CN109829588A - Tensor trajectory path planing method based on context - Google Patents
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Abstract
The tensor trajectory path planing method based on context that the invention discloses a kind of.A kind of tensor trajectory path planing method based on context of the present invention, comprising: tensor modeling: handling obtained GPS path data, Zhang Chengyi three rank tensorsThree dimensions respectively represent driver, road segment segment and period；Zhang Chengyi three rank tensors of track data of L nearest period, tensor are extracted based on known GPS path dataIn each valueIt represents within k-th of period, i-th of driver, the hourage spent on j-th of road is a, and L is the last one period of statistics.Beneficial effects of the present invention: decomposing Tucker, and the algorithm of itself has can be with improved place.The primary iteration value of the iterative algorithm of itself uses random initializtion, and inserts after 0 value and decompose to the unknown solution position of tensor.And the value that this method is come out using the Tensor Method iteration of context-aware is as the initialization of algorithm.
Description
Technical field
The present invention relates to path planning fields, and in particular to a kind of tensor trajectory path planing method based on context.
Background technique
With the increase of population, travelling problem is increasingly taken seriously.The development of science and technology promotes the hair of tourist industry
Exhibition.More and more people are ready to enjoy life.However, enjoying life means to make full use of time and money.Good travelling
Time prediction can provide economical, the outgoing selection in laborsaving and timesaving not only for personal user, can also provide it is basic for example,
The traffic management information of the mechanisms such as traffic management department avoids various traffic congestions by predicting when travelling.
In intelligent transportation system, unquestionably, most important element first is that predicting travel time.In recent years
Come, there are many methods of estimation hourage.In addition, the method based on GPS track data set is existing very much, but these models are
It is limited, such as it is limited to limited data set；GPS track is only limitted to samll cities and towns；It is concerned only with the average hourage of individual and neglects
Relationship etc. between slightly inherent road and time and space, it means that they are not the predicting travel times suitable for various regions
Model.In order to improve these limitations, this method uses the side based on matrix decomposition pretreatment and context-aware tensor resolution
Method carries out hourage estimation.This method is defined according to tensor, the big and relatively sparse GPS track number that city dynamic is provided
According to collection Zhang Chengsan rank tensor, with drive simulating person, relationship between track and period, and combine current and historical track number
According to cooperateing with decomposition tensor by using the contextual information of the correlation between the time and space such as extracted.
Related conventional technology is as follows:
Tucker is decomposed: simple tensor Tucker is decomposed, and is based only upon the non-zero entry of their own to estimate unknown entry,
Without considering any contextual feature.
Hereafter tensor resolution (CATD): it on the basis that tensor Tucker is decomposed, is extracted from GPS track data set
Contextual information matrix X and Y collaboration decompose it.It is a kind of geographical feature considered between section, it is also contemplated that the time
Temporal correlation between section, the decomposition method based on context perception.
Block Region Decomposition and context-aware Tucker decompose (i.e. BTD and CATD combination): BTD unify Tucker and
CANDECOMP/PARAFAC is decomposed, and a constraint has been added during the algorithm iteration of context tensor.Solve unknown entry not
It is based only upon the non-zero entry estimation of their own, it is also contemplated that the contextual information of trajectory path.
There are following technical problems for traditional technology:
Prediction to hourage, in essence, to be exactly by the track behavior of user be user recommends one most
Suitable path.The Tensor Method of the existing choice of technology is all that huge and sparse tensor data are stored as three rank tensors,
User, road segment segment and certain time are respectively represented, evaluation recommendation is carried out to tensor unknown position by tensor resolution method.At this
In a little algorithms, initially for 0 processing of unknown position filling to guarantee that there is value in each position in tensor, but I considers to insert
0 is only a preprocess method the simplest, and I thinks that 0 filling direct to unknown position may make result
At certain error；In addition to this, the method for existing available best result, the context tensor resolution of selection, and add
The similarity matrix between road between space-time is entered and Tucker decomposition is carried out to tensor, this method is a kind of of iteration
Decomposition algorithm is measured, the initial matrix of selection is the matrix of random initializtion, and such initial mode is also not optimal initial side
Formula.
Summary of the invention
The tensor trajectory path planing method based on context that the technical problem to be solved in the present invention is to provide a kind of, it is existing
Technology is when carrying out tensor resolution, after inserting 0 value for unknown position, is cooperateed with and is decomposed using contextual information, finally
Obtain the value of unknown position.This method pre-processes the original tensor of the prior art: according to the definition of tensor, one three
Rank tensor is exactly the combination of multiple second-order tensors (matrix).Using the sectioning of tensor, incomplete value position matrix is taken
Out, an appropriate value being filled using recommender system matrix decomposition and being put into matrix, the matrix after processing puts back to former tensor again.
In addition to this, traditional tensor alternative manner of existing method selection, iteration initial value select random initializtion, this method benefit
Untreated tensor is carried out in advance with being decomposed to traditional tensor Tucker and increasing the method that contextual information collaboration is decomposed
Processing, primary iteration value of the obtained value as this method.
In order to solve the above-mentioned technical problems, the present invention provides a kind of tensor trajectory path planning side based on context
Method, comprising:
Tensor modeling:
Obtained GPS path data is handled, Zhang Chengyi three rank tensorsThree dimensions point
Driver, road segment segment and period are not represented；The track number of L nearest period is extracted based on known GPS path data
According to Zhang Chengyi three rank tensors, tensorIn each valueIt represents within k-th of period, i-th of department
Machine, the hourage spent on j-th of road are a, and L is the last one period of statistics；
Tucker decomposition is carried out to three rank tensors；By tensorResolve into a core tensorWith three
Low-dimensional matrix:Using formula 1 as the error function of Tucker Decomposition iteration, and
And it can be supplemented by formula 2Missing values, obtain tensor
Contextual information:
Introduce another three ranks tensorAs history tensor, same to tensorStructure is identical, and three dimensions respectively represent
Driver, section and period；, tensorHave andIdentical structure, each value in tensorRepresent
In k period, i-th of driver, on j-th of road history be averaged hourage spend be a'；With regard to the meaning of two tensors
For,Indicate the trajectory path of the past period, tensorCompare tensorIt is more sparse；Increase the historical travel time
Tensor, willWithOnly one sparse tensor of decomposition can be reduced by decomposing togetherError；
In addition to the historical travel time tensor extracted, two matrixes X and Y are also obtained by GPS track path；Y table
Show geospatial feature, capture the similitude in geographical space between different sections of highway, it includes the original geographical empty of each section
Between feature；Matrix X, according to the grid divided to the whole city, the temporal characteristics matrix extracted；City is divided into 16 streets
, that is, there are 16 grids in area, and each grid is made of many sections；The temporal characteristics matrix extracted includes two parts, XrWith
Xh；XrIt is the temporal characteristics matrix based on real-time track path, XrIn value indicate in special time period across specifiable lattice
The quantity of vehicle, every row XrIndicate the coarseness traffic condition in special time period in city；In brief, XrIt indicates according to thick
Correlation between the different time sections of granularity traffic condition；XhHave and XrIdentical structure was indicated in past a period of time
The interior history average traffic number across specifiable lattice；In general, X is established on the day before mentioningh, but week is only selected according to current time
Phase,；
Tensor pretreatment:
First with tensor sectioning, this experiment tensor isIt is divided into L matrix according to L period,
Assuming that invisible element is located at the last one period L, then the matrix for being L to label takes out matrixAnd carry out
Processing；
Then completion tensor, selecting the method for matrix decomposition, an element value is filled in invisible position in tensor in advance；
There to be the position of value to be denoted as (i, j) in matrix R, all location indexs observed are denoted as S；Scoring to any position (i, j)
Estimated value isOptimization problem accordingly becomes formula 3, wherein uiqAnd vjqMore
New formula is respectively formula 4 and formula 5, and wherein α > 0 indicates the step-length of gradient decline；J:(i, j) ∈ S and i:(i, j) ∈ S points
It Biao Shi not the location index of all nonzero elements is constituted on vector R (i :) and R (:, j) set；According to the method described above, to square
Battle array ALMissing Data Filling is carried out, the matrix that the stage obtains is filled up into the initialization of invisible position elementIt is put into former
Amount；
Kernel matrix initialization:
Above-mentioned tensor modeling method and context processing method are referred to as context Tensor Method (CATD) altogether；
In CATD method, the tensor Tucker for carrying out context-aware is decomposed, a kernel matrix for solution and three matrixes
It is initialized as random initializtion；In this method, three on the core tensor S and three modes of CATD method iteration out are used
Matrix R, U, T, the initialization as this model；
Tensor resolution:
It is processedIn conjunction with historical track tensorForm a tensorAnd utilize GPS track data
The contextual information extracted, to tensorIt is decomposed；Since contextual information is utilized in the method, then the target optimized
Function is formula 6；
WhereinP is to mark off the number of grid come, and Q is geographical feature
Dimension；MatrixAll it is latent factor matrix, utilizes formulaRestore the element value that tensor obtains invisible position.
A kind of computer equipment can be run on a memory and on a processor including memory, processor and storage
The step of computer program, the processor realizes any one the method when executing described program.
A kind of computer readable storage medium, is stored thereon with computer program, realization when which is executed by processor
The step of any one the method.
A kind of processor, the processor is for running program, wherein described program executes described in any item when running
Method.
Beneficial effects of the present invention:
Existing basic technology is that the basis that tensor Tucker is decomposed is decomposed using contextual information collaboration, existing
Improved method is all in the method plus one constrains.Tucker is decomposed, the algorithm of itself is that have can be with improved place
's.The primary iteration value of the iterative algorithm of itself uses random initializtion, and inserts after 0 value to the unknown solution position of tensor
It decomposes.And the value that this method is come out using the Tensor Method iteration of context-aware is as the initialization of algorithm, for unknown
A value is inserted using the method for matrix decomposition in position in advance.This method levels of precision on operation result is superior to existing
Method.
Detailed description of the invention
Fig. 1 is the model of the processing data set sparsity in the tensor trajectory path planing method the present invention is based on context
Schematic diagram.
Fig. 2 (a) is the signal of construction context matrix in the tensor trajectory path planing method the present invention is based on context
One of figure.
Fig. 2 (b) is the signal of construction context matrix in the tensor trajectory path planing method the present invention is based on context
The two of figure.
Fig. 2 (c) is the signal of construction context matrix in the tensor trajectory path planing method the present invention is based on context
The two of figure.
Fig. 3 is the mean absolute error of the distinct methods in the tensor trajectory path planing method the present invention is based on context
Schematic diagram.
Fig. 4 is the root-mean-square error of the distinct methods in the tensor trajectory path planing method the present invention is based on context
Schematic diagram.
Specific embodiment
The present invention will be further explained below with reference to the attached drawings and specific examples, so that those skilled in the art can be with
It more fully understands the present invention and can be practiced, but illustrated embodiment is not as a limitation of the invention.
What this method proposed is exactly to the improvement in terms of the two.First, being extracted to from trajectory path data set
Tensor pre-processed, using matrix decomposition common in proposed algorithm method to unknown position insert one it is appropriate
Value, judging from the experimental results, such filling method are effective to the promotion of result accuracy compared with 0 value filling before；
Second, being then the processing to the initial value of original iterative algorithm, original method has been selected --- context tensor resolution method
Primary iteration value of the value that iteration comes out as this method.
1, tensor models
In order to tentatively establish our model, obtained GPS path data is handled, Zhang Chengyi three ranks
AmountThree dimensions respectively represent driver, road segment segment and period.It is extracted based on known GPS path data
Zhang Chengyi three rank tensors of track data of L nearest period, such as Fig. 1, tensorIn each value
It represents within k-th of period, i-th of driver, the hourage spent on j-th of road is a, and L is
The last one period of statistics.It can thus be appreciated that this tensor is huge and sparse, the prediction for invisible position is very unfavorable
's.One of the method for unknown quantity typically for processing compared with higher dimensional matrix, is exactly dimensionality reduction.Because the matrix disposal of higher-dimension gets up
It is less susceptible to, is broken down into the matrix disposal of some low dimensionals, divided using the relationship between low-dimensional matrix and higher dimensional matrix
Analysis higher dimensional matrix is more easy and can realize, so the method that we take here is, carries out Tucker decomposition to three rank tensors.
By tensorResolve into a core tensorWith three low-dimensional matrixes:Using formula 1 as the error function of Tucker Decomposition iteration, and can lead to
Cross the supplement of formula 2Missing values, obtain tensor
2, contextual information
In handling actual model process, due to tensorIt is too sparse, so only analyzing the tensor
Very big error can be generated, the decomposition meeting of sparse tensor is so that result is more inaccurate.In order to solve this problem, it introduces another
A three ranks tensorAs history tensor, same to tensorStructure is identical, and three dimensions respectively represent driver, section and time
Section.Such as Fig. 1, tensorHave andIdentical structure, each value in tensorRepresent k-th of period
It is interior, i-th of driver, on j-th of road history be averaged hourage spend be a'.For the meaning of two tensors,Table
Show the trajectory path of the past period, tensorCompare tensorIt is more sparse.Historical travel time tensor is increased, it will
WithOnly one sparse tensor of decomposition can be reduced by decomposing togetherError.
In addition to the historical travel time tensor extracted, we also pass through GPS track path and obtain two matrixes X and Y.
Just shown as shown in Figure 2, Y indicates geospatial feature, captures the similitude in geographical space between different sections of highway, it includes every
The original geospatial feature in a section, such as length, rate limitation and lane quantity etc..Matrix X, divides according to the whole city
Grid, such as Fig. 2 (b), the temporal characteristics matrix extracted.City is divided into 16 blocks, that is, there are 16 grids, each
Grid is all made of many sections.The temporal characteristics matrix extracted includes two parts, XrAnd Xh。XrIt is based on real-time track road
The temporal characteristics matrix of diameter, XrIn value indicate in special time period across specifiable lattice vehicle quantity, every row XrIt indicates
Coarseness traffic condition in special time period in city.In brief, XrWhen indicating the difference according to coarseness traffic condition
Between correlation between section.XhHave and XrIdentical structure indicates the history that specifiable lattice is passed through within past a period of time
Average traffic number.In general, we establish X on the day before mentioningh, but only according to current time selection cycle, as shown in Fig. 2 (c).
3, tensor pre-processes
Pretreatment to tensor, what is selected herein is carried out with two tensor sectioning, matrix decomposition steps.First with
Tensor sectioning, this experiment tensor areIt is divided into L matrix according to L period, it is assumed that invisible element position
In the last one period L, then the matrix for being L to label takes out matrixAnd it is handled.
Then completion tensor, selecting the method for matrix decomposition, an element value is filled in invisible position in tensor in advance.
The works " Recommender systems " published with reference to Charu C.Aggarwal in 2016, it is contemplated that matrix AL's
Each value has the practical significance of reality, so must be non-negative numerical value.One talked about in the book is compared with its other party
More preferably matrix disassembling method, the discussion recommender system common for one give the rating matrix that a size is m × n to method
R, wherein rijIndicate scoring of the user i to project j.The form that R can be written as follow: R=UVT.Wherein U be m × k user because
Submatrix, V are the project factor matrix of n × k.This matrix decomposition process is considered as an approximate procedure, i.e. R ≈ UVT.For
Make the error as small as possible, selects the optimization object function to beBut often matrix R in example
It is sparse, so our target is that known data recommend user in application matrix.There to be the position of value in matrix R
It sets and is denoted as (i, j), all location indexs observed are denoted as S.Scoring estimated value to any position (i, j) isOptimization problem accordingly becomes formula 3, wherein uiqAnd vjqMore new formula point
Not Wei formula 4 and formula 5, wherein α > 0 indicate gradient decline step-length.J:(i, j) ∈ S and i:(i, j) ∈ S respectively indicate to
Measure the set of the location index composition of all nonzero elements on R (i :) and R (:, j).According to the method described above, to matrix ALIt carries out
The initialization of invisible position element is filled up the matrix that the stage obtains by Missing Data FillingIt is put into former tensor.
4, kernel matrix initializes
Above-mentioned tensor modeling method and context processing method are referred to as context Tensor Method (CATD) altogether.
In CATD method, the tensor Tucker for carrying out context-aware is decomposed, a kernel matrix for solution and three matrixes
It is initialized as random initializtion.In this method, three on the core tensor S and three modes of CATD method iteration out are used
Matrix R, U, T, the initialization as this model.
5, tensor resolution
In order to promote the accuracy of tensor resolution, we will be processedIn conjunction with historical track tensorSuch as
Shown in Fig. 1, a tensor is formedAnd the contextual information extracted using GPS track data, to tensorDivided
Solution.Since contextual information is utilized in the method, then the objective function optimized is formula 6.
WhereinP is that the number of grid come is marked off such as Fig. 2 (b), and Q is
The dimension of geographical feature.MatrixIt is all latent factor matrix,
Utilize formulaRestore the element value that tensor obtains invisible position.
Due to tensor be it is very huge, the driver in city and road are thousands of.The decomposition of big tensor is
Time-consuming, especially the tensor is also especially sparse, and only portion has value.In the reference material of this paper, the whole city is divided
For multiple grid divisions, and tensor model is established respectively to the GPS track path data of each subregion respectively, it has already been proven that
One suitable subregion of selection, which carries out decomposition to small tensor respectively, will not influence accuracy to original tensor resolution, that is, pass through
A suitable subregion is chosen, each subregion establishes out a relatively small tensor, and each subregion extracts respective respectively
Contextual information is decomposed, and be can solve and is decomposed huge and sparse tensor bring error and time-consuming problem.
A concrete application scene of the invention is described below:
The data set that we use is the real case based on Beijing city road net, which is saved by 148,110
Point and 196,307 section compositions.Whole city's road network covers the rectangular spatial areas of 40 × 50km, and section total length is more than 21,
985 kilometers.GPS track data for experiment are that September 1st more than 32000 taxis to October 31 in 2013 generate
Data set.GPS number of nodes reaches 673469757, and track road total length is more than 26218407 kilometers, and average oscillation frequency is
Every 96 seconds.
It is four periods by morning peak period 7:00-9:00 points according to bibliography, each period is 30 minutes.
For data set, we delete the section that traversal is less than 50 times (daily less than 1 time), and the hourage on these roads may
It is to have noise, or come because inappropriate map-matching algorithm selects, or since these roads itself do not allow
Vehicle process etc..
Due to the memory allocation problem of computer, 11840 × 32670 × 8 huge and sparse tensor of this data set can not
It is handled, so the experiment of this paper has chosen the data set that can be run to greatest extent, 7400 taxis and 9992 roads
Road is used for our model, and extracts contextual information X and Y from above-mentioned data set.Table 1 is the tensor sum matrix established
Statistical data.As shown in table 1, tensor is particularly sparse, and only portion is visible.
The statistical data of Table I data model
Select the verifying index of mean absolute error (MAE) and root-mean-square error (RMSE) as our models.It is processed
Data set original value be used as the accuracy that basic fact carrys out test evaluation.Estimate that formula is formula 7 and formula 8.
In order to which test evaluation section lacks the accuracy of the journey time of track, we are from real-time tensorThe last one
The known entry of period random erasure 30%, it is original with them then by the values of these entries of our model prediction
The fact calculates mean absolute error (MAE) and root-mean-square error (RMSE) based on value.
2 arithmetic result I of table
3 arithmetic result II of table
| MAE | RMSE | |
| TD | 31.7715 | 62.4658 |
| CATD | 31.3388 | 62.1951 |
| BTD+CATD | 27.2345 | 59.0341 |
| MD+BTD+CATD | 26.9320 | 58.7127 |
Either with original method Tucker decompose or improved context-aware tensor resolution compared with, proposition based on
The context-aware Tensor Method of matrix decomposition all achieves good effect.It is added to the BTD precision of method of matrix decomposition
Also it is improved.In addition, we have also carried out some other tests as shown in Fig. 3 Fig. 4: we are respectively from real-time tensor
In the last one period stochastic censored in addition to 30%, 60%, 90% known items, and test respectively use these methods knot
Fruit.Two histogram displays use three matrixes of core tensor sum for passing through CATD iteration as primary iteration value and fill in advance
The result of the unknown position experiment of tensor is still more preferable.
Embodiment described above is only to absolutely prove preferred embodiment that is of the invention and being lifted, protection model of the invention
It encloses without being limited thereto.Those skilled in the art's made equivalent substitute or transformation on the basis of the present invention, in the present invention
Protection scope within.Protection scope of the present invention is subject to claims.
Claims (4)
1. a kind of tensor trajectory path planing method based on context characterized by comprising
Tensor modeling:
Obtained GPS path data is handled, Zhang Chengyi three rank tensorsThree dimensions generation respectively
Table driver, road segment segment and period；The track data of L nearest period is extracted based on known GPS path data
At a three rank tensors, tensorIn each valueIt represents within k-th of period, i-th of driver,
The hourage spent on j-th of road is a, and L is the last one period of statistics；
Tucker decomposition is carried out to three rank tensors；By tensorResolve into a core tensorWith three low-dimensionals
Matrix:Using formula 1 as the error function of Tucker Decomposition iteration, and can
To be supplemented by formula 2Missing values, obtain tensor
Contextual information:
Introduce another three ranks tensorAs history tensor, same to tensorStructure is identical, three dimensions respectively represent driver,
Section and period；, tensorHave andIdentical structure, each value in tensorWhen represent k-th
Between in section, i-th of driver, it is a' that history, which is averaged that hourage spends, on j-th of road；For the meaning of two tensors,Indicate the trajectory path of the past period, tensorCompare tensorIt is more sparse；Historical travel time tensor is increased,
It willWithOnly one sparse tensor of decomposition can be reduced by decomposing togetherError；
In addition to the historical travel time tensor extracted, two matrixes X and Y are also obtained by GPS track path；Y indicates ground
Space characteristics are managed, the similitude in geographical space between different sections of highway is captured, it includes the original geographical space spy in each section
Sign；Matrix X, according to the grid divided to the whole city, the temporal characteristics matrix extracted；City is divided into 16 blocks, i.e.,
There are 16 grids, each grid is made of many sections；The temporal characteristics matrix extracted includes two parts, XrAnd Xh；XrIt is
Temporal characteristics matrix based on real-time track path, XrIn value indicate the vehicle in special time period across specifiable lattice
Quantity, every row XrIndicate the coarseness traffic condition in special time period in city；In brief, XrExpression is handed over according to coarseness
Correlation between the different time sections of logical situation；XhHave and XrIdentical structure, expression pass through within past a period of time
The history average traffic number of specifiable lattice；In general, X is established on the day before mentioningh, but only according to current time selection cycle,；
Tensor pretreatment:
First with tensor sectioning, this experiment tensor isIt is divided into L matrix according to L period, it is assumed that
Invisible element is located at the last one period L, then the matrix for being L to label takes out matrixAnd located
Reason；
Then completion tensor, selecting the method for matrix decomposition, an element value is filled in invisible position in tensor in advance；By square
There is the position of value to be denoted as (i, j) in battle array R, all location indexs observed are denoted as S；Scoring estimation to any position (i, j)
Value isOptimization problem accordingly becomes formula 3, wherein uiqAnd vjqUpdate it is public
Formula is respectively formula 4 and formula 5, and wherein α > 0 indicates the step-length of gradient decline；J:(i, j) ∈ S and i:(i, j) ∈ S distinguishes table
Show the set that the location index of all nonzero elements on vector R (i :) and R (:, j) is constituted；According to the method described above, to matrix AL
Missing Data Filling is carried out, the matrix that the stage obtains is filled up into the initialization of invisible position elementIt is put into former tensor；
Kernel matrix initialization:
Above-mentioned tensor modeling method and context processing method are referred to as context Tensor Method (CATD) altogether；The side CATD
In method, the tensor Tucker for carrying out context-aware is decomposed, the initialization for a kernel matrix and three matrixes of solution
For random initializtion；In this method, the three matrix R on core tensor S and three modes come out using CATD method iteration,
U, T, the initialization as this model；
Tensor resolution:
It is processedIn conjunction with historical track tensorForm a tensorAnd it is extracted using GPS track data
Contextual information out, to tensorIt is decomposed；Since contextual information is utilized in the method, then the objective function optimized
For formula 6；
WhereinP is to mark off the number of grid come, and Q is the dimension of geographical feature
Degree；MatrixAll it is latent factor matrix, utilizes formulaRestore the element value that tensor obtains invisible position.
2. a kind of computer equipment including memory, processor and stores the meter that can be run on a memory and on a processor
Calculation machine program, which is characterized in that the step of processor realizes claim 1 the method when executing described program.
3. a kind of computer readable storage medium, is stored thereon with computer program, which is characterized in that the program is held by processor
The step of claim 1 the method is realized when row.
4. a kind of processor, which is characterized in that the processor is for running program, wherein right of execution when described program is run
Benefit require 1 described in method.
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| CN110689181A (en) * | 2019-09-18 | 2020-01-14 | 北京航空航天大学 | Travel time judgment method based on collaborative tensor decomposition |
| CN111104792A (en) * | 2019-12-13 | 2020-05-05 | 浙江工业大学 | Traffic track data semantic analysis and visualization method based on topic model |
| CN112652178A (en) * | 2020-12-24 | 2021-04-13 | 航天科工智能运筹与信息安全研究院(武汉)有限公司 | Control system for urban traffic |
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