, validation set, and test set to perform model training, hyperparameter adjustment, and generalization ability evaluation on BI-Transformer, and select the optimal interpolation sample length based on the set evaluation indicators;

[0010] Step 6: Based on the BI-Transformer model trained in step 5 and the selected optimal interpolation sample length, the original continuous geographic time series data with missing values ​​is interpolated to obtain complete geographic time series data.

[0011] Furthermore, in step 1, the original continuous geographic time series data with missing values ​​is segmented, the missing data is removed, and multiple segments of geographic sub-time series data without missing values ​​are obtained. The geographic sub-series data without missing values ​​in each segment are equally divided, n is the number of set sequence lengths, The value of is set according to actual needs, and the geographic data that is less than the set sequence length is discarded to form a geographic time series data sample set with no missing values.

[0012] Furthermore, in step 2, two missing simulation methods, random missing and continuous missing, are used, respectively, according to the missing ratio Delete the sample data in the geographic time series data sample set without missing values ​​constructed in step 1 to construct a geographic time series data sample set with missing values. N is the number of missing proportions set. The value is set according to actual needs.

[0013] Furthermore, the BI-Transformer model in step 4 is composed of two Transformer models and a fully connected network. The Transformer model is constructed using the attention mechanism and consists of an encoder and a decoder. The encoder is stacked with multiple layers of the same structure, each layer contains two sub-layers, namely multi-head attention and feedforward network, residual connections are used around the layer, and then layer normalization is performed. The decoder is stacked with multiple layers of the same structure, each layer contains three sub-layers, namely masked multi-head attention, multi-head attention and feedforward network, residual connections are used around the layer, and then layer normalization is performed; the fully connected network contains multiple fully connected layers.

[0014] Take the sample data in the geographic time series data sample set without missing values ​​constructed in step 1 as the true observation value of the sample ,in is the corresponding observation time, and T is the sample length. Assume that the missing value strategy designed in step 2 is used to obtain the geographic time series data sample with missing values. , introduce the mask vector Mark missing, when When is a missing value, Take 0, otherwise take 1 to get the positive input sample for training ,beg The inversion of ,Will are the reverse input samples for BI-Transformer model training. , Input the Transformer model to get the corresponding positive output result And reverse output results The Transformer model retains the original true observation values ​​for locations with no missing values ​​in the original geographic time series data, and only uses the predicted values ​​for locations with missing values. Invert to get ,Will and Splice to get ,Will Input the fully connected network for feature extraction ,Will The positions without missing values ​​in the original geographic time series data are replaced with the original true observation values ​​to obtain the final prediction results .

[0015] Furthermore, in step 5, the BI-Transformer model is trained using the training set, and the loss function used in the training process is L Including accuracy loss function And the consistency loss function Two parts, and weighted Adjust the proportion of the two parts, the calculation formula is:

[0016] (1)

[0017] (2)

[0018] (3)

[0019] In the formula, Indicates the first The actual observed value corresponding to the value is Indicates the sample prediction result output by the BI-Transformer model. values, T represents the sample length, represents the Pearson correlation coefficient, Represents the first output of the BI-Transformer model values, They represent the reverse output of the BI-Transformer model after inversion. values, represents the mean of the forward output results, They represent the mean of the reverse output results respectively.

[0020] The BI-Transformer model uses different sequence generation modes in the training process and the actual prediction process. The Teacher Forcing mode is used in the training process, that is, it does not rely on the output of the previous training, but directly uses the real observations corresponding to the training data as the input of each training. In the actual prediction, the decoding strategy based on dynamic replacement of non-missing values ​​is used. When the value at position If the position is missing, If there is a missing value, the position generated by the Transformer model is used The predicted value at The value at position, if position If there is no missing value at The original true observation value at prediction The value at position.

[0021] Using the coefficient of determination The interpolation effect of the model is evaluated by four evaluation indicators: mean absolute error (MAE), root mean square error (RMSE) and mean absolute percentage error (MAPE). The larger the value, the smaller the MAE, RMSE and MAPE, indicating that the interpolation effect of the model is better. Considering the four evaluation indicators comprehensively, the sample length used by the model with the best interpolation effect is the optimal interpolation sample length. .

[0022] Furthermore, the optimal interpolation sample length selected in step 6 according to step 5 is , split the original continuous geographic time series data with missing values, and keep each segment of geographic sub-time series data with the previous segment of geographic sub-time series data during segmentation Overlapping bits, , The value is set according to actual needs. The length of the last segment of geographic sub-series data after the overlapping bit segmentation is insufficient , then increase the overlap between the last segment of geographic sub-series data and the previous segment of geographic sub-series data to make its length reach , thus the length of multiple segments is The geographic sub-time series data with no missing values ​​and multiple segments of length The geographic sub-time series data with missing values ​​are input into the trained BI-Transformer model to obtain the corresponding geographic sub-time series prediction data without missing values. Multiple segments of geographic sub-time series prediction data without missing values ​​and multiple segments of geographic sub-time series data without missing values ​​are spliced ​​to obtain the final geographic continuous time series data without missing values. The splicing of geographic sub-time series data refers to taking the average of the data at the overlapping position of two geographic sub-time series data.

[0023] The present invention also provides a system for interpolating missing values ​​of geographic time series data based on a BI-Transformer model, which is used to implement a method for interpolating missing values ​​of geographic time series data based on a BI-Transformer model as described above.

[0024] Furthermore, it includes a processor and a memory, the memory is used to store program instructions, and the processor is used to call the stored instructions in the memory to execute the missing value interpolation method of geographic time series data based on the BI-Transformer model as described above.

[0025] Compared with the prior art, the present invention has the following advantages:

[0026] It does not rely on other variables and makes full use of the time correlation characteristics of time series data, effectively improving the accuracy of time series data interpolation under different sequence lengths, missing patterns, and missing ratios. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0028] Figure 1 It is a flow chart of a method for interpolating missing values ​​of geographic time series data based on a BI-Transformer model according to an embodiment of the present invention.

[0029] Figure 2 It is a structural diagram of the BI-Transformer model of the present invention.

[0030] Figure 3This is a schematic diagram of the operation process of the decoding strategy based on dynamic replacement of non-missing values ​​proposed in the present invention. DETAILED DESCRIPTION

[0031] In order to make the purpose, technical scheme and advantages of the present invention clearer, the technical scheme of the present invention is further described below in conjunction with the accompanying drawings and embodiments. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0032] Example 1

[0033] like Figure 1 As shown, an embodiment of the present invention provides a method for interpolating missing values ​​of geographic time series data based on a BI-Transformer model, comprising the following steps:

[0034] Step 1: split the original PM2.5 ground monitoring continuous time series data with missing values, extract the PM2.5 ground monitoring sub-time series data without missing values, and construct a PM2.5 ground monitoring time series data sample set without missing values.

[0035] The original PM2.5 ground monitoring continuous time series data with missing values ​​were segmented and the missing data were removed to obtain multiple segments of PM2.5 ground monitoring time series data without missing values. Each segment of PM2.5 ground monitoring data without missing values ​​was equally divided according to four sequence lengths of 48, 72, 96 and 120, and the data with less than 48, 72, 96 or 120 sequence lengths were discarded to form a sample set of PM2.5 ground monitoring time series data without missing values.

[0036] Step 2: Construct a PM2.5 ground monitoring time series data sample set with missing values ​​into a PM2.5 ground monitoring time series data sample set with missing values.

[0037] Two missing simulation methods, random missing and continuous missing, were used. The sample data in the PM2.5 ground monitoring time series data sample set without missing values ​​were deleted according to four missing ratios of 10%, 30%, 50% and 70% respectively. The PM2.5 ground monitoring time series data sample set with missing values ​​was constructed to comprehensively measure and compare the interpolation performance of the model.

[0038] Step 3: Divide the PM2.5 ground monitoring time series data sample set with missing values ​​into training set, validation set and test set in a ratio of 7:2:1.

[0039] Step 4: Construct a BI-Transformer (Bidirectional Interpolation Transformer) model to interpolate missing values ​​in PM2.5 ground monitoring time series data with missing values.

[0040] like Figure 2 , BI-Transformer consists of two Transformer models and a fully connected network to overcome the unidirectional limitations caused by the difference in the position of missing values ​​and the different missing conditions on the left and right sides of the missing values. The Transformer model is built using the attention mechanism, and the main architecture consists of an encoder and a decoder. The encoder is stacked with multiple layers of the same structure. Each layer contains two sub-layers, namely multi-head self-attention and feedforward network. Residual connections are used around the layers, followed by layer normalization. The decoder is also stacked with multiple layers of the same structure. Each layer contains three sub-layers, namely masked multi-head attention, multi-head attention and feedforward network. Residual connections are used around the layers, followed by layer normalization. The fully connected network contains multiple fully connected layers.

[0041] Take the sample data in the PM2.5 ground monitoring time series data sample set without missing values ​​constructed in step 1 as the true observation value of the sample ,in is the corresponding observation time, and T is the sample length. Assume that the PM2.5 ground monitoring time series data sample with missing values ​​is obtained by using the missing strategy designed in step 2 , introduce the mask vector Mark missing case (when When is a missing value, Take 0, otherwise take 1), and get the positive input sample for training ,beg The inversion of ,Will are the reverse input samples for BI-Transformer model training. , Input the Transformer model to get the corresponding positive output result And reverse output results It should be noted that the Transformer model retains the original true observation value for the position without missing values ​​in the original time series data, and only uses the predicted value for the position with missing values. Invert to get ,Will and Splice to get ,Will Input the fully connected network for feature extraction ,Will The positions without missing values ​​in the original geographic time series data are replaced with the original true observation values ​​to obtain the final prediction results .

[0042] Step 5: Use the training set, validation set, and test set to perform model training, hyperparameter adjustment, and generalization ability evaluation on BI-Transformer, and select the optimal interpolation sample length based on the set evaluation indicators.

[0043] The final result of the BI-Transformer model is obtained by concatenating the forward output and the reverse output and then processing them through a fully connected network. Ideally, the forward and reverse output results should be exactly the same. In order to strengthen this idea, the loss function is defined as L Including accuracy loss function And the consistency loss function Two parts, and weighted Adjust the proportion of the two parts, the calculation formula is:

[0044] (1)

[0045] (2)

[0046] (3)

[0047] In the formula, Indicates the first The actual observed value corresponding to the value is Indicates the sample prediction result output by the BI-Transformer model. values, T represents the sample length, represents the Pearson correlation coefficient, Represents the first output of the BI-Transformer model values, They represent the reverse output of the BI-Transformer model after inversion. values, represents the mean of the forward output results, They represent the mean of the reverse output results respectively.

[0048] The BI-Transformer model adopts different sequence generation modes during the training process and the actual prediction process. The Teacher Forcing mode is used during the training process, that is, it does not rely on the output of the previous training, but directly uses the real observation values ​​corresponding to the training data as the input of each training. This training method can timely correct the prediction trend of the BI-Transformer model during the training process, avoid error amplification in the process of time series data generation, and make the BI-Transformer model fully parallel in the training process, thereby accelerating the convergence speed of the BI-Transformer model.

[0049] In actual prediction, since there is no real observation to guide, the time series data generation task can only be completed by step-by-step generation. Therefore, a decoding strategy based on dynamic replacement of non-missing values ​​is proposed. When the value at position If the position is missing, If there is a missing value, the position generated by the Transformer model is used The predicted value at The value at position, if position If there is no missing value at The original true observation value at prediction The value at the position, such as Figure 3 middle and Use the original true observation value, and use the predicted value for other positions. By dynamically judging the missing status of each position of the input data of the Transformer model and integrating the true observation value into the complete time series data generation process, the maximum utilization of non-missing data can be achieved, while keeping it consistent with the Teacher Forcing mode in the training process as much as possible, avoiding the problems of weak generalization ability and model fragility caused by differences in training and prediction modes. In addition, during actual prediction, if the time series data to be interpolated with missing values ​​is significantly different from the training data, the decoding strategy based on dynamic replacement of non-missing values ​​can promptly correct the direction of time series data generation, prevent error divergence caused by inaccurate prediction of a certain position, and play a positive role in improving the performance of the BI-Transformer model in long time series data interpolation tasks.

[0050] Using the coefficient of determination ( ), mean absolute error (MAE), root mean square error (RMSE) and mean absolute percentage error (MAPE) are used to evaluate the interpolation effect of the model. The larger the value, the smaller the MAE, RMSE and MAPE, indicating that the interpolation effect of the model is better. Taking the four evaluation indicators into consideration, the sample length used by the model with the best interpolation effect is selected as the optimal interpolation sample length. In this embodiment, the optimal interpolation sample length is 48.

[0051] Step 6: Based on the trained BI-Transformer model and the optimal interpolation sample length, the original PM2.5 ground monitoring continuous time series data with missing values ​​is interpolated to obtain complete time series data.

[0052] According to the optimal interpolation sample length of 48, the original PM2.5 ground monitoring continuous time series data with missing values ​​are segmented. When segmenting, each section of PM2.5 ground monitoring sub-time series data is kept with 8 overlapping bits with the previous section of PM2.5 ground monitoring sub-time series data. If the length of the last section of sub-time series data is less than 48 after segmentation by 8 overlapping bits, the overlapping bits with the previous section of PM2.5 ground monitoring sub-time series data are increased to make its length reach 48, thereby obtaining multiple sections of PM2.5 ground monitoring sub-time series data with no missing values ​​and multiple sections of PM2.5 ground monitoring sub-time series data with missing values ​​of 48. The PM2.5 ground monitoring sub-time series data with missing values ​​are input into the trained BI-Transformer model to obtain the corresponding PM2.5 ground monitoring sub-time series prediction data without missing values. The multiple segments of PM2.5 ground monitoring sub-time series prediction data without missing values ​​and the multiple segments of PM2.5 ground monitoring sub-time series data without missing values ​​are spliced ​​to obtain the final PM2.5 ground monitoring continuous time series data without missing values. Among them, the splicing of PM2.5 ground monitoring sub-time series data is to take the average value of the data at the overlapping position of the two PM2.5 ground monitoring sub-time series data.

[0053] Example 2

[0054] Based on the same inventive concept, the present invention also provides a system for interpolating missing values ​​of geographic time series data based on the BI-Transformer model, including a processor and a memory, the memory being used to store program instructions, and the processor being used to call the program instructions in the memory to execute a method for interpolating missing values ​​of geographic time series data based on the BI-Transformer model as described above.

[0055] In specific implementation, the method proposed in the technical solution of the present invention can be implemented by technical personnel in this field using computer software technology to realize automatic operation process. System devices for implementing the method, such as computer-readable storage media storing the corresponding computer program of the technical solution of the present invention and computer equipment running the corresponding computer program, should also be within the scope of protection of the present invention.

[0056] The specific embodiments described herein are merely examples of the spirit of the present invention. Those skilled in the art may make various modifications or additions to the specific implementation cases described, or replace them with similar methods, without departing from the spirit of the present invention or exceeding the scope defined by the appended claims.

Claims

1. A missing value interpolation method for geographic time series data based on the BI-Transformer model, characterized in that: The following steps are involved: Step 1: Split the original continuous geographic time series data with missing values, extract geographic sub-time series data without missing values, and construct a sample set of geographic time series data without missing values; The original continuous geographic time series data with missing values ​​is split, the missing data is removed, and multiple segments of geographic sub-time series data without missing values ​​are obtained. The geographic sub-series data without missing values ​​in each segment are equally divided, n is the number of set sequence lengths, The value of is set according to actual needs, and the geographic data that is less than the set sequence length is discarded to form a geographic time series data sample set with no missing values; Step 2, constructing the geographic time series data sample set without missing values ​​constructed in step 1 into a geographic time series data sample set with missing values; Step 3, divide the geographic time series data sample set with missing values ​​constructed in step 2 into a training set, a validation set, and a test set; Step 4: Build a BI-Transformer model to interpolate missing values ​​in geographic time series data with missing values; The BI-Transformer model consists of two Transformer models and a fully connected network. The sample data in the geographic time series data sample set without missing values ​​constructed in step 1 is used as the real observation value of the sample. ,in is the corresponding observation time, T is the sample length; assuming that the missing value strategy designed in step 2 is used to obtain the geographic time series data sample with missing values , introduce the mask vector Mark missing, when When is a missing value, Take 0, otherwise take 1 to get the positive input sample for training ,beg The inversion of ,Will are the reverse input samples for BI-Transformer model training. , Input the Transformer model to get the corresponding positive output result And reverse output results The Transformer model retains the original true observation values ​​for the locations with no missing values ​​in the original geographic time series data, and only uses the predicted values ​​for the locations with missing values. Invert to get ,Will and Splice to get ,Will Input the fully connected network for feature extraction ,Will The original geographic time series data without missing values ​​are replaced with the original real observation values ​​to obtain the final prediction results. ; Step 5: Use the training set, validation set, and test set to perform model training, hyperparameter adjustment, and generalization ability evaluation on BI-Transformer, and select the optimal interpolation sample length based on the set evaluation indicators; Step 6: Based on the BI-Transformer model trained in step 5 and the selected optimal interpolation sample length, the original continuous geographic time series data with missing values ​​is interpolated to obtain complete geographic time series data.

2. The missing value interpolation method for geographic time series data based on the BI-Transformer model as claimed in claim 1, characterized in that: In step 2, two missing simulation methods, random missing and continuous missing, are used, respectively according to the missing proportion Delete the sample data in the geographic time series data sample set without missing values ​​constructed in step 1 to construct a geographic time series data sample set with missing values. N is the number of missing proportions set. The value is set according to actual needs.

3. The missing value interpolation method for geographic time series data based on the BI-Transformer model as claimed in claim 1, characterized in that: In step 4, the Transformer model is constructed using the attention mechanism and consists of an encoder and a decoder. The encoder is composed of multiple layers with the same structure. Each layer contains two sublayers, namely multi-head attention and feedforward network. Residual connections are used around the layers, followed by layer normalization. The decoder is composed of multiple layers with the same structure. Each layer contains three sub-layers, namely masked multi-head attention, multi-head attention and feedforward network. Residual connections are used around the layers, followed by layer normalization; the fully connected network contains multiple fully connected layers.

4. The missing value interpolation method for geographic time series data based on the BI-Transformer model as claimed in claim 1, characterized in that: In step 5, the BI-Transformer model is trained using the training set. The loss function used in the training process L Including accuracy loss function And the consistency loss function Two parts, and weighted Adjust the proportion of the two parts, the calculation formula is: （1） （2） （3） In the formula, Indicates the first The actual observed value corresponding to the value is Indicates the sample prediction result output by the BI-Transformer model. values, T represents the sample length, represents the Pearson correlation coefficient, Represents the first output of the BI-Transformer model values, They represent the reverse output of the BI-Transformer model after inversion. values, represents the mean of the forward output results, They represent the mean of the reverse output results respectively.

5. The missing value interpolation method for geographic time series data based on the BI-Transformer model as claimed in claim 4, characterized in that: In step 5, the BI-Transformer model uses different sequence generation modes in the training process and the actual prediction process; the Teacher Forcing mode is used in the training process, that is, it does not rely on the output of the previous training, but directly uses the real observations corresponding to the training data as the input of each training; in the actual prediction, a decoding strategy based on dynamic replacement of non-missing values ​​is used. When the value at position If the position is missing, If there is a missing value, the position generated by the Transformer model is used The predicted value at The value at position, if position If there is no missing value at The original true observation value at prediction The value at position.

6. The missing value interpolation method for geographic time series data based on the BI-Transformer model as claimed in claim 5, characterized in that: Use the coefficient of determination in step 5 The interpolation effect of the model is evaluated by four evaluation indicators: mean absolute error (MAE), root mean square error (RMSE) and mean absolute percentage error (MAPE). The larger the value, the smaller the MAE, RMSE and MAPE, indicating that the interpolation effect of the model is better. Considering the four evaluation indicators comprehensively, the sample length used by the model with the best interpolation effect is the optimal interpolation sample length. .

7. The missing value interpolation method for geographic time series data based on the BI-Transformer model as claimed in claim 6, characterized in that: In step 6, the optimal interpolation sample length selected in step 5 is , split the original continuous geographic time series data with missing values, and keep each segment of geographic sub-time series data with the previous segment of geographic sub-time series data during segmentation Overlapping bits, , The value is set according to actual needs. The length of the last segment of geographic sub-series data after the overlapping bit segmentation is insufficient , then increase the overlap between the last segment of geographic sub-series data and the previous segment of geographic sub-series data to make its length reach , thus the length of multiple segments is The geographic sub-time series data with no missing values ​​and multiple segments of length The geographic sub-time series data with missing values ​​are input into the trained BI-Transformer model to obtain the corresponding geographic sub-time series prediction data without missing values; multiple segments of geographic sub-time series prediction data without missing values ​​are spliced ​​with multiple segments of geographic sub-time series data without missing values ​​to obtain the final geographic continuous time series data without missing values; wherein, the splicing of geographic sub-time series data refers to taking the average of the data at the overlapping position of two geographic sub-time series data.

8. A missing value interpolation system for geographic time series data based on the BI-Transformer model, characterized in that: It includes a processor and a memory, the memory is used to store program instructions, and the processor is used to call the program instructions in the memory to execute a missing value interpolation method for geographic time series data based on a BI-Transformer model as described in any one of claims 1 to 7.

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