A traffic flow parameter collaborative completion method based on multi-view learning

Abstract

This application relates to a collaborative traffic flow parameter completion method based on multi-view learning, comprising: acquiring multiple traffic flow parameters of a target area road network, converting the multiple traffic flow parameters into corresponding traffic flow parameter matrices based on time series length and spatial dimension, and dividing the traffic flow parameter matrix corresponding to each traffic flow parameter into multiple third-order traffic flow parameter tensors along the time series length; extracting corresponding affinity matrices from the traffic flow parameter matrix corresponding to each traffic flow parameter based on subspace representation theory, and stacking the affinity matrices along the view dimension to construct a multi-view affinity tensor; constructing a joint optimization objective function based on the multiple third-order traffic flow parameter tensors and the multi-view affinity tensor; and iteratively solving the joint optimization objective function to complete the missing data in the multiple third-order traffic flow parameter tensors. This application solves the technical problem of low efficiency in processing traffic flow parameters in the prior art.

Description

Technical Field

[0001] This invention relates to the field of traffic data completion technology, and in particular to a collaborative completion method for traffic flow parameters based on multi-view learning and a computer device. Background Technology

[0002] Traffic flow parameters are key indicators for assessing and managing road traffic conditions, playing a crucial role in intelligent transportation systems. These parameters not only reflect basic traffic characteristics such as vehicle mobility, speed, and density, but also provide fundamental data support for downstream applications (such as traffic condition prediction, congestion analysis, and signal control). However, in practical applications, the acquisition of traffic flow parameters often faces the problem of incompleteness. These incompletenesses can stem from various reasons, such as transmission delays, sensor malfunctions, or environmental factors. These incompletenesses not only affect the completeness of traffic data but also severely impact the accuracy of downstream applications. Therefore, effectively supplementing missing traffic flow parameters has become an important direction for improving the effectiveness of intelligent transportation systems.

[0003] Most existing data completion methods focus on completing missing data for a single traffic flow parameter. This approach typically processes each parameter sequentially, resulting in low overall efficiency.

[0004] Therefore, there is an urgent need for a collaborative completion method for traffic flow parameters based on multi-view learning. Summary of the Invention

[0005] (a) Technical problems to be solved

[0006] In view of the above-mentioned shortcomings and deficiencies of the prior art, the present invention provides a traffic flow parameter collaborative completion method based on multi-view learning, which solves the technical problem of low efficiency in processing traffic flow parameters in the prior art.

[0007] (II) Technical Solution

[0008] To achieve the above objectives, the main technical solutions adopted by the present invention include:

[0009] In a first aspect, embodiments of this application provide a method for collaborative completion of traffic flow parameters based on multi-view learning, including:

[0010] S100: Obtain multiple traffic flow parameters of the road network in the target area, and convert the multiple traffic flow parameters into corresponding traffic flow parameter matrices based on the time series length and spatial dimension, and divide the traffic flow parameter matrix corresponding to each traffic flow parameter into multiple third-order traffic flow parameter tensors along the time series length.

[0011] S200, based on subspace representation theory, extracts the corresponding affinity matrix from the traffic flow parameter matrix corresponding to each traffic flow parameter, and stacks the affinity matrices along the view dimension to construct a multi-view affinity tensor;

[0012] S300, a joint optimization objective function is constructed based on multiple third-order traffic flow parameter tensors and a multi-view affinity tensor. The joint optimization objective function is obtained by weighted summation of the capped Schatten-p norm of the multiple third-order traffic flow parameter tensors, the rotation tensor kernel norm of the multi-view affinity tensor, the L1 norm of the observation noise, and the graph Laplace regularization of each affinity matrix.

[0013] S400, the joint optimization objective function is solved iteratively to fill in the missing data in multiple third-order traffic flow parameter tensors.

[0014] Optionally, in some embodiments of this application, the various traffic flow parameters include at least road traffic volume, average speed, and lane occupancy.

[0015] Optionally, in some embodiments of this application, each third-order traffic flow parameter tensor is expressed based on the number of days, the daily time interval, and the spatial nodes for traffic flow parameter collection.

[0016] Optionally, in some embodiments of this application, step S200 includes:

[0017] S210: For each traffic flow parameter matrix, each column is treated as a time series sample, and based on the subspace representation theory, a relational model that can be linearly represented by other samples is constructed for all samples of each traffic flow parameter.

[0018] S220 performs low-rank sparse subspace representation learning on the relationship model of each traffic flow parameter, and obtains the corresponding representation coefficient matrix by solving the objective function that integrates low-rank and sparse constraints.

[0019] S230, the representation coefficient matrix of each traffic flow parameter is symmetric and normalized to generate the corresponding affinity matrix;

[0020] S240, the affinity matrices for each traffic flow parameter are stacked along a newly added view dimension to form the multi-view affinity tensor, wherein the newly added view dimension corresponds to different traffic flow parameter types.

[0021] Optionally, in some embodiments of this application, in step S220, the objective function of the low-rank and sparse constraints includes:

[0022] The nuclear norm of the representation coefficient matrix used to impose low-rank constraints, the L1 norm of the representation coefficient matrix used to impose sparse constraints, and the Frobenius norm of the reconstruction error.

[0023] Optionally, in some embodiments of this application, in step S300, the capped Schatten-p norm term is established for each third-order traffic flow parameter tensor, specifically expressed as:

[0024] ;

[0025] in, For operators that cap the Schatten-p norm, X v Let v be the v-th third-order traffic flow parameter tensor, where v∈{1,2,3}, corresponding to road traffic volume, average speed, and lane occupancy, respectively. For tensor X v The matrix obtained by expanding along the k-th mode, Let i be the i-th singular value of the expanded matrix. α is the capping threshold parameter. k Here, p represents the modal weights, p is the preset norm order, and S is the modal weights. p It is an abbreviation for the Schatten-p norm.

[0026] Optionally, in some embodiments of this application, the capping threshold parameter in the capping Schatten-p norm term is adaptively determined based on the singular value distribution of each third-order traffic flow parameter tensor in different modal expansion matrices.

[0027] Optionally, in some embodiments of this application, the calculation step of the rotation tensor norm term in step S300 includes:

[0028] Modal rotation is performed on the multi-view affinity tensor to obtain the rotated tensor, and tensor singular value decomposition is performed on the rotated tensor to obtain the core tensor and three factor matrices.

[0029] Extract the diagonal elements of the core tensor on different modal slices to form the singular value vectors of each modality, and define the core norm of the rotation tensor based on the minimization of the weighted sum of the singular value vectors of each modality.

[0030] Optionally, in some embodiments of this application, step S400 includes:

[0031] S410, introduce a first type of auxiliary variable and a second type of auxiliary variable, which correspond to the multi-view affinity tensor and each third-order traffic flow parameter tensor respectively, and establish an equality constraint that the multi-view affinity tensor is equal to the first type of auxiliary variable and each third-order traffic flow parameter tensor is equal to the corresponding second type of auxiliary variable;

[0032] S420, the equality constraints are augmented to the joint optimization objective function using Lagrange multipliers to obtain the augmented Lagrange function;

[0033] S430, adopting an alternating optimization strategy, sequentially obtains the sub-problems of the augmented Lagrangian function with respect to the multi-view affinity tensor, the first type of auxiliary variables, each third-order traffic flow parameter tensor, the second type of auxiliary variables, and the noise term, and fixes other variables as the current estimated values ​​when obtaining each sub-problem;

[0034] Repeat step S430 until the iteration converges to complete the tensors of each third-order traffic flow parameter.

[0035] Secondly, embodiments of this application provide a computer device, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the above-described traffic flow parameter collaborative completion method based on multi-view learning.

[0036] (III) Beneficial Effects

[0037] The traffic flow parameter collaborative completion method based on multi-view learning provided in this application significantly improves the accuracy and robustness of missing data completion by collaboratively modeling the implicit correlations between traffic parameters through multi-view affinity matrices. At the same time, it integrates the capped Schatten-p norm and the rotation tensor kernel norm for joint low-rank constraints, and introduces a graph Laplacian regularization term to constrain spatiotemporal adjacency relationships, thereby improving the accuracy and comprehensiveness of road network perception. Furthermore, it achieves synchronous completion of multiple parameters through integrated iterative optimization, resulting in the beneficial effects of avoiding error accumulation and generating a high-quality complete dataset to directly support downstream tasks. Attached Figure Description

[0038] Figure 1 This is a flowchart illustrating a traffic flow parameter collaborative completion method based on multi-view learning according to an embodiment of this application;

[0039] Figure 2 This is a schematic diagram of the process for obtaining a third-order traffic flow parameter tensor according to an embodiment of this application;

[0040] Figure 3 This is a schematic diagram illustrating the process of constructing a multi-view affinity tensor according to an embodiment of this application;

[0041] Figure 4 This is a schematic diagram illustrating the process of completing missing data in each third-order traffic flow parameter tensor according to an embodiment of this application;

[0042] Figure 5This is a schematic diagram of a modal rotation operation on a multi-view affinity tensor according to an embodiment of this application. Detailed Implementation

[0043] To better explain and facilitate understanding of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0044] In existing technologies, traffic flow parameter completion mostly focuses on completing accurate data for a single traffic flow parameter. This method typically processes each parameter sequentially, resulting in low overall efficiency. Furthermore, these methods often fail to fully utilize the inherent correlations between different traffic flow parameters. In fact, traffic flow parameters depict the current spatiotemporal traffic state from different perspectives, thus exhibiting certain interrelationships. By rationally utilizing these correlations for collaborative completion, not only can the accuracy of completion be improved, but the comprehensive perception of the road network situation can also be enhanced. Although modern deep learning technology has provided the possibility for the fusion and completion of multimodal and multi-view data, these methods often rely on high computing power, especially when processing large-scale road network data, easily encountering performance bottlenecks. Therefore, how to achieve collaborative completion of different traffic flow parameters while ensuring efficient algorithm operation and fully leveraging the advantages of multi-view learning is helpful in addressing the challenges currently faced in road network data processing.

[0045] To address this, the traffic flow parameter collaborative completion method based on multi-view learning provided in this application introduces a multi-view affinity matrix and tensor joint optimization framework to explicitly model the intrinsic correlation and spatiotemporal structural consistency among traffic parameters. This overcomes the limitation of traditional single-view completion methods that ignore the synergy of multi-source data, achieving a significant improvement in the accuracy and robustness of missing data repair. Simultaneously, by fusing the capped Schatten-p norm and the rotated tensor kernel norm, it effectively characterizes the low-rank nature of traffic data and the high-order correlation of multiple views, maintaining stability even under scenarios with strong noise and high missing rates. The system improves performance by enhancing the model's anti-interference capabilities and generalization ability. Furthermore, it maintains spatiotemporal adjacency and traffic flow continuity through graph Laplacian regularization and suppresses anomalous noise using the L1 norm, effectively smoothing noise and maintaining the physical rationality of traffic flow parameters while filling in missing values. Finally, this application achieves simultaneous completion of multi-parameter tensors through integrated iterative optimization, avoiding error accumulation caused by step-by-step repair, significantly improving the overall consistency of the data, and generating a high-quality, complete dataset that can directly support traffic state assessment, congestion analysis, and short-term prediction.

[0046] To better understand the above technical solutions, exemplary embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although exemplary embodiments of the present invention are shown in the drawings, it should be understood that the present invention can be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that the present invention can be understood more clearly and thoroughly, and that the scope of the present invention can be fully conveyed to those skilled in the art.

[0047] Figure 1 This is a flowchart illustrating a traffic flow parameter collaborative completion method based on multi-view learning according to an embodiment of this application. Figure 1 As shown, this multi-view learning-based collaborative completion method for traffic flow parameters is used for the repair of multi-source sensing data in intelligent transportation road networks, including:

[0048] Step S100: Obtain multiple traffic flow parameters of the road network in the target area, and convert the multiple traffic flow parameters into corresponding traffic flow parameter matrices based on the time series length and spatial dimension, and divide the traffic flow parameter matrix corresponding to each traffic flow parameter into multiple third-order traffic flow parameter tensors along the time series length;

[0049] The traffic flow parameters include at least road volume, average speed, and lane occupancy. Furthermore, each third-order traffic flow parameter tensor is expressed based on the number of days, daily time intervals, and the spatial nodes from which the traffic flow parameters are collected.

[0050] In the specific implementation process, see Figure 2 Step S100 in this embodiment specifically includes:

[0051] Step S110: Organize the raw data of each traffic flow parameter into a traffic flow parameter matrix of dimension T×N, where T represents the total number of time slices and N represents the number of spatial nodes of the detector.

[0052] Step S120: Divide the traffic flow parameter matrix along the time dimension T into the product of the number of days D and the daily time interval I, which satisfies T=D×I;

[0053] Step S130: Reconstruct the segmented data into a third-order traffic flow parameter tensor with dimensions D×I×N, where the first dimension represents the number of days, the second dimension represents the daily time interval, and the third dimension represents the spatial nodes.

[0054] Specifically, this process organizes the raw data for each parameter into a traffic flow parameter matrix of dimension T×N, where T represents the total number of time slices and N represents the number of spatial nodes of the detectors. For example, if detectors are deployed at 5 key locations and data is collected continuously for 3 days at a frequency of once per minute, then T is 3 days multiplied by the number of minutes per day, and N is 5, forming a large two-dimensional matrix where the rows are time series and the columns are spatial nodes.

[0055] Subsequently, step S120 divides the continuous time dimension T into a daily cycle, decomposing it into the product of the number of days D and the daily time interval I. Continuing the previous example, 3 days of data can be divided into D=3 days, with the daily time interval I being 840 minutes (assuming 14 hours of analysis per day), thus satisfying T=D×I=3×840=2520, which folds the long-term series into a block structure organized by day.

[0056] Finally, step S130 reconstructs the segmented data into a third-order traffic flow parameter tensor with dimensions D×I×N. This reconstruction essentially upgrades the data from a two-dimensional matrix to a third-order tensor. The first dimension, days, represents the date index of the data; for example, 3 days correspond to 3 "slices." The second dimension, daily time intervals, corresponds to each fine-grained time point within a day (e.g., every minute), reflecting intraday changes in traffic conditions. The third dimension, spatial nodes, represents different detector locations. Through this structure, each data point has clear triple coordinates of day, time, and location. For example, the value at position (2, 1, 4) in the flow tensor represents the flow value of detector number 4 on day 2, in the first time slice of that day (e.g., 06:00). This tensor organization not only makes the data structure clearer, but more importantly, it explicitly includes temporal periodicity (daily cycle) and spatial correlation, laying a solid foundation for subsequent use of advanced models such as tensor decomposition and spatiotemporal graph neural networks for feature extraction, missing data repair, and traffic flow prediction.

[0057] Step S200, based on subspace representation theory, extracts the corresponding affinity matrix from the traffic flow parameter matrix corresponding to each traffic flow parameter, and stacks the affinity matrices along the view dimension to construct a multi-view affinity tensor. The core task in this step is to extract the affinity relationships between spatial nodes from the traffic flow parameter matrices of different traffic flow parameters and construct the multi-view tensor. This process first performs subspace representation learning on three types of parameters: flow rate, average speed, and lane occupancy. See [link to relevant documentation]. Figure 3 The specific steps are as follows:

[0058] Step S210: For each traffic flow parameter matrix, each column is treated as a time series sample, and based on subspace representation theory, a relational model that can be linearly represented by other samples is constructed for all samples of each traffic flow parameter.

[0059] For example, suppose the study segment contains 5 key detectors, and observation data for 8 consecutive days has been acquired and processed according to step S100. For the three traffic flow parameters, the raw data is first organized into traffic flow parameter matrices with dimensions T×N=192×5 (assuming each day is divided into 24 time intervals, i.e., I=24, the total number of days D=8, therefore the total time slice T=8×24=192, and the spatial nodes N=5). Subsequently, each matrix is ​​reconstructed into a third-order tensor with dimensions D×I×N=8×24×5, where the first dimension represents days 1 to 8, the second dimension represents the 24 hours in a day, and the third dimension corresponds to the geographical locations of the 5 detectors.

[0060] Next, for each parameter, the corresponding tensor data is transformed into a spatiotemporal matrix suitable for subspace learning. This involves concatenating the observations of each detector across all days and all times to form a long time series sample. Specifically, the 8-day × 24-hour / day data is flattened, resulting in a sequence with 192 time points for each detector. Therefore, for the flow parameter, a sample matrix X is obtained. flow Its dimension is 5×192 (each row is a sequence of 192 time points for one detector, and each column is the observations of all 5 detectors at a specific time point). Similarly, the velocity matrix X is obtained. speed (5×192) and occupancy matrix X occ (5×192). In step S210, each column of the matrix, i.e., the observation vector of all spatial nodes at a certain time point, is regarded as a sample. That is, the time series observation data corresponding to each detector constitutes a sample. Based on the subspace representation theory, it is assumed that each sample can be represented by a linear combination of the remaining samples, thereby constructing a linear representation relationship model.

[0061] The above linear representation relation model can be formalized as:

[0062] X = XZ + E;

[0063] Where X is the traffic flow parameter matrix (D×I×N) for a certain parameter, Z is the coefficient matrix (N×N), and E is the reconstruction error.

[0064] Step S220: Perform low-rank sparse subspace representation learning on the relational model of each traffic flow parameter, and obtain the corresponding representation coefficient matrix by solving the objective function that integrates low-rank and sparse constraints; wherein, the objective function of low-rank and sparse constraints includes: the kernel norm of the representation coefficient matrix for applying low-rank constraints, the L1 norm of the representation coefficient matrix for applying sparse constraints, and the Frobenius norm of the reconstruction error.

[0065] The nuclear norm of the representation coefficient matrix used to impose low-rank constraints encourages Z to be low-rank, which assumes that all detectors originate from a few common underlying traffic patterns (such as morning rush hour, evening rush hour, and off-peak hours), thus making the representation coefficient matrix globally structurally consistent.

[0066] The L1 norm of the representation coefficient matrix used to impose sparsity constraints encourages Z to be sparse. This means that each detector is best reconstructed by only a few of the most relevant and similar "neighbor" detectors, rather than all of them. This aligns with the local similarity assumption and can improve the interpretability and robustness of the model.

[0067] The Frobenius norm is used to ensure that the reconstructed result is as close as possible to the original data.

[0068] Therefore, for example, for the flow parameter, we need to solve the following objective function:

[0069] ;

[0070] Where λ1 and λ2 are regularization parameters that balance low rank, sparsity, and reconstruction error, Z flow X is the coefficient matrix representing the flow parameters. flow This is a sample matrix of flow parameters. The nuclear norm of the flow parameter. The L1 norm of the flow parameter, This is the Frobenius norm corresponding to the flow parameter.

[0071] Then, by solving the objective function using an optimization algorithm (such as the augmented Lagrange multiplier method), the coefficient matrix representing each parameter is obtained.

[0072] Furthermore, the representation coefficient matrix generated in step S220 may be asymmetric and its numerical range may be uncertain. To construct a standard, measurable similarity (affinity) graph, the following operations are required:

[0073] Step S230: Symmetric and normalize the representation coefficient matrix of each traffic flow parameter to generate the corresponding affinity matrix.

[0074] Specifically, the symmetry transformation is performed as follows: calculate W=(∣Z∣+∣Z∣) T ) / 2, where W represents the matrix obtained after symmetry, and |Z| represents taking the absolute value of each element in the coefficient matrix Z to ensure that all weights are non-negative. T This indicates that the transpose of |Z| is performed, that is, the symmetric matrix W is obtained by adding the absolute value matrix to its transpose and then dividing by 2.

[0075] Further, normalization is performed by dividing each element in the pairwise matrix by the square root of the product of the degree of the corresponding node in that row and column, or by performing simple maximum and minimum scaling, to obtain the final 5×5 affinity matrix.

[0076] After obtaining the affinity matrix for each parameter, we have three affinity matrices obtained from different views. They describe the same spatial nodes but have different focuses. For example, the flow view may emphasize flow relationships, while the speed view may reveal congestion propagation relationships. This leads to step S240, which forms a multi-view affinity tensor.

[0077] In step S240, the affinity matrix of each traffic flow parameter is stacked along a newly added view dimension to form a multi-view affinity tensor, wherein the newly added view dimension corresponds to different traffic flow parameter types.

[0078] Specifically, the affinity matrix of each parameter is treated as three independent "slices" and combined into a third-order tensor with dimensions of 5×5×3. The first and second dimensions of this multi-view affinity tensor represent the pairing relationships between five spatial nodes, while the indices 1, 2, and 3 of the third dimension (view dimension) correspond to the three parameter types: traffic flow, average speed, and lane occupancy, respectively. This constructs a tensor data structure capable of comprehensively describing the affinity relationships between spatial nodes in the road network from multiple perspectives (views), laying the foundation for subsequent multi-view clustering or fusion analysis.

[0079] Furthermore, the traffic flow parameter collaborative completion method based on multi-view learning in this application embodiment also includes:

[0080] Step S300: Construct a joint optimization objective function based on multiple third-order traffic flow parameter tensors and a multi-view affinity tensor; wherein the joint optimization objective function is obtained by weighted summation of the capped Schatten-p norm of multiple third-order traffic flow parameter tensors, the rotation tensor kernel norm of the multi-view affinity tensor, the L1 norm of the observation noise, and the graph Laplace regularization of each affinity matrix;

[0081] In this joint optimization objective function, it is assumed that the dimension remains the third-order traffic flow parameter tensor constructed based on traffic flow parameters from 5 detectors over 8 consecutive days (dimension 8 days × 24 hours × 5 detectors). The multi-view affinity tensor dimension in step S200 is 5 detectors × 5 detectors × 3 views. The specific details of each item are as follows:

[0082] The capped Schatten-p norm L1 term for each third-order traffic flow parameter tensor:

[0083] This approach applies an adaptive, robust low-rank constraint to the tensors of three parameters: flow rate, velocity, and occupancy. Taking the flow rate tensor (8×24×5 dimensions) as an example, it is expanded into matrices along three modes: an 8×120 matrix along the "day" dimension, a 24×40 matrix along the "hour" dimension, and a 5×192 matrix along the "detector" dimension. Singular value decomposition is performed on each expanded matrix. Assuming the descending sequence of singular values ​​in the "detector" mode matrix is ​​[210, 85, 30, 10, 0.5], the top N dominant singular values ​​(e.g., the top 3) are selected based on a preset contribution rate threshold (e.g., 95%), and their mean (approximately 108.3) is calculated as the initial capping threshold reference for this mode. Similarly, reference thresholds are obtained for the "day" and "hour" modes. By weighted fusion of the reference values ​​from the three modes, a unified capping threshold parameter for the flow rate tensor is finally determined. When calculating its capped Schatten-p norm, all singular values ​​greater than 100 are treated as 100, thus suppressing excessively strong singular value contributions caused by extreme events and forcing the model to learn more universal and robust spatiotemporal core patterns. The velocity and occupancy tensors adaptively determine their respective thresholds according to this process, and their capped norms are calculated separately. This weighted sum collectively constrains the inherent low-rank structure and robustness of the original data.

[0084] Specifically, the capped Schatten-p norm term is established for each third-order traffic flow parameter tensor, in the form of:

[0085] ;

[0086] Where X1, X2, and X3 are the corresponding traffic flow, speed, and lane occupancy tensors after the segmentation, respectively. The operator for capping the Schatten-p norm, L1 is the term for capping the Schatten-p norm, and its capping Schatten-p norm is defined as:

[0087] ;

[0088] in, For operators that cap the Schatten-p norm, X v Let v be the v-th third-order traffic flow parameter tensor, where v∈{1,2,3}, corresponding to road traffic volume, average speed, and lane occupancy, respectively. For tensor X v The matrix obtained by expanding along the k-th mode, Let i be the i-th singular value of the expanded matrix. α is the capping threshold parameter. k Here, p represents the modal weights, p is the preset norm order, and S is the modal weights. p It is an abbreviation for the Schatten-p norm.

[0089] The capping threshold parameter in the capping Schattenp norm term is adaptively determined based on the singular value distribution of the expansion matrices of each third-order traffic flow parameter tensor in different modes, specifically:

[0090] For each modal expansion matrix, the singular values ​​are sorted in descending order. The top N singular values ​​are selected according to the preset contribution rate threshold, and the mean is calculated as the capping threshold parameter for the corresponding mode. The capping thresholds of each mode are weighted and fused to obtain the final capping threshold parameter.

[0091] L2 of the rotation tensor norm of the multiview affinity tensor:

[0092] This section imposes a low-rank constraint on the multi-view affinity tensor (5×5×3) to mine and fuse the unified spatial structure inherent in the affinity relationships from the three views: flow, velocity, and occupancy. First, a modal rotation operation is performed: the third dimension (view dimension, size 3) of the original tensor is cyclically shifted to the first dimension, resulting in a new 3×5×5 tensor. This operation prioritizes the view mode, with the core objective of analyzing the commonalities between different parameter perspectives. Subsequently, tensor singular value decomposition is performed on this rotated tensor to obtain a core tensor. The diagonal elements of this core tensor on each modal slice are extracted to form singular value vectors representing the joint relationships between views and detector pairs. This section is defined as minimizing the weighted sum of these singular value vectors. Physically, this forces the model to summarize the affinity information of the three views using a compact, low-rank joint representation, thereby extracting a consensus-based, robust spatial relationship map free from view-specific noise.

[0093] Specifically, the calculation of the rotation tensor nuclear norm term includes the following steps:

[0094] Modal rotation operations on multiview affinity tensors, such as... Figure 5 As shown, the original third dimension is moved to the first dimension by a cyclic shift method to obtain the rotated tensor; the rotated tensor is then subjected to tensor singular value decomposition to obtain the core tensor and three factor matrices.

[0095] Extract the diagonal elements of the core tensor on different modal slices to construct the singular value vectors of each modality; the kernel norm of the rotation tensor is defined as the minimum form of the weighted sum of the singular value vectors of each modality, specifically expressed as:

[0096] ;

[0097] in, L1 is the tensor nuclear norm operator, and L2 is the rotation tensor nuclear norm term. The rotation tensor nuclear norm term is defined as the weighted sum of the singular values ​​of the tensor's modal expansion matrix, denoted as:

[0098] ;

[0099] Where, σ （k） Let β be the singular value vector of the core tensor in the k-th mode. k These are the weighting coefficients for the corresponding modes. Let be the nucleus norm of the rotation tensor.

[0100] The L1 norm term L3 of the observation noise:

[0101] This term directly measures the sum of the absolute values ​​of all elements of the residual between the original observation tensor and the model-reconstructed tensor. During the optimization process, the noise tensor corresponding to this term is updated using an iterative algorithm. The update rule is essentially a soft-threshold shrinkage operation: setting the portion of the current residual with amplitudes less than a certain threshold to zero, and shrinking the portion with amplitudes greater than the threshold towards zero. This mechanism enables the model to automatically identify and absorb significant outliers (such as sensor fault data) into the noise estimation, thereby ensuring robustness in learning the main signal.

[0102] Furthermore, the L1 norm term of the observation noise is:

[0103] ;

[0104] in, L1 is the L1 norm identifier, and L3 is the L1 norm term of the observation noise. , and These are the L1 norm terms of the observed noise for flow parameters, average speed, and lane occupancy, respectively.

[0105] L4, a graph Laplacian regularization term based on affinity matrix:

[0106] This step injects the affinity matrix learned from the data in step S200 into the factorization process of the third-order traffic flow parameter tensor. Specifically, using the three generated affinity matrices, a corresponding graph Laplacian matrix is ​​constructed for each view. This step constrains the spatial factor matrix learned by the model, representing the characteristics of the five detectors, requiring it to be smooth on the graph defined by each view: that is, detector pairs that are closely connected (highly similar) in the graph (defined by the affinity matrix) should also have feature representations that are close to each other in the vector space. This ensures that the spatial patterns decomposed from the data are consistent with the node similarity driven by the data itself, enhancing the interpretability of the model's spatial structure.

[0107] Therefore, the formula for the joint optimization objective function is as follows:

[0108] ;

[0109] λ, γ, and σ are balancing hyperparameters that control the relative weights of low-rank multi-view structure, noise sparsity, and spatial smoothness in the overall objective, respectively. By simultaneously minimizing the robust low-rank approximation error of the data tensor, the low-rank fusion error of the multi-view affinity tensor, the sparsity of noise, and the smoothness of multi-view features on the graph structure, this model can collaboratively recover structurally consistent, denoised, smooth, and spatially interpretable complete tensor data from multi-view spatiotemporal data with missing and noisy features.

[0110] In this embodiment, by setting a joint optimization objective function comprising four terms—a capped Schatten-p norm term, a rotation tensor kernel norm term, an L1 noise term, and a graph Laplacian regularization term—coordinated enhancement of multi-source traffic data repair and knowledge mining can be achieved. The capped Schatten-p norm term, through an adaptive singularity capping strategy, effectively suppresses interference from sudden anomalies while constraining the global low-rank structure of the data, ensuring the robustness and reliability of the extracted spatiotemporal principal components. The rotation tensor kernel norm term forces the fusion of multi-view affinity relationships into a compact, consensus-based low-rank representation, thereby extracting a unified spatial association pattern across parameter types. The L1 noise term, acting as a robust safety valve, actively absorbs and isolates local outliers caused by sensor failures or traffic accidents through sparse constraints, preventing them from distorting the learning of the main pattern. The graph Laplacian regularization term injects data-driven spatial similarity priors into the model, ensuring that the learned detector features maintain spatial smoothness and structural consistency. These four aspects mutually constrain and promote each other during the optimization process, ultimately working together to achieve: high-precision repair of missing or abnormal data, essential characterization of the multidimensional spatiotemporal patterns of the traffic system, and interpretable discovery of the spatial functional structure of the road network, providing a high-quality and highly reliable data and analysis foundation for subsequent traffic state perception, prediction, and management decisions.

[0111] Next, step S400 is executed to iteratively solve the above joint optimization objective function to fill in the missing data in multiple third-order traffic flow parameter tensors, generating a complete multi-parameter dataset that can be directly used for subsequent traffic state assessment, congestion analysis, or short-term prediction tasks.

[0112] See Figure 4 In step S400 of this application embodiment, completing the missing data in each third-order traffic flow parameter tensor specifically includes:

[0113] Step S410: Introduce the first type of auxiliary variables and the second type of auxiliary variables, which correspond to the multi-view affinity tensor and each third-order traffic flow parameter tensor, respectively, and establish equality constraints that the multi-view affinity tensor is equal to the first type of auxiliary variables and each third-order traffic flow parameter tensor is equal to the corresponding second type of auxiliary variables.

[0114] Specifically, the first type of auxiliary variable is a tensor with the exact same dimensions as the "multi-view affinity tensor." Mathematically, this is equivalent to "copying" the multi-view affinity tensor so that the special constraint of the "rotated tensor kernel norm" can be independently applied to it later. The second type of auxiliary variable contains three tensors, each corresponding one-to-one with and enforced to be equal to the three traffic flow parameter tensors: flow rate, speed, and occupancy. This is equivalent to creating a "shadow" for each parameter data so that we can independently apply the "capped Schatten-p norm" constraint to these "shadows."

[0115] Step S420: The equality constraints are augmented to the joint optimization objective function using Lagrange multipliers to obtain the augmented Lagrange function;

[0116] Step S430: Using an alternating optimization strategy, sub-problems of the augmented Lagrangian function with respect to the multi-view affinity tensor, the first type of auxiliary variables, each third-order traffic flow parameter tensor, the second type of auxiliary variables, and the noise term are obtained in sequence, and other variables are fixed as the current estimated values ​​when obtaining each sub-problem;

[0117] Step S440: Repeat step S430 until the iteration converges to complete the tensors of each third-order traffic flow parameter.

[0118] In this embodiment, step S400 iteratively solves the joint objective function using an alternating optimization algorithm, achieving high-precision data repair under multi-source information collaboration. This process not only simultaneously completes all missing data in the multi-parameter tensors such as flow rate, speed, and occupancy, but also ensures, through the combined effect of multiple constraints such as low rank, sparsity, and smoothness, that the completed data maintains continuity in temporal evolution, conforms to the characteristics of the road network structure in spatial distribution, and maintains physical consistency among different parameters. This directly produces a high-quality, highly reliable, and complete dataset that can directly drive downstream traffic condition assessment, congestion analysis, and short-term prediction applications.

[0119] The traffic flow parameter collaborative completion method based on multi-view learning in this application automatically extracts and fuses affinity relationships that reflect the essence of the road network spatial structure from multi-source heterogeneous data such as traffic flow, speed, and occupancy through innovative multi-view data organization and subspace representation learning. It then constructs a joint optimization objective function that integrates robust low-rank constraints, multi-view structural constraints, sparse noise constraints, and spatial smoothness constraints, and solves it using an efficient alternating optimization algorithm. This scheme can collaboratively and synchronously repair missing and anomalous data in multi-parameter traffic tensors within a unified framework. The resulting complete dataset not only fills in missing values ​​but also ensures the continuity of data in spatiotemporal evolution, physical consistency among multiple parameters, and compliance with the characteristics of the road network spatial structure. This provides a high-quality, highly reliable, and directly applicable data foundation for subsequent advanced analysis tasks such as accurate traffic state perception, in-depth analysis of congestion causes, and short-term prediction, effectively enhancing the data-driven decision-making capabilities of intelligent transportation systems.

[0120] In addition, this application also proposes a computer device, which includes a memory, a processor, and a computer program stored in the memory. The processor executes the computer program to implement the steps of any of the above-described traffic flow parameter collaborative completion methods based on multi-view learning.

[0121] In the description of this invention, it should be understood that the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0122] In the description of this specification, the terms "one embodiment," "some embodiments," "embodiment," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0123] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make modifications, alterations, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A method for traffic flow parameter collaborative completion based on multi-view learning, characterized in that, include: S100: Obtain multiple traffic flow parameters of the road network in the target area, and convert the multiple traffic flow parameters into corresponding traffic flow parameter matrices based on the time series length and spatial dimension, and divide the traffic flow parameter matrix corresponding to each traffic flow parameter into multiple third-order traffic flow parameter tensors along the time series length. S200, based on subspace representation theory, extracts the corresponding affinity matrix from the traffic flow parameter matrix corresponding to each traffic flow parameter, and stacks the affinity matrices along the view dimension to construct a multi-view affinity tensor; S300, a joint optimization objective function is constructed based on multiple third-order traffic flow parameter tensors and a multi-view affinity tensor. The joint optimization objective function is obtained by weighted summation of the capped Schatten-p norm of the multiple third-order traffic flow parameter tensors, the rotation tensor kernel norm of the multi-view affinity tensor, the L1 norm of the observation noise, and the graph Laplace regularization of each affinity matrix. S400, the joint optimization objective function is solved iteratively to fill in the missing data in multiple third-order traffic flow parameter tensors.

2. The traffic flow parameter collaborative completion method based on multi-view learning according to claim 1, characterized in that, The various traffic flow parameters include at least road traffic volume, average speed, and lane occupancy.

3. The traffic flow parameter collaborative completion method based on multi-view learning according to claim 1, characterized in that, Each third-order traffic flow parameter tensor is expressed based on the number of days, the daily time interval, and the spatial nodes where traffic flow parameters are collected.

4. The traffic flow parameter collaborative completion method based on multi-view learning according to any one of claims 1-3, characterized in that, Step S200 includes: S210: For each traffic flow parameter matrix, each column is treated as a time series sample, and based on the subspace representation theory, a relational model that can be linearly represented by other samples is constructed for all samples of each traffic flow parameter. S220 performs low-rank sparse subspace representation learning on the relationship model of each traffic flow parameter, and obtains the corresponding representation coefficient matrix by solving the objective function that integrates low-rank and sparse constraints. S230, the representation coefficient matrix of each traffic flow parameter is symmetric and normalized to generate the corresponding affinity matrix; S240, the affinity matrices for each traffic flow parameter are stacked along a newly added view dimension to form the multi-view affinity tensor, wherein the newly added view dimension corresponds to different traffic flow parameter types.

5. The traffic flow parameter collaborative completion method based on multi-view learning according to claim 4, characterized in that, In step S220, the objective function of the low-rank and sparse constraints includes: The nuclear norm of the representation coefficient matrix used to impose low-rank constraints, the L1 norm of the representation coefficient matrix used to impose sparse constraints, and the Frobenius norm of the reconstruction error.

6. The traffic flow parameter collaborative completion method based on multi-view learning according to any one of claims 1-3, characterized in that, In step S300, the capped Schatten-p norm term is established for each third-order traffic flow parameter tensor, specifically expressed as follows: ； in, For operators that cap the Schatten-p norm, X v Let v be the v-th third-order traffic flow parameter tensor, where v∈{1,2,3}, corresponding to road traffic volume, average speed, and lane occupancy, respectively. For tensor X v The matrix obtained by expanding along the k-th mode, Let i be the i-th singular value of the expanded matrix. α is the capping threshold parameter. k Here, p represents the modal weights, p is the preset norm order, and S is the modal weights. p It is an abbreviation for the Schatten-p norm.

7. The traffic flow parameter collaborative completion method based on multi-view learning according to claim 6, characterized in that, The capping threshold parameter in the capping Schatten-p norm term is adaptively determined based on the singular value distribution of the expansion matrices of each third-order traffic flow parameter tensor in different modes.

8. The traffic flow parameter collaborative completion method based on multi-view learning according to claim 1, characterized in that, In step S300, the calculation steps for the rotation tensor null term include: Modal rotation is performed on the multi-view affinity tensor to obtain the rotated tensor, and tensor singular value decomposition is performed on the rotated tensor to obtain the core tensor and three factor matrices. Extract the diagonal elements of the core tensor on different modal slices to form the singular value vectors of each modality, and define the core norm of the rotation tensor based on the minimization of the weighted sum of the singular value vectors of each modality.

9. The traffic flow parameter collaborative completion method based on multi-view learning according to claim 1, characterized in that, Step S400 includes: S410, introduce a first type of auxiliary variable and a second type of auxiliary variable, which correspond to the multi-view affinity tensor and each third-order traffic flow parameter tensor respectively, and establish an equality constraint that the multi-view affinity tensor is equal to the first type of auxiliary variable and each third-order traffic flow parameter tensor is equal to the corresponding second type of auxiliary variable; S420, the equality constraints are augmented to the joint optimization objective function using Lagrange multipliers to obtain the augmented Lagrange function; S430, adopting an alternating optimization strategy, sequentially obtains the sub-problems of the augmented Lagrangian function with respect to the multi-view affinity tensor, the first type of auxiliary variables, each third-order traffic flow parameter tensor, the second type of auxiliary variables, and the noise term, and fixes other variables as the current estimated values ​​when obtaining each sub-problem; Repeat step S430 until the iteration converges to complete the tensors of each third-order traffic flow parameter.

10. A computer device, comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the steps of the traffic flow parameter collaborative completion method based on multi-view learning as described in any one of claims 1-9.

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