CN108804392A - A kind of traffic data tensor fill method based on space-time restriction - Google Patents
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Abstract
The present invention relates to a kind of traffic data tensor fill method based on space-time restriction, obtains incomplete traffic data, establishes traffic flow data tensor；It establishes the tensor based on Factorization and fills model；By analyzing data space-time characterisation, space-time restriction tensor is built, the tensor filling model based on Factorization is optimized；The tensor filling that space-time restriction is added is carried out, original traffic data are recovered.A kind of traffic data tensor fill method based on space-time restriction proposed by the present invention, a kind of tensor fill method based on Factorization is applied to traffic data and restores field, and the temporal correlation and low-rank characteristic of traffic data are fully excavated, improve the precision for restoring complete traffic data.
Description
Technical field
The present invention relates to a kind of traffic data tensor fill method based on space-time restriction.
Background technology
With the gradually development and extensive use of technology of Internet of things and big data industry, information content, essence of the people to data
The requirements such as exactness and timeliness are more and more harsh.As the important application scene of Internet of Things, intelligent transportation system
(Intelligent Transportation System) is by advanced information technology, data transmission technology, electronic sensor skill
Art, control technology and computer technology etc. are effectively integrated into entire ground transportation management system, to the one kind established
In real time, accurately and efficiently composite communications transport management system.Therefore intelligent transportation system the acquisition of data, processing, analysis,
Utilize etc. is equally faced with huge challenge.
In traffic information system, due to sensor placement, communication failure and data itself are imperfect etc., lead
The case where causing shortage of data is particularly acute.Specifically, intelligent transportation system can be collected from various fixations and movable sensor
Traffic data, but the fixed sensor of such as circuit detector and road side video camera etc is covered with limited space,
And to collect data with high precision also unstable for the removable sensor of GPS sensor etc.In terms of communications, sensor
It is limited by unstable and wireless-transmission network time delay the transmission node of working environment with the information transmission of data center
Deng because influence, traffic information may be caused to lack, or even data loss rate is high sometimes.
Invention content
The purpose of the present invention is to provide a kind of traffic data tensor fill method based on space-time restriction, it is existing to overcome
There is defect present in technology.
To achieve the above object, the technical scheme is that：A kind of traffic data tensor filling based on space-time restriction
Method is realized in accordance with the following steps：
Step S1：Incomplete traffic data is obtained, traffic flow data tensor is established；
Step S2：It establishes the tensor based on Factorization and fills model；
Step S3：By analyzing data space-time characterisation, space-time restriction tensor is built, is opened based on Factorization to described
Amount filling model optimizes；
Step S4：The tensor filling processing that space-time restriction is added is carried out, original traffic data are recovered.
In an embodiment of the present invention, in the step S1, by being interacted with vehicle GPS, collection vehicle GPS numbers
According to obtaining pending data and restore the i continuous k days road average speed data in section being connected with each other in region；By one day
Equally spaced it is divided into j moment, is constructed to the traffic flow data tensor that a size is i × j × kAnd it will be accessed
Incomplete traffic flow data tensorWith the complete traffic flow data tensor to be recoveredRelationship be expressed as：
Wherein, PΩ() indicates Linear Mapping, and Ω is accessed traffic data subset, by tensorMiddle Ω subsets
The position not included is filled with zero.
In an embodiment of the present invention, in the step S2, the tensor filling model based on Factorization corresponds to
Object function and constraints it is as follows：
Wherein, * indicates tensor product,WithIt is by tensor to be solvedResolve into two smaller tensors, tensorIntermediate tensor is preset for one, | | | |FIndicate tensor Frobenius norms, i.e., after three-dimensional tensor being launched into one-dimensional vector
Frobenius norms are asked to the vector.
In an embodiment of the present invention, in the step S3, further include following steps：
Step S31：Build time-constrain tensor；Time-constrain square is built by the toeplitz matrix T that size is j × j
Battle array, as follows：
The time-constrain tensor that a size is j × j × k is built according to time-constrain matrixThe time-constrain tensorFirst positive section be above-mentioned toeplitz matrix T, other positive sections are null matrix；
Step S32：Build space constraint tensor；Space constraint square is built by the Laplacian Matrix L that size is i × i
Battle array, as shown below：
Wherein, m and n indicates m-th and n-th of node, m, n=1,2 ..., i respectively；kmIt is the degree of freedom of node m, meter
Calculation mode is as follows：
km=∑nAmn
Wherein, AmnIt is the adjacency matrix that size is i × i；It is i × i × k to build a size according to space constraint matrix
Space constraint tensorThe space constraint tensorFirst positive section be above-mentioned Laplacian Matrix L, other are positive
Section is null matrix；
Step S33：By analyzing the space-time characterisation of traffic data, by constructed time-constrain tensor sum space constraint
Tensor increases in the solution procedure of the object function, obtains following updated object function, and Factor minute is based on to described
The tensor filling model of solution optimizes：
s.t.PΩ(Y-M)=0
Wherein,WithIt is time-constrain and space constraint tensor respectively, λ and α are present count magnitude adjusting parameter.
In an embodiment of the present invention, it in the step S4, is carried out by solving object function in the step S33
Original traffic data are restored, and further include following steps：
Step S41：Initialize tensorWith For estimated tensor order, and it is right
WithThe third dimension along tensor carries out Fast Fourier Transform (FFT) processing, obtainsWithExpression on frequency domainWith
Step S42：Use alternating least-squares pairWithCarry out successive ignition processing；It is fixed firstWith
UpdateSecondly fixedWithUpdateFinally fixWithUpdateUntil reach default maximum iteration or
Reach the condition of convergence；
Step S43：By what is finally obtainedWithMultiplication processing is carried out, the restoration result on frequency domain is obtained
Step S44：To restoration resultInverse Fourier transform processing is carried out along the third dimension, obtains final restoration resultBy final restoration resultAs the original traffic data after recovery.
Compared to the prior art, the invention has the advantages that：It is proposed by the present invention a kind of based on space-time restriction
A kind of tensor fill method based on Factorization is applied to traffic data and restores field by traffic data tensor fill method,
And the temporal correlation and low-rank characteristic of traffic data are fully excavated, improve the precision for restoring complete traffic data.
Description of the drawings
Fig. 1 is the flow chart of the traffic data tensor fill method based on space-time restriction in the present invention.
Fig. 2 is traffic flow tensor schematic diagram in one embodiment of the invention.
Fig. 3 is space-time restriction tensor structural schematic diagram in one embodiment of the invention.
Fig. 4 is the phase that method provided by the invention and existing traffic data restoration methods are used in one embodiment of the invention
To error contrast schematic diagram.
Specific implementation mode
Below in conjunction with the accompanying drawings, technical scheme of the present invention is specifically described.
The present invention proposes a kind of traffic data tensor fill method based on space-time restriction, as shown in Figure 1, specific step
It is rapid as follows：
Step S1：Incomplete traffic data is obtained, and establishes traffic flow data tensor；
In the present embodiment, by being interacted with vehicle GPS, processing detection vehicle GPS data, acquisition to be carried out
Data restore the continuous k days road average speed datas in section of i interconnection in region.Equally spaced it was divided into j by one day
A moment is constructed to the traffic data tensor that a size is i × j × kAs shown in Figure 2.What is observed is imperfect
TensorWith the complete tensor to be recoveredIt can be indicated by following formula：
Wherein, PΩ() indicates Linear Mapping, and Ω is the traffic data subset observed, tensorMiddle Ω subsets are not
Including position be filled to be zero.
Step S2：A kind of tensor fill method based on Factorization is applied in traffic data recovery, that is, building
A kind of vertical tensor filling model for solving the problems, such as traffic data recovery and based on Factorization；
In the present embodiment, by using following object function should be solved in the tensor fill method of Factorization：
Wherein, * indicates tensor product,WithIt is by tensor to be solvedResolve into two smaller tensors, tensorIt is an intermediate tensor for calculating introducing for simplicity, | | | |FIndicate tensor Frobenius norms, i.e., by three-dimensional tensor
It is launched into after one-dimensional vector and Frobenius norms is asked to the vector.
Step S3：Data space-time characterisation is analyzed, space-time restriction tensor is built, the tensor based on Factorization is filled and is calculated
Method optimizes；
In the present embodiment, by analyzing the space-time characterisation of traffic data, structure time-constrain tensor sum space constraint
Amount, is added in the solution procedure of above-mentioned object function, obtains following object function：
s.t.PΩ(Y-M)=0
WhereinWithIt is time-constrain and space constraint tensor respectively, λ and α are order of magnitude adjusting parameter.
Further, time-constrain tensor is built in the following manner：The toeplitz matrix T structures for being j × j with size
Time-constrain matrix is built, as follows：
The time-constrain tensor that a size is j × j × k is constituted according to time-constrain matrixFirst of the tensor
Positive section is above-mentioned toeplitz matrix T, other positive sections are null matrix；
Further, in the present embodiment, space constraint tensor, the Laplacian Matrix L structures for being i × i with size are built
Space constraint matrix is built, as shown below：
Wherein, m and n indicates m-th and n-th of node, m, n=1,2 ..., i respectively；kmIt is the degree of freedom of node m, meter
Calculation mode is as follows：
km=∑nAmn
Wherein AmnIt is the adjacency matrix that size is i × i.Constitute the space constraint tensor that a size is i × i × kIt should
The positive section of first of tensor is above-mentioned Laplacian Matrix L, other positive sections are null matrix.
Further, in this embodiment the time-constrain tensor sum space constraint tensor structure constructed is as shown in Fig. 3,
Wherein, the first Sidelong portion is grey parts, i.e., required toeplitz matrix and La Pu Paasche matrixes, white portion is zero moment
Battle array.
Step S4：The tensor filling that space-time restriction is added is carried out, initial data is recovered.
Step S41：Initialize tensorWith For estimated tensor order, and it is right
WithThe third dimension along tensor carries out Fast Fourier Transform (FFT), obtainsWithExpression on frequency domainWith
Step S42：It is right using alternating least-squares (ALS)WithCarry out successive ignition.It is fixed firstWithUpdateThen it fixesWithUpdateFinally fixWithUpdateUntil reaching default maximum iteration
Or reach the condition of convergence；
Step S43：To what is finally obtainedWithBe multiplied the restoration result reached on frequency domain
Step S44：It is rightInverse Fourier transform is carried out along the third dimension, obtains final restoration result
Further, in the present embodiment, in order to allow those skilled in the art to further appreciate that technical scheme of the present invention
And technique effect, the effect of the present invention is weighed by calculating relative error (relative error), computational methods
It is as follows：
This method (TCTF-ST) is compared with a variety of existing traffic data restoration methods below, compares traffic number
According to the relative error under different miss rates (missing rate).As shown in figure 4, this method is in different missings in contrast
Possess lower relative error under rate, illustrates that this method has preferable recovery effect under different traffic data deletion conditions
Fruit is better than existing method, improves the precision for restoring complete traffic data comprehensively, hence it is evident that improves existing traffic data and restores
Effect.
The above are preferred embodiments of the present invention, all any changes made according to the technical solution of the present invention, and generated function is made
When with range without departing from technical solution of the present invention, all belong to the scope of protection of the present invention.
Claims (5)
1. a kind of traffic data tensor fill method based on space-time restriction, which is characterized in that realize in accordance with the following steps：
Step S1：Incomplete traffic data is obtained, traffic flow data tensor is established；
Step S2：It establishes the tensor based on Factorization and fills model；
Step S3：By analyzing data space-time characterisation, space-time restriction tensor is built, the tensor based on Factorization is filled
Model optimizes；
Step S4：The tensor filling processing that space-time restriction is added is carried out, original traffic data are recovered.
2. a kind of traffic data tensor fill method based on space-time restriction according to claim 1, which is characterized in that
The step S1, by being interacted with vehicle GPS, collection vehicle GPS data obtains pending data and restores in region i
The continuous k days road average speed datas in section of interconnection；Equally spaced it was divided into j moment by one day, is constructed to one
A size is the traffic flow data tensor of i × j × k, and by accessed incomplete traffic flow data tensorWith institute
The complete traffic flow data tensor to be recoveredRelationship be expressed as：
Wherein, PΩ() indicates Linear Mapping, and Ω is accessed traffic data subset, by tensorMiddle Ω subsets do not include
Position be filled with zero.
3. a kind of traffic data tensor fill method based on space-time restriction according to claim 2, which is characterized in that
In the step S2, the corresponding object function of tensor filling model and constraints based on Factorization are as follows：
Wherein, * indicates tensor product,WithIt is by tensor to be solvedResolve into two smaller tensors, tensorFor
One default intermediate tensor, | | | |FIt indicates tensor Frobenius norms, i.e., three-dimensional tensor is launched into after one-dimensional vector to this
Vector seeks Frobenius norms.
4. a kind of traffic data tensor fill method based on space-time restriction according to claim 3, which is characterized in that
Further include following steps in the step S3：
Step S31：Build time-constrain tensor；Time-constrain matrix is built by the toeplitz matrix T that size is j × j, such as
Shown in lower：
The time-constrain tensor T that size is j × j × k is built according to time-constrain matrix, the of time-constrain tensor T
One positive section is above-mentioned toeplitz matrix T, other positive sections are null matrix；
Step S32：Build space constraint tensor；Space constraint matrix is built by the Laplacian Matrix L that size is i × i, such as
Shown in figure below：
Wherein, m and n indicates m-th and n-th of node, m, n=1,2 ..., i respectively；kmIt is the degree of freedom of node m, calculation
It is as follows：
km=∑nAmn
Wherein, AmnIt is the adjacency matrix that size is i × i；The space that a size is i × i × k is built according to space constraint matrix
The positive section of first of restricted circle S, space constraint tensor S is above-mentioned Laplacian Matrix L, other positive sections are
Null matrix；
Step S33：By analyzing the space-time characterisation of traffic data, constructed time-constrain tensor sum space constraint tensor is increased
It adds in the solution procedure of the object function, obtains following updated object function, opened based on Factorization to described
Amount filling model optimizes：
s.t.PΩ(Y-M)=0
Wherein, T and S is time-constrain and space constraint tensor respectively, and λ and α are present count magnitude adjusting parameter.
5. a kind of traffic data tensor fill method based on space-time restriction according to claim 4, which is characterized in that
In the step S4, original traffic data recovery is carried out by solving object function in the step S33, further includes walking as follows
Suddenly：
Step S41：Initialize tensorWith For estimated tensor order, and it is rightWith
The third dimension along tensor carries out Fast Fourier Transform (FFT) processing, obtainsWithExpression on frequency domainWith
Step S42：Use alternating least-squares pairWithCarry out successive ignition processing；It is fixed firstWithUpdateSecondly fixedWithUpdateFinally fixWithUpdateUntil reaching default maximum iteration or reaching receipts
Hold back condition；
Step S43：By what is finally obtainedWithMultiplication processing is carried out, the restoration result on frequency domain is obtained
Step S44：To restoration resultInverse Fourier transform processing is carried out along the third dimension, obtains final restoration resultIt will
Final restoration resultAs the original traffic data after recovery.
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| CN110111578A (en) * | 2019-05-25 | 2019-08-09 | 东南大学 | A kind of sporadic traffic jam detection method restored based on tensor |
| CN110111578B (en) * | 2019-05-25 | 2021-06-01 | 东南大学 | Tensor recovery-based sporadic traffic congestion detection method |
| CN110322693A (en) * | 2019-07-10 | 2019-10-11 | 山东大学 | A kind of traffic data complementing method, system, equipment and medium |
| CN110941793A (en) * | 2019-11-21 | 2020-03-31 | 湖南大学 | Network traffic data filling method, device, equipment and storage medium |
| CN110941793B (en) * | 2019-11-21 | 2023-10-27 | 湖南大学 | Network traffic data filling method, device, equipment and storage medium |
| CN111310117A (en) * | 2020-01-19 | 2020-06-19 | 东南大学 | Tensor train decomposition model-based traffic big data filling method |
| CN111640296B (en) * | 2020-05-08 | 2022-07-29 | 同济大学 | Traffic flow prediction method, system, storage medium and terminal |
| CN111640296A (en) * | 2020-05-08 | 2020-09-08 | 同济大学 | Traffic flow prediction method, system, storage medium and terminal |
| CN112329633A (en) * | 2020-11-05 | 2021-02-05 | 南开大学 | Emotion identification method, device, medium and electronic equipment based on tensor decomposition |
| CN112329633B (en) * | 2020-11-05 | 2022-08-23 | 南开大学 | Emotion identification method, device, medium and electronic equipment based on tensor decomposition |
| CN112699608A (en) * | 2020-12-31 | 2021-04-23 | 哈尔滨工业大学 | Time sequence repairing method suitable for data loss caused by sensor power failure |
| CN113256977A (en) * | 2021-05-13 | 2021-08-13 | 福州大学 | Traffic data processing method based on image tensor decomposition |
| CN115083151A (en) * | 2022-06-02 | 2022-09-20 | 福建师范大学 | Traffic data matrix filling method based on Hessian regular space-time low-rank constraint |
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