Space-time traffic data completion method, device and system based on non-convex regularization and medium
By constructing a model that minimizes the sum of nuclear norms based on non-convex regularization and iteratively solving it using the alternating direction multiplier method, the problem of insufficient accuracy in spatiotemporal traffic data completion is solved, and effective data recovery is achieved under high missing rate conditions.
Patent Information
- Application Number
- CN202511888454.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-15
- Publication Date
- 2026-03-06
AI Technical Summary
Existing low-rank tensor completion methods suffer from insufficient accuracy and optimization difficulties when dealing with non-random missing patterns in spatiotemporal traffic data, especially with poor performance under high missing rates.
A non-convex regularization-based approach is adopted. By introducing the TL1 regularization term and the idea of convex function difference, the non-convex regularization model is transformed into a convex optimization model. The alternating direction multiplier method is used to solve the problem iteratively, and a model that minimizes the sum of the nuclear norms is constructed to improve the accuracy of data completion.
It improves the accuracy of spatiotemporal traffic data completion, and can effectively recover data, especially under high missing rate conditions, demonstrating excellent completion ability and robustness.
Smart Images
Figure CN121614748A_ABST
Abstract
Description
Technical Field
[0001] This application relates to, but is not limited to, the field of data processing technology, and in particular to a method, apparatus, system, and medium for spatiotemporal traffic data completion based on non-convex regularization. Background Technology
[0002] Spatiotemporal traffic data, a core input for the widespread application of Intelligent Transportation Systems (ICT), refers to traffic system status data that simultaneously contains spatial and temporal attributes. It is primarily used in intelligent traffic management, route planning optimization, and urban traffic policy formulation. With the proliferation of detection equipment, the scale of this data has grown significantly. However, due to factors such as sensor malfunctions, communication interruptions, and system maintenance, spatiotemporal traffic data often suffers from incompleteness, severely impacting the reliability and overall effectiveness of ICT.
[0003] Spatiotemporal traffic data is essentially a multidimensional time series, recording traffic status indicators at specific geographical locations and points in time. Common data types include traffic flow, average vehicle speed, and time occupancy. Incomplete traffic data exhibits different missing patterns and rates, with missing patterns categorized into random and non-random missing data. Random missing data is primarily caused by accidental factors such as temporary sensor communication interruptions or brief storage failures, manifesting as the random absence of individual data points in the time series. Non-random missing data, on the other hand, can result from continuous communication system failures or periodic maintenance, manifesting as consecutive missing data points spanning several hours or even entire days in the time series. Existing research indicates that non-random missing patterns are more challenging than random missing patterns in data completion problems because their absence is inherently linked to the data's patterns. Therefore, how to complete data with these two missing patterns is a crucial challenge.
[0004] Spatiotemporal traffic data is typically organized into three-dimensional tensors, where the three dimensions correspond to spatial location, time point, and date period, respectively. This structure effectively captures the spatiotemporal correlation of traffic flow. Furthermore, spatiotemporal traffic data is usually low-rank. Therefore, the spatiotemporal traffic data completion problem is transformed into a low-rank tensor completion task. Existing low-rank tensor completion methods include tensor decomposition, which is limited by rank selection and local optima; convex relaxation methods based on kernel norm minimization, which lead to estimation biases of principal components due to the equal contraction of all singular values, resulting in poor performance, especially under high missing rates; and common non-convex substitution functions, which perform well but face challenges in optimization and algorithm design. Therefore, finding more accurate rank function approximation methods to improve the accuracy of traffic data completion has attracted widespread attention from researchers. Summary of the Invention
[0005] The following is an overview of the subject matter described in detail herein. This overview is not intended to limit the scope of the claims.
[0006] This application provides a spatiotemporal traffic data completion method, apparatus, system, and medium based on non-convex regularization to improve the accuracy of traffic data completion.
[0007] In a first aspect, embodiments of this application provide a spatiotemporal traffic data completion method based on non-convex regularization, comprising the following steps:
[0008] S100, based on the model of minimizing the sum of nuclear norms, constructs a non-convex regularized model for traffic data completion by introducing the TL1 regularization term;
[0009] In S100, the non-convex regularization model for traffic data completion is constructed based on the model of minimizing the sum of nuclear norms by introducing a TL1 regularization term, including:
[0010] The model for minimizing the sum of nuclear norms is:
[0011] ;
[0012] in, It is a tensor The expansion matrix along the k-th pattern;
[0013] Introducing TL1 regularization term:
[0014] ;
[0015] The non-convex regularized completion model is constructed as follows:
[0016] ;
[0017] The above non-convex regularization model can be equivalently transformed into:
[0018] ;
[0019] The nuclear norm can be expressed as the L1 norm of all singular vectors.
[0020] ;
[0021] Depend on and The definition can be obtained
[0022] ;
[0023] Therefore, the singular values generated by the convex structure are smaller than the sum of the nuclear norms, and can more accurately approximate the rank function;
[0024] S200 uses the idea of convex function difference to transform a non-convex regularized model into a convex optimization model;
[0025] In S200, the method of transforming a non-convex regularized model into a convex optimization model using the concept of convex function difference includes:
[0026] The non-convex regularized model is transformed into a convex optimization model by using the idea of convex function difference, and the convex optimization model is used for traffic data completion;
[0027] Based on the principle of the Convex Function Difference (DCA) algorithm, After linearization, the transformed convex optimization model is as follows:
[0028] ;
[0029] in, Indicates the first The next iteration;
[0030] Furthermore, to further enhance the robustness and convergence speed of the algorithm, L2 norm neighbor terms are introduced into the subproblems of DCA, forming a neighboring DCA. This strategy ensures that the subproblems are strongly convex, thereby obtaining a unique solution and improving the stability of the algorithm. The convex optimization model is transformed into a neighboring DCA subproblem:
[0031] ;
[0032] in, It is a constant greater than 0;
[0033] S300, acquire the spatiotemporal traffic data to be completed, input the spatiotemporal traffic data to be completed into the convex optimization model, and use the alternating direction multiplier method to iteratively solve the convex optimization model to obtain the completed data;
[0034] In S300, the step of inputting the spatiotemporal traffic data to be completed into the convex optimization model, and using the alternating direction multiplier method to iteratively solve the convex optimization model to obtain the completed data includes:
[0035] S310, Initialize the number of inner and outer iterations, given... Neighbor parameters Penalty parameters Lagrange multipliers ;
[0036] S320, input the spatiotemporal traffic data to be completed into the convex optimization model, and convert the convex optimization model into the following minimization model:
[0037] ;
[0038] S330, the augmented Lagrangian function of the minimized model is expressed as:
[0039] ;
[0040] in, It is the quadratic penalty coefficient; It is a Lagrange multiplier.
[0041] S340, solve sequentially to obtain the minimized model in the minimized model. Solution, minimization Solution and minimization The solutions include:
[0042] The parameters in the minimization model are determined according to the following formula. The terms of the augmented Lagrange function are extracted to obtain...
[0043] ;
[0044] Solving ;
[0045] Shrinking using generalized singular value thresholding:
[0046] ;
[0047] For matrix Performing singular value decomposition (SVD) yields:
[0048] ;
[0049] in The contraction rule for singular values is:
[0050] ;
[0051] get Closed solution:
[0052] ;
[0053] By solving the multimodal expansion matrix Summing and averaging yields the following results Optimize the solution to the subproblem:
[0054] ;
[0055] The parameters in the minimization model are determined according to the following formula. The terms of the augmented Lagrangian function are extracted to obtain:
[0056] ;
[0057] The closed-form solution to this equation is:
[0058] ;
[0059] in, express The complement;
[0060] To obtain the correct solution, the Lagrange multipliers are updated, as follows:
[0061] ;
[0062] S350: Accumulate the number of internal and external iterations of the current generation and determine whether the preset maximum number of iterations has been reached. If yes, proceed to S360; otherwise, minimize the number of iterations. The solution is used as the data to be completed, and S320 is executed;
[0063] S360 will minimize The solution is output as the completed data;
[0064] Secondly, embodiments of this application also provide a spatiotemporal traffic data completion device based on non-convex regularization, the spatiotemporal traffic data completion device based on non-convex regularization comprising:
[0065] The first module is based on the model of minimizing the sum of nuclear norms. It constructs a non-convex regularization model for traffic data completion by introducing the TL1 regularization term.
[0066] The second module uses the idea of convex function difference to transform the non-convex regularized model into a convex optimization model;
[0067] The third module acquires the spatiotemporal traffic data to be completed, inputs the spatiotemporal traffic data to be completed into the convex optimization model, and uses the alternating direction multiplier method to iteratively solve the convex optimization model to obtain the completed data.
[0068] Thirdly, embodiments of this application also provide a spatiotemporal traffic data completion system based on non-convex regularization, including: a collector, a memory, a processor, a display, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements a spatiotemporal traffic data completion method based on non-convex regularization as described in the first aspect.
[0069] Fourthly, embodiments of this application also provide a spatiotemporal traffic data completion medium based on non-convex regularization, which is a computer-readable storage medium storing computer-executable instructions, the computer-executable instructions being used to execute a spatiotemporal traffic data completion method based on non-convex regularization as described in the first aspect.
[0070] The embodiments of this application have the following beneficial effects: Based on the model of minimizing the sum of nuclear norms, the embodiments provided in this application construct a non-convex regularized model for traffic data completion by introducing a TL1 regularization term. This results in smaller singular values and a more accurate approximation of the rank function. The idea of convex function difference is used to transform the non-convex regularized model into a convex optimization model, which is beneficial for solving the optimal solution. Alternating direction multiplier method is used for iterative solving of the above convex optimization model, thereby obtaining the completed data. The model constructed in this application can improve the accuracy of traffic data completion.
[0071] Other features and advantages of this application will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing the application. The objectives and other advantages of this application may be realized and obtained by means of the structures particularly pointed out in the description, claims and drawings. Attached Figure Description
[0072] The accompanying drawings are used to provide a further understanding of the technical solutions of this application and constitute a part of the specification. They are used together with the embodiments of this application to explain the technical solutions of this application and do not constitute a limitation on the technical solutions of this application.
[0073] Figure 1 This is a flowchart of a spatiotemporal traffic data completion method based on non-convex regularization provided in one embodiment of this application;
[0074] Figure 2 This is the effect of time series completion using a 70% random missing rate on four spatiotemporal traffic datasets (G), (B), (H), and (S) provided in one embodiment of this application;
[0075] Figure 3 This is the effect of time series completion using a 70% non-random missing rate for four spatiotemporal traffic datasets (G), (B), (H), and (S) provided in one embodiment of this application;
[0076] Figure 4 This is a structural diagram of a spatiotemporal traffic data completion device based on non-convex regularization provided in one embodiment of this application;
[0077] Figure 5 This is a structural diagram of a spatiotemporal traffic data completion system based on non-convex regularization provided in one embodiment of this application. Detailed Implementation
[0078] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.
[0079] It should be noted that although functional modules are divided in the device schematic diagram and a logical order is shown in the flowchart, in some cases, the steps shown or described may be performed in a different order than the module division in the device or the order in the flowchart. The terms "first," "second," etc., in the specification, claims, or the aforementioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence.
[0080] refer to Figure 1 This application provides a spatiotemporal traffic data completion method based on non-convex regularization, which includes the following steps:
[0081] S100, based on the model of minimizing the sum of nuclear norms, constructs a non-convex regularized model for traffic data completion by introducing the TL1 regularization term;
[0082] In S100, the non-convex regularization model for traffic data completion is constructed based on the model of minimizing the sum of nuclear norms by introducing a TL1 regularization term, including:
[0083] The model for minimizing the sum of nuclear norms is:
[0084] ;
[0085] in, It is a tensor The expansion matrix along the k-th pattern;
[0086] Introducing TL1 regularization term:
[0087] ;
[0088] The non-convex regularized completion model is constructed as follows:
[0089] ;
[0090] The above non-convex regularization model can be equivalently transformed into:
[0091] ;
[0092] The nuclear norm can be expressed as the L1 norm of all singular vectors.
[0093] ;
[0094] Depend on and The definition can be obtained
[0095] ;
[0096] Therefore, the singular values generated by the convex structure are smaller than the sum of the nuclear norms, and can more accurately approximate the rank function;
[0097] S200 uses the idea of convex function difference to transform a non-convex regularized model into a convex optimization model;
[0098] In S200, the method of transforming a non-convex regularized model into a convex optimization model using the idea of convex function difference includes:
[0099] The non-convex regularized model is transformed into a convex optimization model by using the idea of convex function difference, and the convex optimization model is used for traffic data completion;
[0100] Based on the principle of the Convex Function Difference (DCA) algorithm, After linearization, the transformed convex optimization model is as follows:
[0101] ;
[0102] in, Indicates the first The next iteration;
[0103] Furthermore, to further enhance the robustness and convergence speed of the algorithm, L2 norm neighbor terms are introduced into the subproblems of DCA, forming a neighboring DCA. This strategy ensures that the subproblems are strongly convex, thereby obtaining a unique solution and improving the stability of the algorithm. The convex optimization model is transformed into a neighboring DCA subproblem:
[0104] ;
[0105] in, It is a constant greater than 0;
[0106] S300: Obtain the spatiotemporal traffic data to be completed, input the spatiotemporal traffic data to be completed into the convex optimization model, and use the alternating direction multiplier method to iteratively solve the convex optimization model to obtain the completed data.
[0107] In S300, the step of inputting the spatiotemporal traffic data to be completed into the convex optimization model, and using the alternating direction multiplier method to iteratively solve the convex optimization model to obtain the completed data includes:
[0108] S310, Initialize the number of inner and outer iterations, given... Neighbor parameters Penalty parameters Lagrange multipliers ;
[0109] S320, input the spatiotemporal traffic data to be completed into the convex optimization model, and convert the convex optimization model into the following minimization model:
[0110] ;
[0111] S330, the augmented Lagrangian function of the minimized model is expressed as:
[0112] ;
[0113] in, It is the quadratic penalty coefficient; They are Lagrange multipliers;
[0114] S340, solve sequentially to obtain the minimized model in the minimized model. Solution, minimization Solution and minimization The solutions include:
[0115] The parameters in the minimization model are determined according to the following formula. The terms of the augmented Lagrange function are extracted to obtain...
[0116] ;
[0117] Solving ;
[0118] Shrinking using generalized singular value thresholding:
[0119] ;
[0120] For matrix Performing singular value decomposition (SVD) yields:
[0121] ;
[0122] in The contraction rule for singular values is:
[0123] ;
[0124] get Closed solution:
[0125] ;
[0126] By solving the multimodal expansion matrix Summing and averaging yields the following results Optimize the solution to the subproblem:
[0127] ;
[0128] The parameters in the minimization model are determined according to the following formula. The terms of the augmented Lagrangian function are extracted to obtain:
[0129] ;
[0130] The closed-form solution to this equation is:
[0131] ;
[0132] in, express The complement;
[0133] To obtain the correct solution, the Lagrange multipliers are updated, as follows:
[0134] ;
[0135] S350: Accumulate the number of internal and external iterations of the current generation and determine whether the preset maximum number of iterations has been reached. If yes, proceed to S360; otherwise, minimize the number of iterations. The solution is used as the data to be completed, and S320 is executed;
[0136] S360 will minimize The solution is output as the completed data.
[0137] In the embodiments provided in this application, a non-convex regularized model for traffic data completion is constructed based on the model of minimizing the sum of nuclear norms. This model is more flexible and more suitable for spatiotemporal traffic data completion. The non-convex regularized model is transformed into a convex optimization model using the concept of convex function difference, converting the unconstrained problem into an equality-constrained problem, equivalent to multi-block iterative optimization, thereby obtaining the completed traffic data. The non-convex regularized model and corresponding solution method constructed in this application can improve the accuracy of traffic data completion.
[0138] In some embodiments, the maximum number of iterations in the inner loop is preset to 10, and the maximum number of iterations in the outer loop is preset to 20.
[0139] As an optional embodiment, in S300, the method further includes: outputting evaluation index parameters for evaluating the completed traffic data, the evaluation index parameters including mean absolute percentage error (MAPE) and root mean square error (RMSE).
[0140] ;
[0141] ;
[0142] in, It is the total of the estimated values. and These are the actual value and its estimated value, respectively.
[0143] In this embodiment, the completed traffic data is evaluated using the Mean Absolute Percentage Error (MAPE) and the Root Mean Square Error (RMSE). The accuracy.
[0144] The following describes a spatiotemporal traffic data completion experiment conducted based on the model proposed in the embodiments of this application, and a comparison with five baseline models to verify the efficiency and feasibility of the convex optimization model. First, the spatiotemporal traffic data to be completed is obtained, and then input into the convex optimization model to obtain the completed data.
[0145] In some embodiments, four public datasets are selected: Guangzhou City Traffic Speed Dataset, Birmingham Parking Lot Dataset, Hangzhou Metro Passenger Flow Dataset, and Seattle Highway Traffic Speed Dataset, abbreviated as (G), (B), (H), and (S), respectively. After determining the original data, the original data that needs to be supplemented is loaded.
[0146] It should be noted that all the original datasets to be completed were configured with both random and non-random missing values, ranging from 30% to 90%, as the target raw data for the experiment. The purpose of this embodiment is to complete the missing data based on the different missing values and missing patterns.
[0147] like Figure 2 As shown, Figure 2 The graphs show the performance of the proposed model in this application for time series completion using a 70% random missing rate on four spatiotemporal traffic datasets (G), (B), (H), and (S). The black curve represents the true value curve, the red curve represents the completed value curve, and the black circles represent the observed data. (a) is the time series completion graph for dataset (G); (b) is the time series completion graph for dataset (B); (c) is the time series completion graph for dataset (H); and (d) is the time series completion graph for dataset (S). It can be seen that the red curve (completed value) and the black curve (true value) are highly consistent, indicating that the proposed convex optimization model has excellent data completion capabilities for randomly missing time series and is universally applicable to various types of spatiotemporal datasets.
[0148] like Figure 3 As shown, Figure 3The figure shows the effect of time series completion for four spatiotemporal traffic datasets (G), (B), (H), and (S) with a 70% non-random missing rate. The black curve represents the true value, the red curve represents the completed value, the white rectangle represents a whole day of missing data, and the green rectangle represents partial observation data within a day. Figure (a) shows the time series completion plot of dataset (G); Figure (b) shows the time series completion plot of dataset (B); Figure (c) shows the time series completion plot of dataset (H); and Figure (d) shows the time series completion plot of dataset (S). It can be seen that the proposed convex optimization model exhibits excellent completion ability in non-random missing time series of various spatiotemporal traffic data, and can effectively complete the traffic data completion task even under the extremely challenging non-random missing pattern.
[0149] Referring to Table 1, by comparing the experimental results of the model proposed in the embodiments of this application (named SNNDC) and five baseline models in Table 1 with missing rates of 30%-60%, it can be found that the convex optimization model proposed in this application maintains a comprehensive advantage over models BTMF, BGCP, HaLRTC, LRTC-TNN and LSTC-Tubal in all indicators, and has excellent completion effect.
[0150] Table 1: Comparison of imputation performance of different models on four spatiotemporal traffic datasets with missing rates of 30%-60% (MAPE / RMSE)
[0151]
[0152] Referring to Table 2, by comparing the experimental results of the model proposed in the embodiments of this application and the five baseline models in Table 2 under a high missing rate of 70%-90%, it can be found that the various indicators of the convex optimization model proposed in this application have been significantly improved, and the overall effect is better, demonstrating its excellent robustness in a high missing rate environment.
[0153] Table 2: Comparison of imputation performance of different models on four spatiotemporal traffic datasets with missing rates of 70%-90% (MAPE / RMSE)
[0154]
[0155] Additionally, refer to Figure 4 In some embodiments, a spatiotemporal traffic data completion device based on non-convex regularization is also provided. This device includes:
[0156] The first module is based on the model of minimizing the sum of nuclear norms. It constructs a non-convex regularization model for traffic data completion by introducing the TL1 regularization term.
[0157] The second module uses the idea of convex function difference to transform the non-convex regularized model into a convex optimization model;
[0158] The third module acquires the spatiotemporal traffic data to be completed, inputs the spatiotemporal traffic data to be completed into the convex optimization model, and uses the alternating direction multiplier method to iteratively solve the convex optimization model to obtain the completed data.
[0159] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.
[0160] Additionally, refer to Figure 5 An embodiment of this application also provides a spatiotemporal traffic data completion system based on non-convex regularization. The system includes: a data collector 11, a memory 12, a processor 13, a display 14, and a computer program stored on the memory 12 and executable on the processor 13.
[0161] The processor 13 and the memory 12 can be connected via a bus or other means.
[0162] The completion data required to implement the spatiotemporal traffic data completion method based on non-convex regularization in the above embodiments is extracted by the collector 11. The non-transient software program and instructions are stored in the memory 12. When executed by the processor 13, the spatiotemporal traffic data completion method based on non-convex regularization in the above embodiments is executed, and finally the imaging visualization is realized through the display 14.
[0163] Furthermore, one embodiment of this application provides a spatiotemporal traffic data completion medium based on non-convex regularization. This computer-readable storage medium stores computer-executable instructions that are executed by a processor or controller, for example, by a processor in the above-described electronic device embodiment, enabling the processor to execute a spatiotemporal traffic data completion method based on non-convex regularization as described above.
[0164] Those skilled in the art will understand that all or some of the steps and systems disclosed above can be implemented as software, firmware, hardware, and suitable combinations thereof. Certain physical components can be implemented in software via a processor (such as a central processing unit, digital signal processor, or microprocessor) or as hardware or application-specific integrated circuits. This software can be distributed across computer-readable media, including computer storage media (non-transitory) and communication media (transitory). According to the art, computer storage media refers to all media used for storing volatile and non-volatile information, such as RAM, ROM, flash memory, CD-ROM, DVD, magnetic tape, etc., and includes both removable and non-removable forms. Furthermore, communication media typically contain computer-readable instructions and other information, transmitted via carrier waves or transmission mechanisms. The above is a detailed description of preferred embodiments of this application, but this application is not limited to the above embodiments. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of this application, and these equivalent modifications or substitutions are all included within the scope defined by the claims of this application.
Claims
1. A non-convex regularization based spatio-temporal traffic data completion method, characterized in that, The method comprises the following steps: S100, a non-convex regularization model for traffic data completion is constructed by introducing a TL1 regularization term based on a kernel norm sum minimization model; S200, the non-convex regularization model is converted into a convex optimization model by using a convex function difference thought; S300, the to-be-completed spatiotemporal traffic data is input into the convex optimization model, and the convex optimization model is solved by using an alternating direction multiplier method to obtain completed data.
2. The method according to claim 1, wherein in S100, the non-convex regularization model for traffic data completion is constructed by introducing a TL1 regularization term based on a kernel norm sum minimization model, comprising: The kernel norm sum minimization model is: The TL1 regularization term is introduced: ； wherein is the unfolding matrix of the tensor along the k-th mode; The non-convex regularization completion model is constructed as follows: ； The non-convex regularization model can be equivalently converted into: ； The kernel norm can be represented as the L1 norm of all singular vectors, ； Therefore, the singular value generated by the convex difference structure is smaller than the kernel norm sum, and the rank function can be more accurately approximated. ； From the definitions of and it follows that ； 3. The method according to claim 2, wherein in S200, the non-convex regularization model is converted into a convex optimization model by using a convex function difference thought, comprising: The non-convex regularization model is converted into a convex optimization model by using a convex function difference thought, and the convex optimization model is used for traffic data completion; In addition, in order to further enhance the robustness and convergence speed of the algorithm, an L2 norm proximity term is introduced in the subproblem of DCA to form a proximity DCA problem. This strategy ensures that the subproblem has strong convexity, thereby obtaining a unique solution and improving the stability of the algorithm. The convex optimization model is converted into a proximity DCA subproblem:
4. The method according to claim 3, wherein in S300, the to-be-completed spatiotemporal traffic data is input into the convex optimization model, the convex optimization model is solved by using an alternating direction multiplier method, and completed data is obtained, comprising: According to the principle of the difference of convex functions algorithm (DCA), the linearization is performed on the transformed convex optimization model is: ； wherein represents the first iteration; S320, the to-be-completed spatiotemporal traffic data is input into the convex optimization model, and the convex optimization model is converted into the following minimization model: ； wherein is a constant greater than 0. S330, the augmented Lagrangian function of the minimization model is expressed as Generalized singular value threshold shrinkage is used: S310, initialize the inner and outer iteration times, given , neighborhood parameter , penalty parameter , Lagrange multiplier ; The closed solution of the formula is: ； In order to obtain a correct solution, the Lagrange multiplier is updated, and the formula is as follows: ； wherein, is a quadratic penalty coefficient; is a Lagrange multiplier; S340, sequentially solving the solutions of the minimization model , the solution of the minimization , and the solution of the minimization , comprising: The term in the augmented Lagrangian function containing the parameters in the minimization model is extracted according to the following formula, to obtain ; solve for ; The device comprises: ； On matrices Performing singular value decomposition (SVD) gives: ； wherein The shrinkage rule of singular values is: ； The closed solution is obtained of the equation: ； By solving the multi-modal unfolding matrix Summing and averaging can yield The solution of the optimization sub-problem: ； The term in the augmented Lagrangian function containing the parameters in the minimization model is extracted according to the following formula to obtain: ； A first module, a non-convex regularization model for traffic data completion is constructed by introducing a TL1 regularization term based on a kernel norm sum minimization model; ； wherein represents the complement of A second module, the non-convex regularization model is converted into a convex optimization model by using a convex function difference thought; ； S350, accumulate the inner and outer iteration times of the current generation, determine whether the preset maximum iteration times are reached, if yes, execute S360; if no, take the solution of the minimization as the data to be completed, and execute S320; S360, the solution of the minimization is output as the completed data.
5. An apparatus for spatio-temporal traffic data completion based on non-convex regularization, characterized in that, A third module, the to-be-completed spatiotemporal traffic data is input into the convex optimization model, and the convex optimization model is solved by using an alternating direction multiplier method to obtain completed data. 6. A spatio-temporal traffic data completion system based on non-convex regularization, comprising: The collector, the memory, the processor, the display, and a computer program stored in the memory and executable on the processor, wherein the processor implements the method according to any one of claims 1 to 4 when executing the computer program. 7.A non-convex regularization based spatiotemporal traffic data imputation medium, which is a computer readable storage medium, and stores computer executable instructions for implementing the method according to any one of claims 1 to 4.