CN107992536B - Urban traffic missing data filling method based on tensor decomposition - Google Patents
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Abstract
The invention relates to an urban traffic missing data filling method based on tensor decomposition, which comprises the following steps of: s1, constructing tensors of urban traffic data based on dimensions of road sections, dates and time periods; s2, pre-filling missing data to finish initialization of the missing data; s3, performing truncation singular value decomposition on the missing data obtained by pre-filling, and mining to obtain left singular vectors of the missing data in dimensions of road sections, dates and time periods; s4, calculating to obtain a core tensor by using the left singular vectors of the road section, the date and the time interval dimension; and S5, constructing a missing data filling model, inputting left singular vectors of road section, date and time interval dimensions and a core tensor training missing data filling model, continuously optimizing the missing data filling model by combining an optimization algorithm, and filling missing data through the missing data filling model after optimization is finished.
Description
Technical Field
The invention relates to the technical field of intelligent traffic, in particular to a tensor decomposition-based urban traffic missing data filling method.
Background
In the big data era, data-driven analytical methods have brought countless dividends to people. Taking the traffic industry as an example, by collecting and analyzing vehicle speed data, a city manager can master the running condition of a road section. However, in the data acquisition process, the inevitable problem is missing data, which directly hinders the urban managers from mastering the road section operation conditions, and thus effective management decisions cannot be made. Fortunately, urban traffic data often has strong space-time laws, such as morning and evening peaks and the like which often appear on workdays. Therefore, rules can be mined from historical data through a certain method, and missing data can be filled.
How to fully mine the existing data rules through a scientific method and realize the filling of large-scale traffic missing data so as to help city managers master traffic operation conditions and make effective management decisions, which is the key point and the purpose of the research of the invention.
The current domestic and foreign research and technical current situations are mainly as follows:
first, filling scattered missing data of urban traffic. Scholars at home and abroad make a great deal of research on filling methods for scattered urban traffic data loss, and classically, data points closely related to the scattered urban data loss are found out by utilizing an autocorrelation analysis theory, and then the scattered urban data loss is filled by adopting a weighted average method. The algorithm model mainly considers the characteristics among data, the characteristics of the data are less mined, and the algorithm model has the defects of complex calculation and high time consumption and is difficult to popularize on a large scale.
Secondly, filling up urban traffic continuous missing data. The existing continuous missing data filling method mainly takes machine learning related algorithms such as neural networks, support vector regression and the like as main steps, utilizes the existing historical data to train and obtain a regression model, and fills the continuous missing data. Although the filling effect of the algorithm is good, the algorithm also has the defects of complex calculation, more filling model parameters and poor interpretability, and is not beneficial to other users to understand the model and reproduce the model, so that the popularization of related application is limited to a certain extent.
Disclosure of Invention
The method aims to organize data from the time-space characteristics of urban traffic, excavate the internal rules of the data by a tensor decomposition method, establish a missing data filling model with strong interpretability by using the excavated rules, and finally realize effective filling of scattered or continuous missing data.
In order to realize the purpose, the technical scheme is as follows:
a tensor decomposition-based urban traffic missing data filling method comprises the following steps:
s1, constructing tensors of urban traffic data based on dimensions of road sections, dates and time periods;
s2, pre-filling missing data to finish initialization of the missing data;
s3, performing truncation singular value decomposition on the tensor obtained by pre-filling, and mining to obtain a left singular vector of the tensor in dimensions of a road section, a date and a time period;
s4, calculating to obtain a core tensor by using the left singular vectors of the road section, the date and the time interval dimension;
and S5, constructing a missing data filling model, inputting left singular vectors of road section, date and time interval dimensions and a core tensor training missing data filling model, continuously optimizing the missing data filling model by combining an optimization algorithm, and filling missing data through the missing data filling model after optimization is finished.
Preferably, the urban traffic data is vehicle speed data.
Preferably, the step S2 is to perform a pre-filling process on the missing data as follows:
s11, calculating an average value of observed vehicle speed data;
s12, initializing offset vectors in dimensions of road sections, dates and time periods;
s13, calculating a data estimation value by combining the offset vectors on the road section, date and time interval dimensions and the average speed:
wherein
Mu is the average of the observed vehicle speed data as an estimated value,
for the biasing of the vehicle speed data in the road segment dimension,
for the bias of the vehicle speed data in the date dimension,
a bias in a time period dimension for vehicle speed data;
s14, calculating an objective function J:
wherein xijkIs an accurate value; a is an optimization function regular term parameter used for controlling the complexity of the model;
s15, judging whether the numerical value of the target function is minimum, if so, outputting a pre-filling value of the data to be filled
If so, outputting, finishing the initialization of missing data, otherwise, adjusting to a more optimal direction
And then step S13 is performed.
Preferably, in step S3, the specific process of performing truncated singular value decomposition on the missing data obtained by pre-padding is as follows:
s21, performing modal expansion on missing data obtained by pre-filling to obtain 3 matrixes, and recording the matrixes as matrixes A, B and C;
s22, setting a singular value proportion threshold value p;
s23, singular value decomposition is carried out on the matrixes A, B and C, and left singular vectors U are obtained through calculation respectively(SVD)、V(SVD)And W(SVD)Wherein U is(SVD)、V(SVD)And W(SVD)Left singular vectors representing missing data in road segment, date and time segment dimensions, respectively.
Preferably, the modal 1 development of the core tensor is as follows:
Preferably, the specific implementation procedure of step S5 is as follows:
s31, constructing a missing data filling model;
s32, loading
U(SVD)、V(SVD)And W(SVD)As an initial value for the iterative update; inputting the data into a constructed missing data filling model to train the missing data filling model;
s33. missing data padding model utilization
U(SVD)、V(SVD)And W(SVD)Reducing to obtain tensor x;
s34, calculating an error function:
s35, judging whether the error function is converged, if so, outputting a missing data filling model and a complete tensor x, and otherwise, performing optimization algorithm pair
U(SVD)、V(SVD)And W(SVD)The optimization is performed and then step S32 is performed.
Preferably, the specific process of obtaining the tensor x by restoring the missing data filling model is as follows:
. Preferably, the step S35 outputs the factor matrix U when the error function converges(SVD)、V(SVD)And W(SVD)To U, to U(SVD)、V(SVD)And W(SVD)And analyzing to obtain the change modes of the vehicle speed data in the road section dimension, the date dimension and the time interval dimension, and improving the explanatory power of the missing data filling model.
Preferably, the step S35 adopts a pair of gradient optimization algorithm, newton method or simulated annealing algorithm
U(SVD)、V(SVD)And W(SVD)And optimizing.
Compared with the prior art, the invention has the beneficial effects that:
(1) the method is different from the traditional data filling algorithm, can effectively fill scattered and continuous missing data, and has wide applicability;
(2) a filling model is established based on the data internal rule, the filling model has good interpretability and can be reproduced and applied in a large scale;
(3) the calculation method is simple, and the missing data filling efficiency is high.
Drawings
Fig. 1 is a frame diagram of a large-scale traffic missing data filling method based on tensor decomposition.
Fig. 2 is a graph showing the average vehicle speed variation in different road sections.
Fig. 3 is a graph showing the change in average vehicle speed on different days.
Fig. 4 is a graph showing the change in average vehicle speed at different times.
FIG. 5 is a flow chart of missing data initialization.
FIG. 6 is a flow diagram of truncated singular value decomposition.
FIG. 7 is a schematic diagram of a Tucker decomposition.
Fig. 8 is a flow chart of constructing a missing data padding model based on tensor decomposition.
FIG. 9 is a comparison graph of the effect of the neural network-based method of the present invention on filling up scattered data under different miss rates.
FIG. 10 is a comparison graph of the effect of the neural network-based method of the present invention on filling up continuous data loss at different loss rates.
FIG. 11 is a graph of a factor matrix filling the date dimension in the model.
Detailed Description
The drawings are for illustrative purposes only and are not to be construed as limiting the patent;
the invention is further illustrated below with reference to the figures and examples.
Example 1
As shown in fig. 1, the method provided by the present invention comprises the following steps:
one, constructing tensors
As shown in table 1 (where the time interval refers to the division of the time of day at intervals of 10 minutes), the vehicle speed data collected by the sensor is visualized, the time-space characteristic change rule is preliminarily explored, and as seen from the observation results in fig. 2 to fig. 4, the average vehicle speed has more obvious changes in different road sections, different dates and different time intervals: the average vehicle speed difference of the congested easy-to-send road section and the congested difficult-to-send road section is large; the average speed difference of working days, weekends and holidays is large; the average speed difference of the early peak, the late peak and the flat peak is large; fourthly, the change of the average speed has no obvious periodicity. Therefore, according to the result of the visual preliminary exploration, the tensor of the vehicle speed data based on the dimensions of the road section, the date and the time period is constructed.
TABLE 1 map matching results data sheet
Second, missing data initialization
From the analysis results of fig. 2-4, the vehicle speed data is affected by different road sections, different dates and different time periods, so the vehicle speed data can be regarded as the average vehicle speed plus the offset of the vehicle speed in the dimension of road section, day and time, as shown in equation (1).
Wherein the content of the first and second substances,
mu is the average of the observed vehicle speed data as an estimated value,
for the biasing of the vehicle speed data in the road segment dimension,
for the bias of the vehicle speed data in the date dimension,
is the offset of the vehicle speed data in the time period dimension.
Then, solving the magnitude of each offset value, and setting an objective function J, as shown in formula (2), which mainly comprises two parts, wherein one part is a measurement estimation value
And the exact value xijkAn error term for the error; the other part is a regularization term that measures the complexity of the model. By minimizing the objective function J, the optimum size of each offset value can be found.
The overall flow chart of this section is shown in fig. 5.
Three, truncated singular value decomposition
After the initialization step of missing data, although a complete tensor is obtained, the data filling effect is limited and the filling method is not strong enough in explanation, so that rules contained in the tensor are further mined. And performing modal expansion on the pre-filled tensor, namely matrixing the high-order tensor, and converting the abstract high-order tensor into a matrix of a two-dimensional space so as to facilitate subsequent matrix operation.
The invention constructs 3-order tensor for vehicle speed data, and 3 matrixes can be obtained after modal expansion and are recorded as matrixes A, B and C. Then, singular value decomposition is carried out on the matrixes A, B and C to obtain a left singular vector U(SVD)、V(SVD)And W(SVD)Wherein U is(SVD)、V(SVD)And W(SVD)And respectively representing left singular vectors of the missing data in the dimensions of the road section, the date and the time interval so as to obtain main characteristics of each matrix and remove data noise in the matrix. The singular values and the main left singular vectors of the matrix are controlled by setting a singular value proportion threshold p. If the singular value proportion threshold value p is set to be too small, the regular mining in the matrix is insufficient; if the setting is too large, noise of data in the matrix cannot be removed, and a method of repeated experiments is needed to determine a proper singular value proportion threshold value p in formal application.
After the step, left singular vectors of all dimensions are obtained. The overall flow chart of this section is shown in fig. 6.
Calculation of the four, core tensor
The concept of the core tensor comes from tensor decomposition, and common tensor decomposition includes CP decomposition, Tucker decomposition, etc., and here, a simple description is given by taking the Tucker decomposition as an example, as shown in fig. 7, and the calculation method is shown in formula (3). The tensor is used as a high-dimensional data structure, a complex data rule is hidden in the tensor, the tensor is decomposed into a plurality of factor matrixes and a core tensor through Tucker decomposition, the factor matrixes can reveal features of all dimensions of the tensor to guarantee interpretability of a final model, and the core tensor describes connection among all dimensions.
For the next step capable of decomposing the tensorThe structure is trained, and the core tensor needs to be obtained by calculation
Core tensor
The mode 1 expansion form can be obtained by calculating the left singular vector and the matrix A obtained in the last step, and the calculation method is shown as a formula (4).
Missing data filling model based on tensor decomposition
Obtaining a factor matrix U through the steps of four and five(SVD)、W(SVD)And V(SVD)And core tensor
The tensor x can be obtained by reduction by the formula (3):
therefore, in this step, only the factor matrix U is required(SVD)、W(SVD)And V(SVD)And core tensor
The value of (A) is optimized, and the filled complete tensor x can be obtained. And in the optimizing process, a gradient optimizing algorithm is adopted to find the optimal tensor decomposition structure, so that an optimal missing data filling model is constructed.
EstablishingAn error function as shown in equation (5), where
The data loss in the tensor is recorded for the binary tensor, and if some data in the tensor is lost, the tensor is formed
The record of the middle corresponding position is 0; if some data in the tensor is not missing, the tensor
The record of the corresponding position in (1). Tensor
The existence of the model is beneficial to better judging the real filling effect of the model.
The process of model construction using the gradient optimization algorithm is shown in fig. 8.
By analysing the tensor decomposition structure U under the minimum error function(SVD)、V(SVD)And W(SVD)The change modes of the vehicle speed data in the road section dimension, the date dimension and the time interval dimension can be mined, and the explanatory power of the filling model is improved.
Example 2
In order to test the missing data filling effect of the method provided by the invention, 1855589 pieces of vehicle speed detection data of 214 road sections in Guangzhou city, 8/month 1/2016 to 9/month 30/2016 (61 days in total) are selected for experiment, and the following experiment scenes are set: testing the filling effect of scattered data deletion and continuous data deletion under different data deletion rates, and comparing the effect with the effect of a common neural network filling method; testing the interpretability of the filling model, namely the mining effect of the time-space change mode of the vehicle speed data.
And (3) introducing an average absolute error MAE as a filling effect evaluation index, wherein the calculation method is shown as a formula (6).
Where N is the number of padding data, yiTo fill in value, ziAre true values.
The error calculation results are shown in fig. 9-10, and it can be found that (i) under the condition of low loss rate or high loss rate, the method provided by the invention can better fill scattered data loss and continuous data loss, and the average absolute error of filling is between 2.5km/h and 3 km/h; secondly, the method provided by the invention is more stable. Whether filling scattered data loss or continuous data loss, the filling effect change fluctuation under different loss rates is small, and compared with a data filling method of a neural network, filling is more stable.
Taking the factor matrix of the date dimension as an example, the factor matrix of the date dimension in the final filling model is shown in fig. 11, and different colors represent different values. Observing the second column of the factor matrix, the occurrence of the dark blue stripe is found to have certain regularity, and combining with an actual calendar, several places where the dark blue stripe occurs are found to correspond to weekends (such as 8 months 6 days, 8 months 7 days, 8 months 13 days, 8 months 14 days and the like) or holidays (middle autumn festival from 9 months 15 days to 9 months 17 days), which shows that the vehicle speed change mode under different date conditions is successfully excavated by the method provided by the invention, and the method has strong explanatory property.
It should be understood that the above-described embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the claims of the present invention.
Claims (7)
1. A tensor decomposition-based urban traffic missing data filling method is characterized by comprising the following steps: the method comprises the following steps:
s1, constructing tensors of urban traffic data based on dimensions of road sections, dates and time periods;
the urban traffic data is vehicle speed data;
the specific process of pre-filling the missing data in step S2 is as follows:
s11, calculating an average value of observed vehicle speed data;
s12, initializing offset vectors in dimensions of road sections, dates and time periods;
s13, calculating a data estimation value by combining the offset vectors on the road section, date and time interval dimensions and the average speed:
wherein
Mu is the average of the observed vehicle speed data as an estimated value,
for the biasing of the vehicle speed data in the road segment dimension,
for the bias of the vehicle speed data in the date dimension,
a bias in a time period dimension for vehicle speed data;
s14, calculating an objective function J:
wherein xijkIs an accurate value; alpha is an optimization function regular term parameter and is used for controlling the complexity of the model;
s15, judging whether the numerical value of the target function is minimum, if so, outputting a pre-filling value of the data to be filled
Finishing the initialization of missing data; otherwise, the direction is adjusted to a more optimal direction
Then step S13 is performed;
s2, pre-filling missing data to finish initialization of the missing data;
s3, performing truncation singular value decomposition on the tensor obtained by pre-filling, and mining to obtain a left singular vector of the tensor in dimensions of a road section, a date and a time period;
s4, calculating to obtain a core tensor by using the left singular vectors of the road section, the date and the time interval dimension;
and S5, constructing a missing data filling model, inputting left singular vectors of road section, date and time interval dimensions and a core tensor training missing data filling model, continuously optimizing the missing data filling model by combining an optimization algorithm, and filling missing data through the missing data filling model after optimization is finished.
2. The tensor decomposition-based urban traffic missing data filling method according to claim 1, characterized in that: the specific process of performing truncated singular value decomposition on the missing data obtained by pre-padding in step S3 is as follows:
s21, performing modal expansion on missing data obtained by pre-filling to obtain 3 matrixes, and recording the matrixes as matrixes A, B and C;
s22, setting a singular value proportion threshold value p;
s23, singular value decomposition is carried out on the matrixes A, B and C, and left singular vectors U are obtained through calculation respectively(SVD)、V(SVD)And W(SVD)Wherein U is(SVD)、V(SVD)And W(SVD)Left singular vectors representing missing data in road segment, date and time segment dimensions, respectively.
3. The tensor decomposition-based urban traffic missing data filling method according to claim 2, wherein: the modal 1 development of the core tensor is as follows:
4. The tensor decomposition-based urban traffic missing data filling method according to claim 3, wherein: the specific implementation process of step S5 is as follows:
s31, constructing a missing data filling model;
s32, loading
U(SVD)、V(SVD)And W(SVD)As an initial value for the iterative update; inputting the data into a constructed missing data filling model to train the missing data filling model;
s33. missing data padding model utilization
U(SVD)、V(SVD)And W(SVD)Reducing to obtain tensor
S34, calculating an error function:
s35, judging whether the error function is converged, if so, outputting a missing data filling model and a complete tensor
Otherwise, the optimization algorithm pair
U(SVD)、V(SVD)And W(SVD)The optimization is performed and then step S32 is performed.
5. The tensor decomposition-based urban traffic missing data filling method according to claim 4, wherein: restoring the missing data filling model to obtain tensor
The specific process is as follows:
6. the tensor decomposition-based urban traffic missing data filling method according to claim 4, wherein: when the error function converges, the step S35 outputs the factor matrix U(SVD)、V(SVD)And W(SVD)To U, to U(SVD)、V(SVD)And W(SVD)And analyzing to obtain the change modes of the vehicle speed data in the road section dimension, the date dimension and the time interval dimension, and improving the explanatory power of the missing data filling model.
7. The tensor decomposition-based urban traffic missing data filling method according to claim 4, wherein: the step S35 adopts a gradient optimization algorithm, a Newton method or a simulated annealing algorithm pair
U(SVD)、V(SVD)And W(SVD)And optimizing.
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