A traffic data repairing method based on non-convex low-rank tensor representation

Abstract

The application discloses a traffic data repairing method based on non-convex low-rank tensor representation, comprising the following steps: S1, constructing a traffic data three-order tensor; S2, defining a Capped Schatten p norm of the tensor; S3, constructing an improved Laplace regularization term; S4, solving an optimization problem by using an iterative method until a termination condition is satisfied. The method uses the Capped Schatten p norm of the tensor as a non-convex approximation of the rank to better represent the inherent low-rank characteristics of the traffic data; and integrates the improved Laplace regularization term as a spatial smoothing constraint to utilize the traffic state change characteristics of similar road sections to assist in repairing the missing data, thereby completing high-precision repairing of the traffic data, meeting the urgent demand for high-quality data in intelligent transportation system applications, and having theoretical significance and application value.

Description

Technical Field

[0001] This invention belongs to the field of intelligent transportation, specifically relating to a traffic data repair method based on non-convex low-rank tensor representation. Background Technology

[0002] In the era of big data, the rapid development of information and sensing technologies provides valuable opportunities for the application of intelligent transportation systems. Through precise perception and analysis of traffic data, transportation service providers can accurately estimate the real-time traffic conditions of the road network and plan more convenient and efficient travel routes for travelers. However, the unavoidable data loss caused by signal interruptions or detector malfunctions is one of the main challenges in the practical application of intelligent transportation systems. Therefore, many scholars have adopted methods such as interpolation, statistics, and neural network models to repair missing traffic data. In recent years, the inherent sparse and low-rank characteristics of traffic spatiotemporal data have been further explored and applied to data repair techniques. The basic idea is to construct historical traffic data into the form of a matrix or a third-order tensor, and then use the principle of minimum rank in such data structures to complete the repair of missing data. Generally speaking, traffic data repair methods based on low-rank representation can be roughly divided into two categories: bilinear decomposition and minimum rank representation.

[0003] Bilinear decomposition transforms the observed traffic data matrix into a linear product of two low-rank matrices, achieving success in some data restoration tasks. However, this method requires pre-defining the ranks of the two decomposed matrices, which is difficult to control in practice. Furthermore, this method requires numerous matrix decomposition operations, resulting in relatively high computational complexity for high-dimensional traffic data. Rank minimization, on the other hand, leverages the low-rank nature of traffic data to seek a set of missing values ​​that minimizes the rank of the completed matrix (or tensor) to repair the original data. Directly using rank as the objective function is an NP-hard problem. In practical applications, researchers typically use the kernel norm of the matrix (or tensor) as an approximation of the rank for easier solution. However, as a convex approximation, the kernel norm has limited substitutive power, incurring the same penalty coefficient for larger singular values ​​as for smaller singular values, leading to the destruction of the principal components of the data. Summary of the Invention

[0004] To address the technical problems mentioned in the background section, this invention proposes a traffic data repair method based on non-convex low-rank tensor representation. The method constructs traffic data into a third-order tensor form, approximates the rank of the data tensor using a non-convex function, and combines it with the traffic change characteristics of similar road segments to achieve high-precision repair of traffic data, effectively improving the quality and usability of traffic data.

[0005] To achieve the above-mentioned technical objectives, the technical solution of the present invention is as follows:

[0006] A traffic data repair method based on non-convex low-rank tensor representation includes the following steps:

[0007] Step 1: Construct the traffic status data with missing values ​​collected by the detector into a third-order tensor form of "location × date × time";

[0008] Step 2: Define the Capped Schatten p-norm of the traffic state data tensor constructed in Step 1 as the optimization objective; the expression for the Capped Schatten p-norm of the traffic state data tensor is as follows:

[0009]

[0010] In the formula, Let n1, n2, and n3 be a third-order traffic data tensor, representing location, date, and time, respectively. Let α be the defined Capped Schatten p-norm, τ>0 be the capping parameter, and α be the α-norm. k For tensor Expansion matrix along the k-th mode The weights, k∈{1,2,3}, σ i (·) represents the i-th singular value of the matrix, and p∈(0,1] represents the exponent;

[0011] Step 3: By measuring the similarity of traffic states between road segments, an improved Laplace matrix and its corresponding regularization constraints are constructed as regularization terms for the optimization problem; the mathematical expression of the improved Laplace regularization term is Tr(Z T LZ), where Tr(·) represents the trace of the matrix. Using the expansion matrix of the traffic data tensor along the first mode as an auxiliary variable, Z T This is the transpose of the Z matrix. This is the improved Laplace matrix;

[0012] Step 4: With the goal of minimizing the Capped Schatten p-norm of the traffic state data tensor defined in Step 2 and the Laplace regularization term constructed in Step 3, solve the above optimization problem iteratively. The converged result is the output of the repaired traffic data.

[0013] Preferably, the p-th power form of the Capped Schatten p-norm is optimal, as expressed by the following formula:

[0014]

[0015] Preferably, the specific calculation process of the improved Laplace matrix is ​​as follows:

[0016] Step 3-1: Select the traffic status data collected by the detectors deployed on each road segment in the road network within a week, and use it as the traffic status feature vector of each road segment.

[0017] Step 3-2: Use the dynamic time warping method to calculate the DTW distance between each feature vector, which is used as the distance matrix of the road segment with a dimension of n1×n1.

[0018] Step 3-3: Set a threshold. When the distance between two road segments calculated in step 3-2 is less than the predetermined threshold, the two road segments are considered to be logically adjacent, and the corresponding similarity matrix value is 1. Otherwise, they are not logically adjacent, and the corresponding similarity matrix value is 0. The result is a similarity matrix W containing only two values, 0 and 1, with a dimension of n1×n1, which is a symmetric matrix.

[0019] Steps 3-4 involve performing max-min normalization on the data for each road segment, assuming the data vector corresponding to road segment m is z. m The normalization calculation formula is as follows:

[0020]

[0021] Where, z′ m This is the data vector of road segment m after maximum-minimum value normalization;

[0022] Steps 3-5: Calculate the improved Laplacian matrix L = DW, where D is the degree matrix of the similarity matrix W, and this degree matrix has values ​​only on its diagonal, with each value d. m This is equal to the sum of each row of the similarity matrix W, denoted as d. m =∑ n W mn All values ​​except for the diagonal are 0.

[0023] Preferably, step 4 employs the alternating direction multiplier method to solve the optimization problem, the augmented Lagrangian form of which is as follows:

[0024]

[0025] in To augment the Lagrange function, Let be the k-th mode of the tensor and its corresponding Lagrange multiplier, respectively, and let <·> be the inner product operator of the two tensors. ρ is the folding operator for folding a matrix into a third-order tensor along the first mode. k >0 is the penalty coefficient for the Kth mode of the tensor, ‖·‖ F Let F be the F-norm of the third-order tensor, μ be the coefficient of the Laplace regularization term, and Tr(·) denote the trace of the matrix. Using the expansion matrix of the traffic data tensor along the first mode as an auxiliary variable, Z T This is the transpose of the Z matrix. For the improved Laplace matrix, Let n1, n2, and n3 be a third-order traffic data tensor, representing location, date, and time, respectively. Let α be the defined Capped Schatten p-norm, τ>0 be the capping parameter, and α be the α-norm. k For tensor Expansion matrix along the k-th mode The weights, k∈{1,2,3}, σ i (·) represents the i-th singular value of the matrix, and p∈(0,1] represents the exponent.

[0026] Preferably, the specific iterative solution process is as follows:

[0027] Step 4-1, input parameters Y,Ω,α,p,τ,μ,L,max_iter,ρ max Where max_iter is the maximum number of iterations, ρ max This represents the maximum value of the penalty coefficient.

[0028] Step 4-2, Initialize parameters ρ = 10 -5 ;

[0029] Step 4-3, Update Update in each iteration The value of is used to solve the following minimization problem:

[0030]

[0031] Where l represents the l-th iteration process;

[0032] Step 4-4, update Z. In each iteration, update the value of Z to solve the following minimization problem:

[0033]

[0034] Steps 4-5, Update Update in each iteration The formula is as follows:

[0035]

[0036] Steps 4-6 involve inverse normalizing the observed data using the maximum-minimum ratio. The normalization formula is as follows:

[0037] z m =(max(2) m )-min(z m))z′ m +min(z m );

[0038] Steps 4-7, Iteration Termination Condition Check: If the current iteration number exceeds the maximum iteration number, i.e., l ≥ max_iter, or the optimization algorithm converges, i.e. The optimization algorithm then terminates, outputting the repaired traffic data tensor. Otherwise, update l = l + 1 and return to steps 4-5 above to continue a new round of iteration.

[0039] Preferably, step 4-3 solves for about The optimal solution to the minimization problem is:

[0040]

[0041] in, This is the operator for folding a matrix into a tensor along the k-th mode, where U and V are the matrix... The left and right singular vectors after singular value decomposition, diag{·} is the diagonalization operator, ψ * For matrix The singular values ​​are optimized into a singular value vector.

[0042] Preferably, step 4-4 solves for the optimal solution to the Z minimization problem as follows:

[0043]

[0044] Among them, L T Let L be the transpose of the Laplace matrix, and I be the n1×n1 identity matrix. The operator for expanding a third-order tensor along the first mode.

[0045] The beneficial effects of adopting the above technical solution are as follows:

[0046] 1. This invention uses the tensor Capped Schatten p-norm as a non-convex substitute for the rank of traffic data tensors, which can alleviate the problem of insufficient convex approximation of existing kernel norms, better characterize the inherent low-rank characteristics of traffic data, and thus effectively improve the accuracy of missing data repair, meeting the urgent need for high-quality data in intelligent transportation system applications.

[0047] 2. This invention uses an improved Laplace regularization term as a spatial smoothing constraint, which can effectively utilize the traffic state change characteristics of similar road segments in the road network to assist in repairing missing data, thereby improving the accuracy of data repair. It has theoretical significance and application value. Attached Figure Description

[0048] Figure 1This is a flowchart of a traffic data repair method based on non-convex low-rank tensor representation according to the present invention;

[0049] Figure 2 This is a schematic diagram illustrating the convergence performance of the present invention in an extreme missing scenario;

[0050] Figure 3 This is an example diagram showing the fitting effect of detector #0 in implementing traffic data repair according to the present invention;

[0051] Figure 4 This is a comparison chart showing the effects of different repair algorithms on data repair in different scenarios. Detailed Implementation

[0052] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings.

[0053] like Figure 1 The diagram shows a flowchart of a traffic data repair method based on non-convex low-rank tensor representation according to the present invention. The specific steps are as follows:

[0054] Step 1: Represent the traffic status data collected by the detector as a third-order tensor in the form of "location × date × time";

[0055] Step 2, define the Capped Schatten p-norm of the third-order tensor in Step 1;

[0056] Step 3, define the Laplace regularization term of the third-order tensor in Step 1;

[0057] Step 4: Solve the optimization problem iteratively using the Capped Schatten p-norm from Step 2 and the improved Laplace regularization term from Step 3. The converged result is the output of the repaired traffic data.

[0058] The Capped Schatten p-norm of the tensor is a non-convex algebraic rank representation that can approximate the zero norm of the tensor. Its definition is as follows:

[0059]

[0060] In the formula, Let n1, n2, and n3 be a third-order traffic data tensor, representing location, date, and time, respectively. Let a be the defined Capped Schatten p-norm, τ>0 be the capping parameter, and a k For tensor Expansion matrix along the k-th mode The weights, k∈{1,2,3}, σ i (·) represents the i-th singular value of the matrix, and p∈(0,1] represents the exponent.

[0061] As a preferred embodiment of the present invention, the p-th power form of the Capped Schatten p-norm of the tensor is used in actual optimization, as expressed by the following formula:

[0062]

[0063] The improved Laplace regularization term is expressed as Tr(Z) T LZ), where Tr(·) represents the trace of the matrix. Using the expansion matrix of the traffic data tensor along the first mode as an auxiliary variable, Z T The transpose of the Z matrix. This is the improved Laplace matrix.

[0064] As a preferred embodiment of the present invention, the specific calculation process of the improved Laplace matrix is ​​as follows:

[0065] Step 3-1: Select the traffic status data collected by the detectors deployed on each road segment in the road network within a week, and use it as the traffic status feature vector of each road segment.

[0066] Step 3-2: Use the dynamic time warping method to calculate the DTW distance between each feature vector, which is used as the distance matrix of the road segment with a dimension of n1×n1.

[0067] Step 3-3: Set a threshold. When the distance between two road segments calculated in step 3-2 is less than the predetermined threshold, the two road segments are considered to be logically adjacent, and the corresponding similarity matrix value is 1. Otherwise, they are not logically adjacent, and the corresponding similarity matrix value is 0. The result is a similarity matrix W containing only two values, 0 and 1, with a dimension of n1×n1, which is a symmetric matrix.

[0068] Steps 3-4 involve performing max-min normalization on the data for each road segment, assuming the data vector corresponding to road segment m is z. m The normalization calculation formula is as follows:

[0069]

[0070] Where, z′ m This is the data vector of road segment m after maximum-minimum value normalization;

[0071] Steps 3-5: Calculate the improved Laplacian matrix L = DW, where D is the degree matrix of the similarity matrix W, and this degree matrix has values ​​only on its diagonal, with each value d. m This is equal to the sum of each row of the similarity matrix W, denoted as d. m =∑ n W mnAll values ​​except for the diagonal are 0.

[0072] As a preferred embodiment of the present invention, step 4 employs the alternating direction multiplier method to solve the optimization problem, the augmented Lagrangian form of which is as follows:

[0073]

[0074] in To augment the Lagrange function, Let be the k-th mode of the tensor and its corresponding Lagrange multiplier, respectively, and let <·> be the inner product operator of the two tensors. ρ is the folding operator for folding a matrix into a third-order tensor along the first mode. k >0 is the penalty coefficient for the k-th mode of the tensor, ‖·‖ F Let F be the F-norm of the third-order tensor, μ be the coefficient of the Laplace regularization term, and Tr(·) denote the trace of the matrix. Using the expansion matrix of the traffic data tensor along the first mode as an auxiliary variable, Z T This is the transpose of the Z matrix. For the improved Laplace matrix, Let n1, n2, and n3 be a third-order traffic data tensor, representing location, date, and time, respectively. Let α be the defined Capped Schatten p-norm, τ>0 be the capping parameter, and α be the α-norm. k For tensor Expansion matrix along the k-th mode The weights, k∈{1,2,3}, σ i (·) represents the i-th singular value of the matrix, and p∈(0,1] represents the exponent.

[0075] The specific iterative solution process for the above problem is as follows:

[0076] Step 4-1, input parameters Y,Ω,α,p,τ,μ,L,max_iter,ρ max Where max_iter is the maximum number of iterations, ρ max This represents the maximum value of the penalty coefficient.

[0077] Step 4-2, Initialize parameters ρ = 10 -5 ;

[0078] Step 4-3, Update Update in each iteration The value of is used to solve the following minimization problem:

[0079]

[0080] Where l represents the l-th iteration process;

[0081] Step 4-4, update Z. In each iteration, update the value of Z to solve the following minimization problem:

[0082]

[0083] Steps 4-5, Update Update in each iteration The formula is as follows:

[0084]

[0085] Steps 4-6 involve inverse normalizing the observed data using the maximum-minimum ratio. The normalization formula is as follows:

[0086] z m =(max(z) m )-min(z m ))z′ m +min(z m );

[0087] Steps 4-7, Iteration Termination Condition Check: If the current iteration number exceeds the maximum iteration number, i.e., l ≥ max_iter, or the optimization algorithm converges, i.e. The optimization algorithm then terminates, outputting the repaired traffic data tensor. Otherwise, update l = l + 1 and return to steps 4-5 above to continue a new round of iteration.

[0088] As a preferred embodiment of the present invention, step 4-3 solves for... The optimal solution to the minimization problem is:

[0089]

[0090] in, This is the operator for folding a matrix into a tensor along the k-th mode, where U and V are the matrix... The left and right singular vectors after singular value decomposition, diag{·} is the diagonalization operator, ψ * For matrix The singular values ​​are optimized into a singular value vector.

[0091] As a preferred embodiment of the present invention, step 4-4, which solves for the optimal solution to the Z minimization problem, is as follows:

[0092]

[0093] Among them, L T Let L be the transpose of the Laplace matrix, and I be the n1×n1 identity matrix. The operator for expanding a third-order tensor along the first mode.

[0094] Experiments were conducted using real-world road network vehicle speed data, and the results were compared with existing traffic data repair methods to verify the effectiveness of the proposed method.

[0095] This invention uses the Seattle road network vehicle speed dataset, which contains the average vehicle speed data of 323 road segments in the Seattle road network from January 1, 2015 to January 28, 2015 (a total of 28 days). The sensor detection interval is 5 minutes, so there are 288 data points in a day. The data is constructed into a third-order tensor structure of "location × date × time" with a value of 323 × 28 × 288.

[0096] This invention selects random missing (single point missing) and non-random missing (continuous missing) scenarios to simulate traffic data missing scenarios in the real world, and adopts missing rates of 20%, 40%, 60%, and 80% for each scenario to cover most missing scenarios in the real world, so as to test the data repair capability of the method proposed in this invention under different missing scenarios.

[0097] This experiment compares several mainstream traffic data repair methods, namely BPMF, BGCP, HaLRTC, and LSTC. Among them, BPMF and BGCP are representative of bilinear decomposition models, while HaLRTC and LSTC are representative of rank minimum models.

[0098] This experiment was conducted on a desktop computer with an Intel i5-9500 (@3.00GHz, 6 cores) and 16GB of RAM. The experiment used Python 3.8 as the development environment.

[0099] This experiment selects two commonly used accuracy evaluation metrics, MAPE and RMSE, to measure the performance of different data repair methods.

[0100] Table 1 compares the repair performance of different traffic data restoration methods under different missing scenarios, where CSPTC is the abbreviation for the method proposed in this study. Figure 2 This is a schematic diagram illustrating the convergence performance of the method proposed in this invention under an extreme missing data scenario with a missing rate of 80%. Figure 3 This is an example of the fitting effect of detector #0 when implementing traffic data repair using the method proposed in this invention. Figure 4 The diagram provides a direct comparison of the data repair effects of different repair algorithms in various scenarios. It can be seen that the CSPTC traffic data repair method proposed in this invention has higher repair accuracy than existing methods in various missing scenarios, and also has a high-efficiency convergence speed. The repaired data can also effectively fit the changing trend of the original data, which proves the effectiveness of the traffic data repair method proposed in this invention.

[0101] Table 1 Comparison of data restoration performance of different data restoration methods in different scenarios

[0102]

[0103] In summary, the traffic data repair method based on non-convex low-rank tensor representation proposed in this invention employs the Capped Schatten p-norm, which can more fully characterize the inherent low-rank characteristics of traffic data. Furthermore, the constructed improved Laplace regularization term can achieve spatial smoothing. By utilizing observations of similar road segments to assist in repairing missing data, the accuracy of traffic missing data repair can be effectively improved, thus meeting the urgent need for high-quality data in intelligent transportation system applications.

[0104] The embodiments are merely illustrative of the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solution based on the technical concept proposed in this invention shall fall within the scope of protection of this invention.

Claims

1. A traffic data repair method based on non-convex low-rank tensor representation, characterized in that, Includes the following steps: Step 1: Construct the traffic status data with missing values ​​collected by the detector into a third-order tensor form of "location × date × time"; Step 2: Define the Capped Schatten p-norm of the traffic state data tensor constructed in Step 1 as the optimization objective; the expression for the Capped Schatten p-norm of the traffic state data tensor is as follows: In the formula, Let n1, n2, and n3 be a third-order traffic data tensor, representing location, date, and time, respectively. Let α be the defined Capped Schatten p-norm, τ>0 be the capping parameter, and α be the α-norm. k For tensor Expansion matrix along the k-th mode The weights, k∈{1,2,3}, σ i (·) represents the i-th singular value of the matrix, and p∈(0,1] represents the exponent; Step 3: By measuring the similarity of traffic states between road segments, an improved Laplace matrix and its corresponding regularization constraints are constructed as regularization terms for the optimization problem; the mathematical expression of the improved Laplace regularization term is Tr(Z T LZ), where Tr(·) represents the trace of the matrix. Using the expansion matrix of the traffic data tensor along the first mode as an auxiliary variable, Z T The transpose of the Z matrix. This is the improved Laplace matrix; Step 4: With the goal of minimizing the Capped Schatten p-norm of the traffic state data tensor defined in Step 2 and the Laplace regularization term constructed in Step 3, solve the above optimization problem iteratively. The converged result is the output of the repaired traffic data.

2. The traffic data repair method based on non-convex low-rank tensor representation according to claim 1, characterized in that, The optimal form is the p-th power of the Capped Schatten p-norm, expressed by the following formula:

3. The traffic data repair method based on non-convex low-rank tensor representation according to claim 1, characterized in that, The specific calculation process for the improved Laplace matrix is ​​as follows: Step 3-1: Select the traffic status data collected by the detectors deployed on each road segment in the road network within a week, and use it as the traffic status feature vector of each road segment. Step 3-2: Use the dynamic time warping method to calculate the DTW distance between each feature vector, which is used as the distance matrix of the road segment with a dimension of n1×n1. Step 3-3: Set a threshold. When the distance between two road segments calculated in step 3-2 is less than the predetermined threshold, the two road segments are considered to be logically adjacent, and the corresponding similarity matrix value is 1. Otherwise, they are not logically adjacent, and the corresponding similarity matrix value is 0. The result is a similarity matrix W containing only two values, 0 and 1, with a dimension of n1×n1, which is a symmetric matrix. Steps 3-4 involve performing max-min normalization on the data for each road segment, assuming the data vector corresponding to road segment m is z. m The normalization calculation formula is as follows: Where, z′ m This is the data vector of road segment m after maximum-minimum value normalization; Steps 3-5: Calculate the improved Laplacian matrix L = DW, where D is the degree matrix of the similarity matrix W, and this degree matrix has values ​​only on its diagonal, with each value d. m This is equal to the sum of each row of the similarity matrix W, denoted as d. m =∑ n W mn All values ​​except for the diagonal are 0.

4. The traffic data repair method based on non-convex low-rank tensor representation according to claim 1, characterized in that, Step 4 employs the alternating direction multiplier method to solve the optimization problem. The augmented Lagrangian form of this problem is as follows: in To augment the Lagrange function, Let be the k-th mode of the tensor and its corresponding Lagrange multiplier, respectively, and let <·> be the inner product operator of the two tensors. ρ is the folding operator for folding a matrix into a third-order tensor along the first mode. k >0 is the penalty coefficient for the k-th mode of the tensor, ‖·‖ F Let F be the F-norm of the third-order tensor, μ be the coefficient of the Laplace regularization term, and Tr(·) denote the trace of the matrix. Using the expansion matrix of the traffic data tensor along the first mode as an auxiliary variable, Z T The transpose of the Z matrix. For the improved Laplace matrix, Let n1, n2, and n3 be a third-order traffic data tensor, representing location, date, and time, respectively. Let α be the defined Capped Schattenp norm, τ>0 be the capping parameter, and α be the α-norm. k For tensor Expansion matrix along the k-th mode The weights, k∈{1,2,3}, σ i (·) represents the i-th singular value of the matrix, and p∈(0,1] represents the exponent.

5. The traffic data repair method based on non-convex low-rank tensor representation according to claim 4, characterized in that, The specific iterative solution process is as follows: Step 4-1, input parameters Y,Ω,α,p,τ,μ,L,max_iter,ρ max Where max_iter is the maximum number of iterations, ρ max This represents the maximum value of the penalty coefficient. Step 4-2, Initialize parameters ρ = 10 -5 ; Step 4-3, Update Update in each iteration The value of is used to solve the following minimization problem: Where l represents the l-th iteration process; Step 4-4, update Z. In each iteration, update the value of Z to solve the following minimization problem: Steps 4-5, Update Update in each iteration The formula is as follows: Steps 4-6 involve inverse normalizing the observed data using the maximum-minimum ratio. The normalization formula is as follows: With m =(max(of m )-min(z m ))With' m +min(z m ); Steps 4-7, Iteration Termination Condition Check: If the current iteration number exceeds the maximum iteration number, i.e., l ≥ max_iter, or the optimization algorithm converges, i.e. The optimization algorithm then terminates, outputting the repaired traffic data tensor. Otherwise, update l = l + 1 and return to steps 4-5 above to continue a new round of iteration.

6. The traffic data repair method based on non-convex low-rank tensor representation according to claim 5, characterized in that, Step 4-3 solves for... The optimal solution to the minimization problem is: in, This is the operator for folding a matrix into a tensor along the k-th mode, where U and V are the matrix... The left and right singular vectors after singular value decomposition, diag{·} is the diagonalization operator, ψ * For matrix The singular values ​​are optimized into a singular value vector.

7. The traffic data repair method based on non-convex low-rank tensor representation according to claim 5, characterized in that, The optimal solution to the Z minimization problem in step 4-4 is as follows: Among them, L T Let L be the transpose of the Laplace matrix, and I be the n1×n1 identity matrix. The operator for expanding a third-order tensor along the first mode.

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