A beidou space-time data filling method based on neural network deep transformation low-rank tensor recovery

Abstract

The application discloses a Beidou space-time data filling method based on neural network deep transformation low-rank tensor recovery, relates to the technical field of space-time big data and artificial intelligence, and simplifies and extracts a transformation low-rank tensor recovery step based on an iterative optimization algorithm, learns from the idea of a deep unfolding network, unfolds an iterative optimization process into a network layer of a neural network, sets parameters and key operators in the original optimization algorithm as learnable network parameters, constructs a deep transformation tensor recovery network, and finally carries out missing value filling experiments on space-time traffic flow data in a real Beidou scenario. The application not only can effectively improve the filling effect of an original transformation tensor low-rank recovery algorithm based on optimization iterative solving on space-time data, but also can utilize a deep learning framework and GPU parallel computing resources to improve algorithm running speed and actual use efficiency.

Description

Technical Field

[0001] This invention relates to the fields of spatiotemporal big data and artificial intelligence technology, and in particular to a method for filling in BeiDou spatiotemporal data based on low-rank tensor recovery of neural network deep transform. Background Technology

[0002] BeiDou positioning technology generates massive amounts of spatiotemporal data, such as meteorological and traffic data. This data can generate significant value across various industries through modern big data and artificial intelligence methods. However, taking traffic data as an example, the raw data collected often suffers from large areas of missing or randomly missing data due to factors such as weather and building obstruction, severely reducing data quality and affecting the quality of practical applications.

[0003] Constructing data into tensors and recovering it using low-rank tensor optimization theory is a novel and theoretically sound technique. However, most existing algorithms solve optimization problems using iterative optimization algorithms. This approach has two significant problems: first, it requires manually constructing or finding parameters that significantly affect the algorithm's results, such as iterative update factors and transformation factors, based on prior knowledge, which limits the algorithm's capabilities; second, the algorithms are computationally intensive, making it difficult to utilize advanced parallel computing frameworks and resulting in low efficiency. Summary of the Invention

[0004] To overcome the shortcomings of the existing technology, this invention provides a BeiDou spatiotemporal data filling method based on low-rank tensor recovery of neural network deep transform. This method can fully utilize the advantages of optimization algorithms and deep learning to more accurately identify the multi-dimensional coupling characteristics of spatiotemporal data streams and fill in missing values ​​with high precision, providing a good foundation for data mining, data analysis and other applications.

[0005] To achieve the above objectives, the present invention adopts the following technical solution, including:

[0006] A method for BeiDou spatiotemporal data incomplete based on low-rank tensor recovery using neural network depth transform includes the following steps:

[0007] S1 acquires the raw traffic data stream and organizes it into a three-dimensional spatiotemporal tensor for use as input, training, and testing of neural networks;

[0008] S2, analyze the transformation low-rank tensor recovery algorithm process using iterative optimization algorithm, and select and extract key sub-problems as the computational update module in the neural network;

[0009] S3 collects the update parameters and transformation operators involved in the iterative optimization algorithm, sets them as learnable network parameters, and serves as the parameter learning module.

[0010] S4. Combine the calculation update module in step S2 and the parameter learning module in step S3 to construct a deep transformation tensor recovery network;

[0011] S5. Construct a loss function under the deep learning framework and select an optimizer for backpropagation training;

[0012] S6. Use the model trained in step S5 to fill in the spatio-temporal data on the test data.

[0013] Preferably, step S1 is specifically as follows:

[0014] S11. Organize the data from the Beidou satellite navigation and positioning, and construct a three-dimensional tensor of longitude × latitude × time , where the length of the longitude dimension is denoted as m, the length of the latitude dimension is denoted as n, and the length of the time dimension is denoted as t;

[0015] s12. Set a ratio a, 0 < a < 1, divide the three-dimensional tensor in step S11 along the time dimension, and take the tensor with the first t×a time length as the training data, and the remaining tensor with the time length of t×(1 - a) as the test data .

[0016] Preferably, step S2 is specifically as follows:

[0017] S21. Select a Beidou spatio-temporal traffic data recovery method based on transformation-induced low-rank tensors, and extract the optimization problem:

[0018]

[0019] where, is the tensor to be recovered; , , is the tensor expansion multiplication defined in a Beidou spatio-temporal traffic data recovery method based on transformation-induced low-rank tensors; is the new tensor transformed from the original tensor through tensor expansion multiplication; is the activation function; is the tensor containing only observed values; is the identity matrix; i represents the th positive slice; G, H, and T are three semi-orthogonal transformation matrices; is the projection operator mapping to the sampling space ;

[0020] S22. Analyze the solution process of this optimization problem, and perform iterative solution of sub-problems in the following order:

[0021]

[0022] in, superscript k The iterative algorithm represents the first... k The iteration results of the round;

[0023] S23, Select one of them , , Sub-problems, construct neural network modules M, D, and P as computation and update modules, and use... , , The closed-loop solution process in the optimization problem in step S21 and the iterative solution process in step S22 are respectively used as the forward propagation process inside the neural network modules M, D, and P.

[0024] in, The closed-form solution process for the subproblem is as follows:

[0025]

[0026] in, , Represents the sampling space The complement space (complement set), real number The update parameters are set; A tensor containing the original collected data; the neural network module M is a tensor containing the original collected data. , As input, with This is the network processing module for output;

[0027] according to The closed-form solution process of the subproblem, with The closed-form solution process of the subproblem constructs a neural network module D. The closed-form solution process for the subproblem is as follows:

[0028]

[0029] in, This represents the singular value reduction operator.

[0030] according to The closed-form solution process of the subproblem, with The closed-form solution process of the subproblem constructs a neural network module P. The closed-form solution process for the subproblem is as follows:

[0031]

[0032] in, For a third-order tensor The index in is The corresponding element, For a third-order tensor The index in is The corresponding element, This subproblem can be broken down into: A one-dimensional quadratic nonlinear optimization problem can be solved using Newton's method;

[0033] S24. Connect the neural network modules M, D, and P in sequence to form a network layer, and set... K The number of network layers constitutes the structure. K The forward propagation process of the layer.

[0034] Preferably, step S3 is as follows:

[0035] S31. Collect the parameters involved in the neural network modules M, D, P constructed in step S23, as well as the transformation matrices G, H, T, and set them as learnable parameters in the network.

[0036] S32. Organize the parameter vector and operators obtained in step S31 into a parameter learning module U.

[0037] Preferably, step S5 is as follows:

[0038] S51. Using the absolute error (MAE) as the training loss function, its expression is:

[0039]

[0040] in, The first tensor representing the result of restoration (filling) ijk The element at the position is , For the original tensor in the th case ijk Elements at position, N This represents the total number of elements in the tensor.

[0041] S52. Use the Adam optimizer as the neural network training optimizer;

[0042] S53. Set the initial learning rate, and set the learning decay strategy and the total number of training rounds;

[0043] S54. Set the operator matrix to orthogonal initialization;

[0044] S55. Train the model on the training dataset and save the trained model parameters.

[0045] Preferably, step S4 is as follows:

[0046] The parameter learning module obtained in step S3 is coupled with the neural network modules M, D, and P obtained in step S2. The parameters are stored, provided, and updated for the propagation process of the three modules. This whole constitutes the depth transform tensor recovery network.

[0047] Preferably, GPU parallel computing technology is used within a deep learning framework to improve the algorithm's computation speed.

[0048] The present invention also provides a readable storage medium storing a computer program thereon, which, when executed, implements the aforementioned method for BeiDou spatiotemporal data filling based on neural network deep transform low-rank tensor recovery.

[0049] The present invention also provides an electronic device, which includes a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the aforementioned method for BeiDou spatiotemporal data filling based on neural network deep transform low-rank tensor recovery.

[0050] The present invention also provides a computer program product comprising a computer program / instruction that, when executed by a processor, implements the aforementioned method for BeiDou spatiotemporal data filling based on neural network deep transform low-rank tensor recovery.

[0051] The advantages of this invention are:

[0052] (1) This invention can make full use of the advantages of optimization algorithms and deep learning to more accurately identify the multi-dimensional coupling characteristics of spatiotemporal data streams and fill in the missing values ​​with high precision, providing a good foundation for data mining, data analysis and other applications.

[0053] (2) The present invention can also effectively utilize GPU parallel computing technology to accelerate the algorithm's solution speed and improve practical efficiency.

[0054] (3) This invention is based on the tensor low-rank recovery algorithm of optimization theory. Under the guidance of the recovery theory guarantee, the iterative solution process is transformed into a neural network of low-rank tensor recovery. On the one hand, it has theoretical feasibility and interpretability. On the other hand, it makes full use of the advantage of deep learning that it can flexibly learn parameters based on data, which solves the difficulty of setting up factors that have a significant impact on the algorithm results, such as the need to manually construct or find iterative update factors and transformation factors in combination with prior knowledge in traditional iterative optimization algorithms. The simulation effect on real-world spatiotemporal traffic flow data shows that the invention surpasses the existing advanced tensor optimization algorithms in the recovery effect of traffic data collected by Beidou.

[0055] (4) This invention is scalable. It draws on the idea of ​​deep unfolded networks in the field of spatiotemporal data filling. Similar modification ideas and methods can be extended to arbitrary tensor recovery algorithms and applied to the problem of missing spatiotemporal data recovery and filling.

[0056] (5) By simplifying and modifying the iterative optimization algorithm into a neural network, the present invention can learn and recover important parameters in the algorithm on its own, which not only improves the algorithm effect, but also takes advantage of the GPU for parallel computing under the deep learning framework, speeds up the algorithm's solution speed, and improves the actual utilization efficiency. Attached Figure Description

[0057] Figure 1 This is a schematic diagram of the method of the present invention.

[0058] Figure 2 This is a simplified model diagram of the depth transform tensor recovery network of the present invention.

[0059] Figure 3 This is a schematic diagram of the original spatiotemporal data slices of the present invention.

[0060] Figure 4 This is an experimental result diagram of the data recovery method according to the present invention.

[0061] Figure 5 This is a schematic diagram to verify that the transformation matrix obtained through training is an orthogonal matrix in this invention. Detailed Implementation

[0062] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0063] Example 1

[0064] Depend on Figure 1 As shown, this invention provides a method for BeiDou spatiotemporal data incomplete based on low-rank tensor recovery using neural network depth transform, comprising the following specific steps:

[0065] S1. Acquire the original spatiotemporal data stream and organize it into a three-dimensional spatiotemporal tensor to facilitate the input, training, and testing of neural networks.

[0066] Step S1 is as follows:

[0067] S11 utilizes Python's NumPy and Pandas data processing packages to organize data originating from the BeiDou satellite navigation and positioning system, constructing a three-dimensional tensor of longitude (X) × latitude (Y) × time (T). , where the length of the longitude (X) dimension is denoted as m, the length of the latitude (Y) dimension is denoted as n, and the length of the time (T) dimension is denoted as t;

[0068] S12. Set a ratio a (0 < a < 1), divide the three-dimensional tensor in step S11 along the time dimension, and take the tensor with the first t×a time length as the training data, and the tensor with the remaining t×(1 - a) time length as the test data .

[0069] S2. Analyze the steps of the transform low-rank tensor recovery algorithm solved using the iterative optimization algorithm, screen and extract the key sub-problems therein as the calculation update module in the neural network.

[0070] Step S2 is specifically as follows:

[0071] S21. Select the transform low-rank tensor recovery algorithm, such as a Beidou spatio-temporal traffic data recovery method based on transform-induced low-rank tensors with Chinese Patent Publication No. CN118445284A, and extract the optimization problem:

[0072]

[0073] where, is the tensor to be recovered; , , is the tensor expansion multiplication defined in a Beidou spatio-temporal traffic data recovery method based on transform-induced low-rank tensors; is the new tensor transformed from the original tensor through tensor expansion multiplication; is the activation function; is the tensor containing only the observed values; is the identity matrix; represents the i th positive slice; G, H, and T are three semi-orthogonal transformation matrices; is the projection operator mapping to the sampling space ;

[0074] S22. Analyze the solution process of this optimization problem, and specifically perform iterative solution of sub-problems in the following order:

[0075]

[0076] where, , and the superscript k represents the iterative result of the k th round of the iterative algorithm; ]>

[0077] S23. Select the , , Subproblems are used to construct neural network modules M, D, and P. The closed-loop solution processes in the optimization problem in step S21 and the optimization solution steps in step S22 are used as the forward propagation processes inside neural network modules M, D, and P, respectively.

[0078] Specifically, in step S22 The closed-form solution process for the subproblem is as follows:

[0079]

[0080] in, , Represents the sampling space The complement space (complement set), real number The update parameters are set; It is a tensor containing the original collected data;

[0081] Then the neural network module M is based on , As input, with This is the network processing module for output;

[0082] Similarly, according to The closed-form solution process of the subproblem, with The closed-form solution process of the subproblem constructs a neural network module D. The closed-form solution process for the subproblem is as follows:

[0083]

[0084] in, This represents the singular value reduction operator, which is defined in the reference "A singular valuethresholding algorithm for matrix completion". Cai, J.-F., Candès, EJ, and Shen, Z. SIAM Journal on optimization, 20(4):1946–1982, 2010.

[0085] Similarly, according to The closed-form solution process of the subproblem, with The closed-form solution process of the subproblem constructs a neural network module P. The closed-form solution process for the subproblem is as follows:

[0086]

[0087] in, For a third-order tensor The index in is The corresponding element, For a third-order tensor The index in is The corresponding element, This subproblem can be broken down into: A one-dimensional quadratic nonlinear optimization problem can be solved using Newton's method. In the method of this invention, the first-order gradient descent method can also be used directly to replace Newton's method to accelerate network propagation.

[0088] S24. Connect the neural network modules M, D, and P in sequence to form a network layer, and set... K The number of network layers constitutes the structure. K The forward propagation process of the layer.

[0089] S3. Collect the update parameters and transformation operators involved in the optimization algorithm, set them as learnable network parameters, and use them as the parameter learning module.

[0090] Step S3 is as follows:

[0091] S31. Collect the parameters involved in the neural network modules M, D, and P constructed in step S23, such as... , And so on, along with the transformation matrices G, H, and T, are set as learnable parameters in the network. Specifically, each parameter is constructed as a matrix of length [missing information]. K vectors, such as The parameters are updated during training following the vector, while each transformation matrix is ​​updated individually with each training round.

[0092] S32. Organize the parameter vectors, operators, etc. obtained in step S31 into a parameter learning module U.

[0093] S4. Merge the calculation update module in step S2 and the parameter learning module in step S3 to construct a depth transformation tensor recovery network.

[0094] Specifically, the parameter learning module U obtained in step S3 is coupled with the neural network modules M, D, and P obtained in step S2 to store, provide, and update parameters for the propagation process of the three modules; the whole constitutes the depth transform tensor recovery network.

[0095] S5. Construct a loss function within the deep learning framework, set hyperparameters such as learning rate and parameter initialization method, and select an optimizer for backpropagation training.

[0096] Step S5 is as follows:

[0097] S51. Using the absolute error (MAE) as the training loss function, its expression is:

[0098]

[0099] in, The first tensor representing the result of restoration (filling) ijk The element at the position is , For the original tensor in the th case ijk Elements at position, N This represents the total number of elements in the tensor.

[0100] S52. Use the Adam optimizer as the neural network training optimizer;

[0101] S53. Select 0.001 as the initial learning rate and set a learning decay strategy of 10% / 10 rounds, with a total of 100 training rounds;

[0102] S54. Set the operator matrix to orthogonal initialization;

[0103] S55, in the training dataset The model is trained and the trained model parameters are saved.

[0104] S6. Use the model trained in step S5 to perform spatiotemporal data imputation on the test data.

[0105] Step S6 is as follows;

[0106] S61. Load the model parameters trained in step S5 onto the test dataset. The spatiotemporal data restoration (filling) effect was then tested.

[0107] S62. Compare the test results with other low-rank tensor recovery algorithms based on iterative optimization.

[0108] This invention simplifies and modifies the iterative optimization algorithm into a neural network, which can learn and recover important parameters in the algorithm on its own. This not only improves the algorithm's performance, but also leverages the advantages of GPU parallel computing within the deep learning framework to accelerate the algorithm's solution speed and improve practical utilization efficiency.

[0109] This invention is based on the tensor low-rank recovery algorithm of optimization theory. Driven by the heuristics of recovery theory, the iterative solution process is transformed into a neural network for low-rank tensor recovery. On the one hand, it has theoretical feasibility and interpretability; on the other hand, it makes full use of the advantage of deep learning that it can flexibly learn parameters based on data, solving the difficulty of setting up factors that have a significant impact on the algorithm results, such as iterative update factors and transformation factors, which need to be manually constructed or found in combination with prior knowledge in traditional iterative optimization algorithms. The simulation results on real-world spatiotemporal traffic flow data show that the invention surpasses the existing advanced tensor optimization algorithms in the recovery effect of traffic data collected by Beidou.

[0110] Table 1 shows a comparison of the experimental results in this invention. The comparison results show that the method proposed in this invention performs well on the selected experimental slice data, and even surpasses other tensor optimization data recovery methods that do not incorporate deep unfolded neural networks. The inference speed of the network is significantly improved compared to the recovery speed of the optimization method, demonstrating the advantages of this method in terms of portability, parallel computing, and offline inference after training.

[0111] Table 1

[0112]

[0113] Figure 3 This is a schematic diagram of the original spatiotemporal data slices of the present invention. Figure 4 This is an experimental result diagram of the data recovery method according to the present invention. Figure 5 This is a schematic diagram to verify that the transformation matrix obtained through training is an orthogonal matrix in this invention.

[0114] Example 2

[0115] An electronic device includes a processor, a memory, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the method of Embodiment 1 described above.

[0116] The electronic device in this application embodiment may be the mobile device itself, or a standalone device independent of it. The standalone device may communicate with the mobile device to receive the collected input signals from it and send the selected target decision behavior to it.

[0117] An electronic device includes one or more processors and memory. The processor may be a central processing unit (CPU) or other processing unit with data processing capabilities and / or instruction execution capabilities, and may control other components in the electronic device to perform desired functions. The memory may include one or more computer program products, which may include various forms of computer-readable storage media, such as volatile memory and / or non-volatile memory. The volatile memory may, for example, include random access memory (RAM) and / or cache memory. The non-volatile memory may, for example, include read-only memory (ROM), hard disk, flash memory, etc. One or more computer program instructions may be stored on the computer-readable storage medium, and the processor may execute the program instructions to implement the decision-making behavior and decision-making methods of the various embodiments of this application described above, and / or other desired functions.

[0118] Electronic devices may also include input devices and output devices.

[0119] Example 3

[0120] In addition to the methods and devices described above, embodiments of this application may also be computer program products, which include computer program instructions that, when executed by a processor, cause the processor to perform the steps in the decision-making behavior decision-making method according to various embodiments of this application as described in Embodiment 1 above.

[0121] The computer program product can be written in any combination of one or more programming languages ​​to perform the operations of the embodiments of this application. The programming languages ​​include object-oriented programming languages ​​such as Java and C++, as well as conventional procedural programming languages ​​such as C or similar languages. The program code can be executed entirely on the user's computing device, partially on the user's computing device, as a standalone software package, partially on the user's computing device and partially on a remote computing device, or entirely on a remote computing device or server.

[0122] Example 4

[0123] Embodiments of this application may also be computer-readable storage media storing computer program instructions thereon, which, when executed by a processor, cause the processor to perform the steps in the decision-making behavior decision-making method according to various embodiments of this application described in Embodiment 1 above.

[0124] The computer-readable storage medium may be any combination of one or more readable media. A readable medium may be a readable signal medium or a readable storage medium. A readable storage medium may, for example, include, but is not limited to, electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatuses, or devices, or any combination thereof. More specific examples of readable storage media (a non-exhaustive list) include: electrical connections having one or more wires, portable disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof.

[0125] The above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for filling in BeiDou spatiotemporal data based on low-rank tensor recovery using neural network depth transform, characterized in that, Includes the following steps: S1 acquires the raw traffic data stream and organizes it into a three-dimensional spatiotemporal tensor for use as input, training, and testing of neural networks; S2, analyze the transformation low-rank tensor recovery algorithm process using iterative optimization algorithm, and select and extract key sub-problems as the computational update module in the neural network; S3 collects the update parameters and transformation operators involved in the iterative optimization algorithm, sets them as learnable network parameters, and serves as the parameter learning module. S4, merge the calculation update module in step S2 and the parameter learning module in step S3 to construct a depth transformation tensor recovery network; S5. Construct a loss function within the deep learning framework and select an optimizer for backpropagation training. S6. Use the model trained in step S5 to perform spatiotemporal data filling on the test data; Step S2 is detailed below: S21. Select a BeiDou spatiotemporal traffic data recovery method based on transformation-induced low-rank tensors and extract the optimization problem: in, For the tensor to be recovered; , , For tensor expansion multiplication; It is a new tensor transformed from the original tensor through tensor expansion and multiplication; For activation functions; A tensor that contains only observations; G is the identity matrix; G, H, and T are three semi-orthogonal transformation matrices. To map to the sampling space The projection operator; S22. Analyze the solution process of this optimization problem, and perform iterative solutions to the subproblems in the following order: in, superscript k The iterative algorithm represents the first... k The iteration results of the round; S23, Select one of them , , Sub-problems, construct neural network modules M, D, and P as computation and update modules, and use... , , The closed-loop solution process in the optimization problem in step S21 and the iterative solution process in step S22 are respectively used as the forward propagation process inside the neural network modules M, D, and P. in, The closed-form solution process for the subproblem is as follows: in, , Represents the sampling space Fill space, real number The update parameters are set; A tensor containing the original collected data; the neural network module M is a tensor containing the original collected data. , As input, with This is the network processing module for output; according to The closed-form solution process of the subproblem, with The closed-form solution process of the subproblem constructs a neural network module D. The closed-form solution process for the subproblem is as follows: in, This represents the singular value reduction operator; Indicates the first i A frontal slice; according to The closed-form solution process of the subproblem, with The closed-form solution process of the subproblem constructs a neural network module P. The closed-form solution process for the subproblem is as follows: in, For a third-order tensor The index in is The corresponding element, For a third-order tensor The index in is The corresponding element, This subproblem can be broken down into: A one-dimensional quadratic nonlinear optimization problem can be solved using Newton's method; real numbers The update parameters are set; S24. Connect the neural network modules M, D, and P in sequence to form a network layer, and set... K The number of network layers constitutes the structure. K The forward propagation process of the layer.

2. The method for BeiDou spatiotemporal data incomplete based on low-rank tensor recovery using neural network depth transform according to claim 1, characterized in that, Step S1 is as follows: S11. Organize the data originating from BeiDou satellite navigation and positioning to construct a three-dimensional tensor of longitude × latitude × time. Wherein, the length of the longitude dimension is denoted as m, the length of the latitude dimension is denoted as n, and the length of the time dimension is denoted as t; S12. Set a ratio a, where 0 < a < 1. Divide the three-dimensional tensor in step S11 along the time dimension, and take the tensor with the time length of the first t×a as the training data, and the tensor with the remaining time length of t×(1 - a) as the test data For the training data, and the remaining t×(1 - a) time length of the tensor is the test data .

3. The method for BeiDou spatiotemporal data filling based on low-rank tensor recovery using neural network depth transform according to claim 1, characterized in that, Step S3 is as follows: S31. Collect the parameters involved in the neural network modules M, D, P constructed in step S23, as well as the transformation matrices G, H, T, and set them as learnable parameters in the network. S32. Organize the parameter vector and operators obtained in step S31 into a parameter learning module U.

4. The method for BeiDou spatiotemporal data filling based on low-rank tensor recovery using neural network depth transform according to claim 1, characterized in that, Step S5 is as follows: S51. Using the absolute error (MAE) as the training loss function, its expression is: in, The first tensor representing the recovery result tensor ijk The element at the position is , For the original tensor in the th case ijk Elements at position, N This represents the total number of elements in the tensor. S52. Use the Adam optimizer as the neural network training optimizer; S53. Set the initial learning rate, and set the learning decay strategy and the total number of training rounds; S54. Set the operator matrix to orthogonal initialization; S55. Train the model on the training dataset and save the trained model parameters.

5. The method for BeiDou spatiotemporal data incomplete based on low-rank tensor recovery using neural network depth transform according to claim 1, characterized in that, Step S4 is as follows: The parameter learning module obtained in step S3 is coupled with the neural network modules M, D, and P obtained in step S2. The parameters are stored, provided, and updated for the propagation process of the three modules. This whole constitutes the depth transform tensor recovery network.

6. The method for BeiDou spatiotemporal data incomplete based on low-rank tensor recovery using neural network depth transform according to claim 1, characterized in that, By utilizing GPU parallel computing technology within a deep learning framework, the computation speed of algorithms can be improved.

7. A readable storage medium, characterized in that, It stores a computer program, which, when executed, implements the BeiDou spatiotemporal data filling method based on low-rank tensor recovery of neural network depth transform as described in any one of claims 1 to 6.

8. An electronic device, characterized in that, It includes a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the BeiDou spatiotemporal data filling method based on low-rank tensor recovery of neural network deep transform as described in any one of claims 1 to 6.

9. A computer program product, characterized in that, It includes a computer program / instruction that, when executed by a processor, implements the BeiDou spatiotemporal data filling method based on low-rank tensor recovery of neural network depth transform as described in any one of claims 1 to 6.

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