CN115630211A - Traffic data tensor completion method based on space-time constraint - Google Patents

Traffic data tensor completion method based on space-time constraint Download PDF

Info

Publication number
CN115630211A
CN115630211A CN202211126160.1A CN202211126160A CN115630211A CN 115630211 A CN115630211 A CN 115630211A CN 202211126160 A CN202211126160 A CN 202211126160A CN 115630211 A CN115630211 A CN 115630211A
Authority
CN
China
Prior art keywords
tensor
time
traffic
region
objective function
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN202211126160.1A
Other languages
Chinese (zh)
Inventor
孙秋霞
胡亚馨
李勍
王淇
姜红妍
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Shandong University of Science and Technology
Original Assignee
Shandong University of Science and Technology
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Shandong University of Science and Technology filed Critical Shandong University of Science and Technology
Priority to CN202211126160.1A priority Critical patent/CN115630211A/en
Publication of CN115630211A publication Critical patent/CN115630211A/en
Pending legal-status Critical Current

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F16/00—Information retrieval; Database structures therefor; File system structures therefor
    • G06F16/90—Details of database functions independent of the retrieved data types
    • G06F16/907—Retrieval characterised by using metadata, e.g. metadata not derived from the content or metadata generated manually
    • G06F16/909—Retrieval characterised by using metadata, e.g. metadata not derived from the content or metadata generated manually using geographical or spatial information, e.g. location
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Mathematical Physics (AREA)
  • Data Mining & Analysis (AREA)
  • Databases & Information Systems (AREA)
  • General Engineering & Computer Science (AREA)
  • Computational Mathematics (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Pure & Applied Mathematics (AREA)
  • Computing Systems (AREA)
  • Library & Information Science (AREA)
  • Algebra (AREA)
  • Software Systems (AREA)
  • Traffic Control Systems (AREA)

Abstract

The invention discloses a traffic data tensor completion method based on space-time constraint, which belongs to the technical field of traffic data completion and comprises the following steps: modeling traffic flow data from one region to another as a space-time tensor; modeling the tensor by using a Tucker decomposition algorithm; establishing a tensor completion optimization objective function based on Tucker decomposition; adding a spatial regularization constraint; obtaining a Toeplite matrix T by time series analysis ° Capturing the time dependency, and further adding a time regularization constraint; adding the L2 norm to obtain a final optimization objective function; performing iterative computation on the optimized objective function; and recovering to obtain a supplemented traffic flow data tensor. The invention adopts a new tensor decomposition completion algorithm, effectively fuses the space-time information of urban traffic with the tensor decomposition algorithm, and effectively improves the accuracy of traffic data completion.

Description

Traffic data tensor completion method based on space-time constraint
Technical Field
The invention belongs to the technical field of traffic data completion, and particularly relates to a traffic data tensor completion method based on space-time constraint.
Background
The intelligent traffic system is a key component of a smart city, and estimation and prediction of road traffic states are important for capturing and managing urban traffic congestion. Although traffic congestion can be effectively relieved by urban road planning, the process is too complex and only a certain part of road conditions can be solved, so that modeling and analyzing traffic data becomes a method used by most people to estimate and predict traffic states currently. The rapid development of urban traffic brings a great deal of traffic data which is easy to obtain, and convenience is provided for people who research traffic. However, the traffic data is inevitably sparse, incomplete and noisy due to equipment or other reasons, and the conclusions and decisions obtained by using unprocessed raw traffic data may be greatly deviated, so that the completion of the traffic data is one of the most important research problems in traffic and is also the premise and the basis for accurate traffic data prediction.
The main idea of traffic data completion is to find the internal relationship between data by establishing a model according to the known data, so as to completely supplement the missing traffic data. Since the traffic data is time series with fixed time intervals, data interpolation can be performed by using time series analysis methods in the past years, such as a regression model, a moving average model and the like, but the methods simply consider nearby values of missing data and cannot guarantee the accuracy of data recovery. In addition, the neural network is a popular method for traffic data completion, but it usually requires a large amount of historical data for training, and may have a long training time. In recent years, tensor-complete algorithms have been proposed to solve the traffic data loss problem, for example by solving the rank-minimized convex relaxation problem.
Tensor decomposition is a traffic data complementing method which is commonly used in recent years, and the main idea is to interpolate a missing term by using low-rank characteristics of traffic data. The data is modeled into a multi-order tensor, the tensor can well integrate the space and time dimension information of the traffic data together, then known data is utilized to carry out tensor decomposition to obtain parameters of the model, and missing data is completed according to the parameters. At present, CP decomposition and Tucker decomposition are commonly used tensor completion methods. However, the existing tensor resolution algorithm has some problems: the traffic data has high space-time dependence and periodicity, and good interpolation accuracy cannot be obtained only by using a simple CP or Tucker decomposition algorithm; the spatial dependence of the city is not fused into a model, so that the physical meaning of tensor decomposition on traffic is not exact enough; the temporal similarity of traffic data fails to integrate well into the tensor resolution.
Disclosure of Invention
Aiming at the problem that the current transport data completion algorithm based on tensor decomposition does not fully consider the importance of space-time dependence and the influence of the space-time dependence on a result, the invention provides a transport data tensor completion method based on space-time constraint.
The technical scheme of the invention is as follows:
a traffic data tensor completion method based on space-time constraint comprises the following steps:
step 1, modeling traffic flow data from one area to another area into a space-time tensor;
step 2, decomposing the tensor by adopting a Tucker decomposition algorithm;
step 3, establishing a tensor completion optimization objective function based on Tucker decomposition;
step 4, adding space regularization constraint, analyzing the category ratio, the category richness and the traffic convenience degree of each area according to the number and the category of POI in the research area, obtaining the city characteristic vector of each area, and further obtaining a city similarity matrix;
and 5, obtaining the Toeplite matrix T through time sequence analysis. Capturing the time dependency, and further adding a time regularization constraint;
step 6, adding the L2 norm to obtain a final optimization objective function;
step 7, performing iterative computation on the optimized objective function to obtain a final factor matrix and a final core tensor;
and 8, carrying out tensor supplementation on the basis of the factor matrix and the core tensor to obtain a traffic flow data tensor after final supplementation.
Further, the specific process of step 1 is: firstly, a research area is averagely divided into N areas with equal area size by a method based on grids, T time periods are given, and an original tensor X belonging to a traffic flow is formed N×N×T Entry X in tensor X ijk Appears in the region N when representing the time period k i And in N j The number of all objects that a region also appears.
Further, the specific process of step 2 is:
traffic flow data for T time segments of N regions are modeled as follows:
Figure BDA0003848356880000021
wherein, A, B and C are factor matrixes decomposed by Tucker, A and B are space potential factor matrixes and represent space characteristics, a p 、b q The p column vector of A and the q column vector of B respectively; c is a time latent factor matrix representing a temporal feature, C r Is the r-th column vector of C; g is the core tensor, where each entry is a separate feature representing the mutual strength between the fundamental components in the different modality factors; g is a radical of formula pqr Denotes a p 、b q And c r The strength of the interaction between the three fundamental components.
Further, in step 3, firstly, a tensor completion optimization objective function based on the Tucker decomposition is established, as follows:
Figure BDA0003848356880000022
then, the objective function is weighted, as shown in (3):
Figure BDA0003848356880000023
wherein W is a binary indication tensor with the same dimension as X, and the tensor W is an entry W in the tensor W ijk As shown in the following formula,
Figure BDA0003848356880000031
and (4) obtaining an optimized factor matrix A, B, C and a core tensor G through the minimization target function of the formula (3), thereby obtaining the complete recovered data tensor.
Further, the specific process of step 4 is:
step 4.1, obtaining the POI number and the category number of each divided area, and then obtaining the category ratio C of each area according to the data ns ：
Figure BDA0003848356880000032
Wherein, P ns Representing the number of POI in the s category of the nth area;
step 4.2, defining the richness R of each region category n (N =1,2, …, N) and traffic convenience Q n (N =1,2, …, N), where Q n Is the POI quantity proportion related to the public transport station and the parking lot traffic category, thereby obtaining the city characteristic vector v of each area n ＝[C n1 ，C n2 ，……，C ns ，R n ，Q n ]；
4.3, constructing a city similarity matrix M; defining the (p, q) th element of the city similarity matrix M as M pq ，M pq Representing the similarity of region p and region q:
Figure BDA0003848356880000033
wherein v is p City special for representing region pEigenvectors, v q A city feature vector representing region q;
in addition, A is a spatial latent factor matrix after tensor decomposition, and a row vector of the matrix is a i Representing the score of the ith region for all starting point spatial patterns, similar urban regions should have similar spatial patterns, and therefore, the score is used
Figure BDA0003848356880000036
To represent the similarity of region i and region j; similarly, the row vectors of the spatial latent factor matrix B represent the similarity between regions, and are used to represent the similarity between regions
Figure BDA0003848356880000037
To represent the similarity of region i and region j, so that the following relationship is obtained:
M＝AA T +ε A ，M＝BB T +ε B (6)
ε A and epsilon B All represent random error matrices;
and 4.4, improving on the basis of the model formula (3), wherein the optimization objective function after the spatial regularization constraint is added is as follows:
Figure BDA0003848356880000034
wherein, alpha and beta are regularization parameters,
Figure BDA0003848356880000035
the constrained portion is spatially regularized.
Further, in step 5, correlation between two adjacent time series is described by using Pearson correlation coefficient, which is in the range of-1 to 1; through T. -Toeplite (0,1, -2,0) matrix to capture time dependencies; adding a temporal regularization constraint to the objective function, the improved model is as follows:
Figure BDA0003848356880000041
wherein the content of the first and second substances,
Figure BDA0003848356880000042
for the temporal regularization constraint component, ε is the regularization parameter.
Further, the final optimization objective function is:
Figure BDA0003848356880000043
where σ denotes a penalty factor.
Further, in step 7, iterative computation is performed on the optimized objective function by using an alternating least square method, the parameters to be optimized are the factor matrix A, B, C and the core tensor G, any three parameters are fixed, the fourth parameter is updated, the formulas (10) - (13) are updated, iteration is performed in sequence until a convergence condition is reached, and then the iteration is stopped,
G (l) ＝argmin G f * (G，A (l-1) ，B (l-1) ，C (l-1) )+σ||G|| 2 (10)
A (l) ＝argmin A f * (G (l) ，A，B (l-1) ，C (l-1) )+σ||A|| 2 (11)
B (l) ＝argmin B f * (G (l) ，A (l) ，B，c (l-1) )+σ||B|| 2 (12)
C (l) ＝argmin C f * (G (l) ，A (l) ，B (l) ，C)+σ||C|| 2 (13)
wherein, l represents the number of iterations, and four parameters are initialized firstly: g (0) 、A (0) 、B (0) 、C (0) And then iterate sequentially according to the above formula.
Further, in step 8, after the final factor matrix A, B, C and the core tensor G are obtained, the original tensor is completely supplemented by the calculation of the formula (14), the missing value is interpolated,
Figure BDA0003848356880000044
the invention has the following beneficial technical effects:
the invention provides spatial regularization constraint based on cities according to interest points of the cities, successfully embeds spatial information of traffic data into an algorithm of tensor decomposition, thereby better integrating spatial dependency of traffic into tensor decomposition, and simultaneously provides time regularization constraint based on time sequences, and combines the constraint with the spatial constraint to ensure that the tensor decomposition can fully combine the space-time dependency of the traffic data. Compared with the existing tensor decomposition algorithm, the new tensor decomposition completion algorithm adopted by the invention obviously improves the accuracy of traffic data completion.
Drawings
FIG. 1 is a flow chart of the traffic data tensor completion method based on the space-time constraint of the invention.
Detailed Description
The invention is described in further detail below with reference to the following figures and detailed description:
the invention has the following key points:
first, it is found through research that the travel behaviors of people are closely related to the spatial pattern, and similar urban areas have similar traffic patterns. For example, at 5 pm, the traffic in business building areas is slow, while in residential building areas there are fewer pedestrians and vehicles, and the traffic is relatively smooth. Based on this finding, the present invention constructs a city matrix using POI (POI Of Interests), and then represents the similarity between the regions according to the factor matrix, thereby forming a spatial regularization constraint.
Second, the time dependence of the general traffic domain can be manifested by adjacent time periods. The invention constructs a Toeplite matrix by using time sequence analysis, and decomposes and fuses the Toeplite matrix and a tensor to capture time dependence.
And thirdly, combining the space regularization constraint formed based on the city matrix and the time regularization constraint constructed based on the Toeplite matrix with tensor decomposition, fully utilizing the space-time dependence characteristic of traffic, and improving the interpolation accuracy of traffic data.
The idea of the tensor decomposition model is to decompose high-dimensional data into a plurality of low-dimensional data, and then the original tensor can be reconstructed. The invention uses tensor decomposition to model traffic flow data in different areas at different times. As shown in fig. 1, a method for complementing a traffic data tensor based on a spatiotemporal constraint includes the following steps:
step 1, modeling traffic flow data from one region to another region into a space-time tensor, firstly, averagely dividing a research region into N regions with equal area size by a grid-based method, and setting T time periods to form an original tensor X belonging to R of the traffic flow N×N×T Entry X in tensor X ijk Appears in the region N when representing the time period k i And in N j The number of all objects (including pedestrians, vehicles, etc.) that the area also presents.
And 2, decomposing the tensor by using a Tucker decomposition algorithm.
Traffic flow data for T time periods for N regions are modeled as follows:
Figure BDA0003848356880000051
(1) The formula is an expression of the Tucker decomposition. Wherein, A, B and C are factor matrixes decomposed by Tucker, A and B are space potential factor matrixes and represent space characteristics, a p 、b q Respectively, the p-th column vector of a and the q-th column vector of B. C is a time latent factor matrix representing a temporal feature, C r Is the r-th column vector of C. G is the core tensor, where each entry is a separate feature that represents the mutual strength between the fundamental components in the different modality factors. g is a radical of formula pqr Denotes a p 、b q And c r The strength of the interaction between the three fundamental components, i.e. at the r-th temporal characteristic, from AThe traffic flow intensity from the p-th spatial feature to the q-th spatial feature in B.
Step 3, establishing a tensor completion optimization objective function based on Tucker decomposition, as follows:
Figure BDA0003848356880000052
wherein | · | charging F Representing the Frobenius norm. To improve interpolation accuracy, the present invention uses a weighted version of the optimization function, as shown in (3):
Figure BDA0003848356880000061
wherein W is a binary indication tensor with the same dimension as X, and the tensor W is an entry W in the tensor W ijk As shown in the following formula,
Figure BDA0003848356880000062
the optimized factor matrix A, B, C and the core tensor G can be obtained by minimizing the objective function of the formula (3).
And 4, improving on the basis of the model formula (3) and adding space regularization constraint. According to the method, the category proportion, the category richness and the traffic convenience degree of each area are analyzed according to the number and the category of POI in the research area, the city characteristic vector v of each area is obtained, and further the city similarity matrix M is obtained. The specific process is as follows:
step 4.1, firstly obtaining the POI number and the category number of each divided area, and then obtaining the category ratio C of each area according to the data ns ：
Figure BDA0003848356880000063
Wherein, P ns Indicating the number of POIs in the s-th category of the nth region.
Step 4.2, in addition, defining the richness R of each region category n (N =1,2, …, N) and traffic convenience Q n (N =1,2, …, N), where Q n Is the POI quantity proportion related to the traffic categories such as public traffic stations, parking lots and the like, thereby obtaining the city characteristic vector v of each area n ＝[C n1 ，C n2 ，……，C ns ，R n ，Q n ]。
And 4.3, constructing a city similarity matrix M. Defining the (p, q) th element of the city similarity matrix M as M pq ，M pq Representing the similarity of region p and region q:
Figure BDA0003848356880000064
wherein v is p City feature vector, v, representing region p q The city feature vector representing region q.
Furthermore, A is the spatial latent factor matrix after tensor decomposition, the row vector of which is a i Representing the scores of the ith area for all starting point spatial patterns, similar urban areas should have similar spatial patterns, and therefore, the scores can be used
Figure BDA0003848356880000065
To indicate the similarity of region i and region j. Similarly, the row vectors of the spatial latent factor matrix B may also represent the similarity between regions, i.e.
Figure BDA0003848356880000066
The following relationship is thus obtained:
M＝AA T +ε A ，M＝BB T +ε B (6)
here epsilon A And ε B Both represent random error matrices.
And 4.4, improving on the basis of the model formula (3), wherein the optimization objective function after the spatial regularization constraint is added is as follows:
Figure BDA0003848356880000071
wherein, alpha and beta are regularization parameters,
Figure BDA0003848356880000072
the constrained portion is spatially regularized.
And 5, obtaining the Toeplite matrix T through time series analysis. To capture temporal dependencies and to add temporal regularization constraints.
The time dependency is usually shown at adjacent time stamps, and the correlation of two adjacent time series is described by using Pearson correlation coefficients, which range from-1 to 1, the larger the absolute value, the stronger the correlation. It is calculated that the closer the time interval, the stronger the correlation and hence the T. A matrix of = Toeplite (0,1, -2,0) to capture the time dependence.
Since the Tucker decomposition can be written as follows:
Figure BDA0003848356880000073
Figure BDA0003848356880000074
Figure BDA0003848356880000075
wherein, X (D) (D =1,2,3) is the result of the matrix of tensor X at order D, G (D) (D =1,2,3) is the result of matrixing the core tensor G at D-order.
Adding a temporal regularization constraint to the objective function, the improved model is as follows:
Figure BDA0003848356880000076
wherein the content of the first and second substances,
Figure BDA0003848356880000077
for the temporal regularization constraint component, ε is the regularization parameter.
Step 6, in order to prevent overfitting, adding an L2 norm to obtain a final optimization objective function (an error objective function) as follows:
Figure BDA0003848356880000078
where σ represents a penalty factor.
And 7, performing iterative calculation on the optimized objective function to obtain the final G, A, B, C.
The invention uses an alternating least square method to carry out iterative calculation on an optimized objective function, the parameters to be optimized are a factor matrix A, B, C and a core tensor G, any three parameters are fixed, the fourth parameter can be updated, formulas (10) - (13) are updated, and the iteration is carried out in sequence until a convergence condition is reached.
G (l) ＝argmin G f * (G，A (l-1) ，B (l-1) ，C (l-1) )+σ||G|| 2 (10)
A (l) ＝argmin A f * (G (l) ，A，B (l-1) ，C (l-1) )+σ||A|| 2 (11)
B (l) ＝argmin B f * (G (l) ，A (l) ，B，C (l-1) )+σ||B|| 2 (12)
C (l) ＝argmin C f * (G (l) ，A (l) ，B (l) ，C)+σ||C|| 2 (13)
Wherein, l represents the number of iterations, and four parameters are initialized firstly: g (0) 、A (0) 、B (0) 、C (0) And then iterate sequentially according to the above formula.
And 8, recovering the tensor X to obtain a final supplemented traffic flow data tensor Y. After the final factor matrix A, B, C and the core tensor G are obtained in step 7, the original tensor can be completely supplemented by the calculation of the formula (14), and the purpose of interpolating the missing value is further achieved.
Figure BDA0003848356880000081
It is to be understood that the above description is not intended to limit the present invention, and the present invention is not limited to the above examples, and those skilled in the art may make various changes, modifications, additions and substitutions within the spirit and scope of the present invention.

Claims (9)

1. A traffic data tensor completion method based on space-time constraint is characterized by comprising the following steps:
step 1, modeling traffic flow data from one area to another area into a space-time tensor;
step 2, decomposing the tensor by adopting a Tucker decomposition algorithm;
step 3, establishing a tensor completion optimization objective function based on Tucker decomposition;
step 4, adding space regularization constraint, analyzing the category ratio, the category richness and the traffic convenience degree of each area according to the number and the category of POI in the research area, obtaining the city characteristic vector of each area, and further obtaining a city similarity matrix;
step 5, obtaining a Toeplite matrix T through time sequence analysis o Capturing the time dependency, and further adding a time regularization constraint;
step 6, adding the L2 norm to obtain a final optimization objective function;
step 7, performing iterative computation on the optimized objective function to obtain a final factor matrix and a final core tensor;
and 8, tensor supplementation is carried out on the basis of the factor matrix and the core tensor to obtain a finally supplemented traffic flow data tensor.
2. The tensor traffic data completion method based on spatiotemporal constraints as claimed in claim 1, wherein the concrete process of step 1 is as follows: firstly, a research area is averagely divided into N areas with equal area size by a method based on grids, T time periods are given, and an original tensor X belonging to a traffic flow is formed N×N×T Entry X in tensor X ijk Appears in the region N when representing the time period k i And in N j The number of all objects that a region also appears.
3. The method for complementing the traffic data tensor based on the spatiotemporal constraint as recited in claim 1, wherein the concrete process of the step 2 is as follows:
traffic flow data for T time periods for N regions are modeled as follows:
Figure FDA0003848356870000011
wherein, A, B and C are factor matrixes decomposed by Tucker, A and B are space potential factor matrixes and represent space characteristics, a p 、b q The p column vector of A and the q column vector of B respectively; c is a time latent factor matrix representing a temporal feature, C r Is the r-th column vector of C; g is the core tensor, where each entry is a separate feature representing the mutual strength between the fundamental components in the different modality factors; g pqr Denotes a p 、b q And c r The strength of the interaction between the three fundamental components.
4. The method for tensor completion of traffic data based on spatio-temporal constraints as recited in claim 1, wherein in the step 3, a tensor completion optimization objective function based on a Tucker decomposition is first established as follows:
Figure FDA0003848356870000012
then, the objective function is weighted, as shown in (3):
Figure FDA0003848356870000013
wherein W is a binary indication tensor with the same dimension as X, and the tensor W is an entry W in the tensor W ijk As shown in the following formula,
Figure FDA0003848356870000021
and (3) obtaining the optimized factor matrix A, B, C and the core tensor G through the minimized objective function of the formula (3), thereby obtaining the recovered complete data tensor.
5. The method for complementing the traffic data tensor based on the spatiotemporal constraint as recited in claim 1, wherein the specific process of the step 4 is as follows:
step 4.1, obtaining the POI number and the category number of each divided area, and then obtaining the category ratio C of each area according to the data ns ：
Figure FDA0003848356870000022
Wherein, P ns Representing the number of POI in the s category of the nth area;
step 4.2, defining the richness R of each region category n (N =1,2, …, N) and traffic convenience Q n (N =1,2, …, N), where Q n Is the POI quantity proportion related to the public transport station and the parking lot traffic category, thereby obtaining the city characteristic vector v of each area n ＝[C n1 ,C n2 ,……,C ns ,R n ,Q n ]；
4.3, constructing a city similarity matrix M; definition cityThe (p, q) th element of the market similarity matrix M is M pq ，M pq Representing the similarity of region p and region q:
Figure FDA0003848356870000023
wherein v is p City feature vector, v, representing region p q A city feature vector representing region q;
in addition, A is a spatial latent factor matrix after tensor decomposition, and a row vector of the matrix is a i Representing the score of the ith region for all starting point spatial patterns, similar urban regions should have similar spatial patterns, and therefore, the score is used
Figure FDA0003848356870000024
To indicate the similarity of region i and region j; similarly, the row vectors of the spatial latent factor matrix B represent the similarity between regions, and are used to represent the similarity between regions
Figure FDA0003848356870000025
To represent the similarity of region i and region j, so that the following relationship is obtained:
M＝AA T +ε A ，M＝BB T +ε B (6)
ε A and epsilon B All represent random error matrices;
and 4.4, improving on the basis of the model formula (3), wherein the optimization objective function after the spatial regularization constraint is added is as follows:
Figure FDA0003848356870000026
wherein, alpha and beta are regularization parameters,
Figure FDA0003848356870000027
the constrained portion is spatially regularized.
6. The tensor filling method for traffic data based on space-time constraint as recited in claim 1, wherein in the step 5, correlation of two adjacent time series is described by using Pearson correlation coefficient, and the coefficient range is-1 to 1; through T ° A matrix of = Toeplite (0,1, -2,0) to capture the time dependence; adding a temporal regularization constraint to the objective function, the improved model is as follows:
Figure FDA0003848356870000031
wherein the content of the first and second substances,
Figure FDA0003848356870000032
for the temporal regularization constraint component, ε is the regularization parameter.
7. The method for completing the traffic data tensor based on the space-time constraint as recited in claim 1, wherein in the step 6, the final optimization objective function is:
Figure FDA0003848356870000033
where σ denotes a penalty factor.
8. The method for complementing the traffic data tensor based on the space-time constraint as recited in claim 1, wherein in the step 7, an iterative calculation is performed on the optimized objective function by using an alternating least square method, the parameters to be optimized are a factor matrix A, N, C and a core tensor G, any three parameters are fixed, a fourth parameter is updated, equations (10) - (13) are updated, and the iteration is sequentially performed until a convergence condition is reached,
G (l) ＝argmin G f * (G,A (l-1) ,B (l-1) ,C (l-1) )+σ‖G‖ 2 (10)
A (l) ＝argmin A f * (G (l) ,A,B (l-1) ,C (l-1) )+σ‖A‖ 2 (11)
B (l) ＝argmin B f * (G (l) ,A (l) ,B,C (l-1) )+σ‖B‖ 2 (12)
C (l) ＝argmin c f * (G (l) ,A (l) ,B (l) ,C)+σ‖C‖ 2 (13)
wherein, l represents the number of iterations, and four parameters are initialized firstly: g (0) 、A (0) 、B (0) 、C (0) And then iterate sequentially according to the above formula.
9. The tensor completion method for traffic data based on spatio-temporal constraints as claimed in claim 1, wherein in step 8, after the final factor matrix A, B, C and the core tensor G are obtained, the original tensor is completely supplemented by the calculation of equation (14) to interpolate the missing value,
Figure FDA0003848356870000034
CN202211126160.1A 2022-09-16 2022-09-16 Traffic data tensor completion method based on space-time constraint Pending CN115630211A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202211126160.1A CN115630211A (en) 2022-09-16 2022-09-16 Traffic data tensor completion method based on space-time constraint

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202211126160.1A CN115630211A (en) 2022-09-16 2022-09-16 Traffic data tensor completion method based on space-time constraint

Publications (1)

Publication Number Publication Date
CN115630211A true CN115630211A (en) 2023-01-20

Family

ID=84902378

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202211126160.1A Pending CN115630211A (en) 2022-09-16 2022-09-16 Traffic data tensor completion method based on space-time constraint

Country Status (1)

Country Link
CN (1) CN115630211A (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115827335A (en) * 2023-02-06 2023-03-21 东南大学 Time sequence data missing interpolation system and method based on modal crossing method

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115827335A (en) * 2023-02-06 2023-03-21 东南大学 Time sequence data missing interpolation system and method based on modal crossing method

Similar Documents

Publication Publication Date Title
CN109887282B (en) Road network traffic flow prediction method based on hierarchical timing diagram convolutional network
CN111612206B (en) Neighborhood people stream prediction method and system based on space-time diagram convolution neural network
CN111612243B (en) Traffic speed prediction method, system and storage medium
CN110766942B (en) Traffic network congestion prediction method based on convolution long-term and short-term memory network
CN113313947B (en) Road condition evaluation method of short-term traffic prediction graph convolution network
CN110827544A (en) Short-term traffic flow control method based on graph convolution recurrent neural network
CN114299723B (en) Traffic flow prediction method
CN110570035B (en) People flow prediction system for simultaneously modeling space-time dependency and daily flow dependency
CN112532439A (en) Network flow prediction method based on attention multi-component space-time cross-domain neural network model
Ye et al. Attention-based spatio-temporal graph convolutional network considering external factors for multi-step traffic flow prediction
CN112071062B (en) Driving time estimation method based on graph convolution network and graph attention network
CN109344992B (en) Modeling method for user control behavior habits of smart home integrating time-space factors
CN115510174A (en) Road network pixelation-based Wasserstein generation countermeasure flow data interpolation method
Tang et al. Dynamic origin‐destination flow estimation using automatic vehicle identification data: A 3D convolutional neural network approach
CN115630211A (en) Traffic data tensor completion method based on space-time constraint
Hu et al. Air quality prediction using spatio-temporal deep learning
Wang et al. Urban traffic pattern analysis and applications based on spatio-temporal non-negative matrix factorization
Wang et al. TYRE: A dynamic graph model for traffic prediction
CN114580617A (en) National road transport capacity distribution prediction method based on space-time graph convolutional network
Putra et al. Forecasting air quality using massive-scale wsn based on convolutional LSTM network
Son et al. Partial convolutional LSTM for spatiotemporal prediction of incomplete data
CN117392830A (en) Space-time normalization graph convolution neural network traffic flow prediction method, system and medium
CN116258253A (en) Vehicle OD prediction method based on Bayesian neural network
Huang et al. Multistep coupled graph convolution with temporal-attention for traffic flow prediction
CN115938112A (en) Traffic demand prediction method, system, electronic device, and computer storage medium

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination