CN110689181A - Travel time judgment method based on collaborative tensor decomposition - Google Patents

Travel time judgment method based on collaborative tensor decomposition Download PDF

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CN110689181A
CN110689181A CN201910883851.8A CN201910883851A CN110689181A CN 110689181 A CN110689181 A CN 110689181A CN 201910883851 A CN201910883851 A CN 201910883851A CN 110689181 A CN110689181 A CN 110689181A
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于海洋
刘帅
任毅龙
姜涵
刘成生
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Beijing University of Aeronautics and Astronautics
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Abstract

The patent discloses a travel time judgment method based on collaborative tensor decomposition, which comprises the following steps: step one, constructing a travel time tensor; step two, constructing a feature matrix; and step three, tensor filling. By means of the collaborative history tensor and the factor matrix of the tensor under different dimensions, implicit characteristics are provided for the original tensor, and therefore calculation accuracy is improved. And after the tensor filling is completed, the travel time of the vehicle passing through any road section in any time period can be obtained.

Description

Travel time judgment method based on collaborative tensor decomposition
Technical Field
The invention relates to the field of intelligent traffic, in particular to a method for judging road section travel time of urban traffic based on a tensor decomposition method.
Background
The travel time is one of important parameters for evaluating the traffic running state in the intelligent traffic system, and is also an important basis for realizing traffic planning and management and vehicle path guidance. Vehicle travel time data is often missing due to failures of the detection equipment itself, environmental influences, inherent defects of the detection equipment, and the like. Tensor decomposition is a better missing data filling method and is very suitable for missing travel time filling, tensor is a high-dimensional array, travel time has three dimensions of road sections, vehicles and time, and the high-dimensional characteristic of tensor can be fully exerted. In the prior art, patents for travel time estimation by tensor decomposition are few, and data sparse conditions cannot be well adapted, so the invention provides a travel time estimation method based on collaborative tensor decomposition, and a tensor decomposition process is assisted from different dimensions by using a collaborative factor, so that the defect of travel time estimation precision reduction caused by data sparse is overcome.
Disclosure of Invention
Tensor decomposition can fully mine multidimensional characteristics of data to fill the data, but the tensor is too sparse when the data volume is small, so that the calculation accuracy is reduced. Based on the method, the travel time estimation method based on the collaborative tensor decomposition is provided, and implicit characteristics are provided for the original tensor through the collaborative historical tensor and the factor matrix of the tensor under different dimensions, so that the calculation precision is improved. And after the tensor filling is completed, the travel time of the vehicle passing through any road section in any time period can be obtained.
The travel time estimation method based on tensor decomposition specifically comprises the following steps:
step one, constructing a travel time tensor
(1) Constructing an original tensor, and setting the original tensor to be A because the detected travel time data are generated when a vehicle passes a certain path section at a certain timen∈RN×M×LThe specification is expressed as NxM × L. Wherein three dimensions of the tensor are road section, vehicle and time, tensor AnThe (i, j, k) th element in (i, j, k) represents the travel time of the vehicle j through the link i in the k-th time period. The time period length in the time dimension can be set according to specific requirements.
(2) Constructing historical tensors, wherein the original tensors are quite sparse under general conditions, and the original tensors A are directly usednTravel time estimation by tensor decompositionThe value error is too large, so the historical travel time tensor A needs to be constructedhAs auxiliary tensor pair tensor AnAnd (4) supplementing. History tensor AhWith the original tensor AnThe structures being identical, i.e. Ah∈RN×M×LAnd A ishAnd AnThe time window length and the time interval need to be kept consistent, only AhThe element in (1) is the corresponding historical travel time average. A. thehAnd (i, j, k) ═ a represents that the average value of the historical travel time of the vehicle j passing through the link i in the time period k is a. The data volume of the historical data can be comprehensively selected according to factors such as estimated longitude and calculation efficiency. The larger the data amount of the history data is, the greater the history tensor AhThe denser the final calculation is, the more accurate the result is. Conversely, the smaller the data amount of the history data, the smaller the history tensor AhThe more sparse the final calculation results are, the less accurate the final calculation results are.
(3) Obviously, tensor AhAnd tensor AnThe comparison is a very dense tensor that contains the numerical characteristics of the travel time of the vehicle for the road segment at the historical time. Two tensors need to be combined into one tensor and then follow-up calculation is carried out, namely the two tensors are stacked according to the time dimension, and the tensor A belongs to the RN×M×2LThe formula is as follows:
A＝An||Ah(1)
step two, constructing a feature matrix
(1) A vehicle similarity matrix Z is constructed in which each element represents the degree of travel characteristic between each two vehicles, represented by a value between 0 and 1. Firstly, the historical travel time average value of the vehicle to be estimated passing through each road section is obtained from historical data, and the vehicle travel time characteristic vector F is obtainedp，Fp＝{f1，f2，…，fn}. Wherein FpFeature vectors, f, determined for the historical travel time of the vehicle p on the respective routenRepresenting the historical travel time average for vehicle p on the nth road segment. Then, the similarity between every two vehicles is obtained, and the driving similarity between the vehicles is measured by adopting a Pearson correlation coefficient, as shown in formula (2):
Figure BDA0002205442540000021
where rhopqRepresenting the degree of similarity in the running characteristics between the vehicle p and the vehicle q;
Figure BDA0002205442540000022
represents a vector FpThe difference of each element in (a) and its vector element average. The similarity of the driving characteristics of M vehicles in the tensor can be obtained through the formula, and finally a vehicle similarity matrix Z belonging to R can be obtainedM×M。
(2) And constructing a time characteristic matrix Y reflecting the traffic flow change situation of each road section along with time, wherein each AND element represents the value of a certain road section after the flow normalization in a certain time period. First, the original tensor A is calculatednThe time of the day feature matrix Y can be obtained according to the flow of each road section in the corresponding time periodn∈RL×NThe matrix reflects the time-varying traffic of the road segment on the day. Secondly, the historical data is used for obtaining the average flow of each road section in the corresponding time period, and a historical time characteristic matrix is constructed
Figure BDA0002205442540000023
Are respectively aligned with matrix YnAnd matrix YhAfter normalization processing, merging along a time axis to obtain a time characteristic matrix Y epsilon R2L×NAs shown in equations (3), (4), (5):
Figure BDA0002205442540000024
Figure BDA0002205442540000025
Y＝Yn||Yh(5)
whereinRepresentation matrix YnAll elements of column iThe expression (3) means a matrix YnEach element value in column i is divided by the maximum value in the column vector, as is the case with equation (4).
(3) And constructing a spatial feature matrix X to reflect the attribute features of the road sections, wherein each element represents the value of the road sections after the quantity of the interest points is normalized. The points of interest are scattered on the main road and the branch roads in the research range, but the researched road network may not contain all roads, so each road segment in the researched road network is extended outwards by a distance of gamma meters to form a buffer area. Constructing a spatial feature matrix according to the number of various types of interest points in each road section buffer area
Figure BDA0002205442540000027
Wherein N represents that N road sections exist in the road network, and Q represents that Q types of interest points are selected to express the road section attributes. Finally, the matrix is normalized, and the formula is as follows:
X:i＝X:i/max(X:i) (6)
in the formula, X:iRepresenting all the elements in the ith column of the matrix, and formula (6) means that the value of each element in the ith column of the matrix X is divided by the maximum value in the vector of this column.
Step three, tensor filling
(1) The tensor A is decomposed by adopting a decomposition form of BTD, and a form of adding several small terms can be obtained, wherein each small term is a form of Tucker decomposition. The Tucker decomposition may decompose a tensor into a form of multiplying a core tensor by several factor matrices, the number of factor matrices being equal to the order of the tensor. Introducing the three characteristic matrixes to obtain a collaborative tensor decomposition objective function:
Figure BDA0002205442540000028
in the formula, b represents the b-th sub-term in BTD decomposition; s represents a core tensor in the Tucker decomposition; r represents a factor matrix corresponding to the first dimension of the tensor; c represents a factor matrix corresponding to the second dimension of the tensor; the third dimension of the tensor is denoted by TA corresponding factor matrix; u is a geographical characteristic recessive factor matrix; g is a road section recessive factor matrix; lambda [ alpha ]1,λ2,λ3,λ4,λ5Respectively representing each coefficient in the formula; cTRepresents the transpose of matrix C; l isZThe matrix Z is obtained by calculation, and the calculation formula is as follows:
LZ＝D-Z (8)
Dii＝∑iZij(9)
(2) solving the objective function by using a random gradient descent method to obtain an updated formula of each variable:
Figure BDA0002205442540000031
Figure BDA0002205442540000032
Figure BDA0002205442540000033
Figure BDA0002205442540000034
Figure BDA0002205442540000035
Figure BDA0002205442540000036
wherein
Figure BDA0002205442540000037
An estimate representing the (i, j, k) th element in tensor A;
Figure BDA0002205442540000038
the tensor outer product is represented. The number of each variable can be updated in each iteration process by the updating formulaValue, finally finding the locally optimal estimated tensor
Figure BDA0002205442540000039
Closest to tensor a.
(3) The iterative update process first needs to initialize each core tensor and factor matrix, and assigns smaller values to its elements. Then, the updating formula is used for calculating the updating value of each variable, so that a new core tensor and a factor matrix can be obtained, and a new estimated tensor can be obtained
Figure BDA00022054425400000310
Estimating tensor after certain iterationThe update terminates after the error between the tensor A and the tensor A is gradually reduced to be less than epsilon. At this time, the estimated tensor is obtained
Figure BDA00022054425400000312
I.e. the tensor after completion, in which the element values are the corresponding estimated travel times.
Description of the drawings:
FIG. 1 is a flow chart of link travel time estimation based on collaborative tensor decomposition
FIG. 2 is a schematic diagram of a travel time tensor stack
FIG. 3 is a diagram illustrating a buffer establishment method
FIG. 4 is a schematic diagram of a BTD decomposition form
Fig. 5 is a flowchart of the collaborative tensor resolution algorithm.
The specific implementation mode is as follows:
the method for estimating the travel time of the link based on the collaborative tensor decomposition according to the present invention is further described below with reference to an example. The flow chart of the embodiment is shown in fig. 1, and data of the card port in the city of rean is taken as an example for explanation.
Step one, constructing a travel time tensor
(1) Constructing an original tensor, wherein the travel time of a vehicle passing through a road section can be obtained through the data calculation of adjacent gate detectors, and500 vehicles are extracted to calculate their travel time on 108 road segments of the road network under study. The time period is divided into half an hour for a total of 48 periods of time a day. So set the original tensor to An∈R108×500×48The specification of the three-dimensional matrix is expressed as a 108 × 500 × 48 matrix. Wherein three dimensions of the tensor are road section, vehicle and time, tensor AnThe (i, j, k) th element in (i, j, k) represents the travel time of the vehicle j through the link i in the k-th time period. The time period length in the time dimension can be set according to specific requirements.
(2) Constructing historical tensor, wherein the original tensor is quite sparse, the proportion of non-zero elements is only 0.82%, and the original tensor A is directly usednThe travel time estimated value obtained by tensor decomposition has too large error, so that the historical travel time tensor A needs to be constructedhAs auxiliary tensor pair tensor AnAnd (4) supplementing. History tensor AhWith the original tensor AnThe structures being identical, i.e. Ah∈R108×500×48And A ishAnd AnIs also half an hour long and the time intervals need to be kept consistent, only ahThe element in (1) is the corresponding historical travel time average. A. thehThe (20,10,2) ═ 115 indicates that the average value of the travel time history of the vehicle 10 passing through the link 20 in the time zone 2 is 115 seconds. The data volume of the historical data can be comprehensively selected according to factors such as estimated longitude and calculation efficiency. The larger the data amount of the history data is, the greater the history tensor AhThe denser the final calculation is, the more accurate the result is. Conversely, the smaller the data amount of the history data, the smaller the history tensor AhThe more sparse the final calculation results are, the less accurate the final calculation results are.
(3) Obviously, tensor AhAnd tensor AnThe comparison is a very dense tensor that contains the numerical characteristics of the travel time of the vehicle for the road segment at the historical time. Two tensors need to be combined into one tensor and then follow-up calculation is carried out, namely the two tensors are stacked according to the time dimension, and the tensor A belongs to the R108×500×96As shown in fig. 2, the formula is as follows:
A＝An||Ah(1)
step two, constructing a feature matrix
(1) A vehicle similarity matrix Z is constructed in which each element represents the degree of travel characteristic between each two vehicles, represented by a value between 0 and 1. Firstly, the historical travel time average value of the vehicle to be estimated passing through each road section is obtained from historical data, and the vehicle travel time characteristic vector F is obtainedp，Fp＝{f1，f2，…，fn}. Wherein FpFeature vectors, f, determined for the historical travel time of the vehicle p on the respective routenRepresenting the historical travel time average for vehicle p on the nth road segment. Then, the similarity between every two vehicles is obtained, and the driving similarity between the vehicles is measured by adopting a Pearson correlation coefficient, as shown in formula (2):
Figure BDA0002205442540000041
where rhopqRepresenting the degree of similarity in the running characteristics between the vehicle p and the vehicle q;
Figure BDA0002205442540000042
represents a vector FpThe difference of each element in (a) and its vector element average. The running characteristic similarity between every two 500 vehicles in the tensor can be obtained through the formula, and finally, a vehicle similarity matrix Z belonging to R can be obtained500×500。
(2) And constructing a time characteristic matrix Y reflecting the traffic flow change situation of each road section along with time, wherein each AND element represents the value of a certain road section after the flow normalization in a certain time period. First, the original tensor A is calculatednThe time of the day feature matrix can be obtained according to the flow of each road section in the corresponding time period
Figure BDA0002205442540000043
The matrix reflects the time-varying traffic of the road segment on the day. Secondly, the historical data is used for obtaining the average flow of each road section in the corresponding time period, and a historical time characteristic matrix is constructedAre respectively aligned with matrix YnAnd matrix YhAfter normalization processing, merging along a time axis to obtain a time characteristic matrix
Figure BDA0002205442540000045
As shown in equations (3), (4), (5):
Figure BDA0002205442540000046
Figure BDA0002205442540000047
Y＝Yn||Yh(5)
whereinRepresentation matrix YnAll elements in column i, formula (3) means matrix YnEach element value in column i is divided by the maximum value in the column vector, as is the case with equation (4).
(3) And constructing a spatial feature matrix X to reflect the attribute features of the road sections, wherein each element represents the value of the road sections after the quantity of the interest points is normalized. The road segment attribute is represented by six types of interest point data such as food, shopping, bus stations, living services, leisure and entertainment, transportation facilities and the like. Points of interest are scattered around the trunk and branches within the study, but the study road network may not contain all roads, so each road segment in the study road network is first extended outward by a distance of γ meters to form a buffer area, as shown in fig. 3. Constructing a spatial feature matrix according to the number of various types of interest points in each road section buffer area
Figure BDA0002205442540000049
Finally, the matrix is normalized, and the formula is as follows:
X:i＝X:i/max(X:i) (6)
in the formula, X:iRepresenting all the elements in the ith column of the matrix, and formula (6) means that the value of each element in the ith column of the matrix X is divided by the maximum value in the vector of this column.
Step three, tensor filling
(1) The tensor A is decomposed by adopting a decomposition form of BTD, and a form of adding several small terms can be obtained, wherein each small term is in a form of Tucker decomposition, and is shown in figure 4. The Tucker decomposition may decompose a tensor into a form of multiplying a core tensor by several factor matrices, the number of factor matrices being equal to the order of the tensor. Introducing the three characteristic matrixes to obtain a collaborative tensor decomposition objective function:
Figure BDA00022054425400000410
in the formula, b represents the b-th sub-term in BTD decomposition; s represents a core tensor in the Tucker decomposition; r represents a factor matrix corresponding to the first dimension of the tensor; c represents a factor matrix corresponding to the second dimension of the tensor; t represents a factor matrix corresponding to the third dimension of the tensor; u is a geographical characteristic recessive factor matrix; g is a road section recessive factor matrix; lambda [ alpha ]1,λ2,λ3,λ4,λ5Respectively representing each coefficient in the formula; cTRepresents the transpose of matrix C; l isZThe matrix Z is obtained by calculation, and the calculation formula is as follows:
LZ＝D-Z (8)
Dii＝∑iZij(9)
(2) solving the objective function by using a random gradient descent method to obtain an updated formula of each variable:
Figure BDA0002205442540000051
Figure BDA0002205442540000052
Figure BDA0002205442540000053
Figure BDA0002205442540000055
Figure BDA0002205442540000056
wherein
Figure BDA0002205442540000057
An estimate representing the (i, j, k) th element in tensor A;
Figure BDA0002205442540000058
the tensor outer product is represented. The numerical values of the variables can be updated in each iteration process by the updating formula, and finally, the locally optimal estimation tensor is obtained
Figure BDA0002205442540000059
Closest to tensor a.
(3) The iterative update process first needs to initialize each core tensor and factor matrix, and assigns smaller values to its elements. Then, the updating formula is used for calculating the updating value of each variable, so that a new core tensor and a factor matrix can be obtained, and a new estimated tensor can be obtainedEstimating tensor after certain iteration
Figure BDA00022054425400000511
The update terminates after the error between the tensor A and the tensor A is gradually reduced to be less than epsilon. At this time, the estimated tensor is obtained
Figure BDA00022054425400000512
I.e. the tensor after completion, in which the element values are the corresponding estimated travel times, the flow chart of the algorithm is shown in fig. 5.

Claims (1)

1. A travel time determination method based on collaborative tensor decomposition, the method comprising:
step one, constructing a travel time tensor
Constructing an original tensor, and setting the original tensor to be An∈RN×M×LIt is expressed that the specification is NxM xL; of which three dimensions N, M, L of the tensor are road section, vehicle and time, tensor AnThe (i, j, k) th element represents the travel time of the vehicle j through the link i in the k time period;
construction of the historical tensor, historical tensor Ah∈RN×M×LAnd A ishAnd AnThe time window length and the time interval need to be kept consistent, AhThe element in (1) is the corresponding historical travel time average; a. theh(i, j, k) ═ a denotes that the average value of the history of the travel time of the vehicle j passing through the link i in the time period k is a;
will tensor AhAnd tensor AnMerging into a tensor, namely stacking the two tensors according to the time dimension to obtain the tensor A belonging to the RN ×M×2LThe formula is that A is An||Ah(1)
Step two, constructing a feature matrix
(1) Constructing a vehicle similarity matrix Z, wherein each element in the matrix represents the similarity degree of the driving characteristics between every two vehicles and is represented by a value between 0 and 1; firstly, the historical travel time average value of the vehicle to be estimated passing through each road section is obtained from historical data, and the vehicle travel time characteristic vector F is obtainedp＝{f1，f2，…，fn}; wherein FpFeature vectors, f, determined for the historical travel time of the vehicle p on the respective routenRepresenting the historical travel time average of the vehicle p on the nth road segment; then, the similarity between every two vehicles is solved, and the formula is adopted:
Figure FDA0002205442530000011
calculating the similarity of the running characteristics between the vehicle p and the vehicle q, where ρpqRepresenting the degree of similarity in the running characteristics between the vehicle p and the vehicle q;represents a vector FpThe difference of each element in (a) and its vector element average; the similarity of the driving characteristics of M vehicles in the tensor can be obtained through the formula, and finally a vehicle similarity matrix Z belonging to R can be obtainedM×M；
(2) And constructing a time characteristic matrix Y, wherein the time characteristic matrix Y reflects the traffic flow change situation of each road section along with time, and each AND element represents the value of a certain road section after the flow normalization in a certain time period. First, the original tensor A is calculatednThe time of the day feature matrix Y can be obtained according to the flow of each road section in the corresponding time periodn∈RL×NThe matrix reflects the time-varying traffic of the road segment on the day. Secondly, the historical data is used for obtaining the average flow of each road section in the corresponding time period, and a historical time characteristic matrix Y is constructedh∈RL×N. Are respectively aligned with matrix YnAnd matrix YhAfter normalization processing, merging along a time axis to obtain a time characteristic matrix Y epsilon R2L×NAs shown in equations (3), (4), (5):
Figure FDA0002205442530000014
Y＝Yn||Yh(5)
wherein
Figure FDA0002205442530000016
Representation matrix YnAll elements in column i, formula (3) means matrix YnDividing each element value in the ith column byThe maximum value in this column vector, as does equation (4).
(3) And constructing a spatial feature matrix X to reflect the attribute features of the road sections, wherein each element represents the value of the road sections after the quantity of the interest points is normalized. The points of interest are scattered on the main roads and branch roads within the research area, but the research area may not include all roads, so each road segment in the research area is first extended by γ meters to form a buffer area. Constructing a spatial feature matrix according to the number of various types of interest points in each road section buffer area
Figure FDA0002205442530000015
Wherein N represents that N road sections exist in the road network, and Q represents that Q types of interest points are selected to express the road section attributes. Finally, the matrix is normalized, and the formula is as follows:
X：i＝X：i/max(X：i) (6)
in the formula, X：iRepresenting all the elements in the ith column of the matrix, and formula (6) means that the value of each element in the ith column of the matrix X is divided by the maximum value in the vector of this column.
Step three, tensor filling
(1) The tensor A is decomposed by adopting a decomposition form of BTD, and a form of adding several small terms can be obtained, wherein each small term is a form of Tucker decomposition. The Tucker decomposition may decompose a tensor into a form of multiplying a core tensor by several factor matrices, the number of factor matrices being equal to the order of the tensor. Introducing the three characteristic matrixes to obtain a collaborative tensor decomposition objective function:
Figure FDA0002205442530000021
in the formula, b represents the b-th sub-term in BTD decomposition; s represents a core tensor in the Tucker decomposition; r represents a factor matrix corresponding to the first dimension of the tensor; c represents a factor matrix corresponding to the second dimension of the tensor; t represents a factor matrix corresponding to the third dimension of the tensor; u is a geographical characteristic recessive factor matrix; g is hidden in road sectionA sex factor matrix; lambda [ alpha ]1，λ2，λ3，λ4，λ5Respectively representing each coefficient in the formula; cTRepresents the transpose of matrix C; l isZThe matrix Z is obtained by calculation, and the calculation formula is as follows:
LZ＝D-Z (8)
Dii＝∑iZij(9)
(2) solving the objective function by using a random gradient descent method to obtain an updated formula of each variable:
Figure FDA0002205442530000022
Figure FDA0002205442530000023
Figure FDA0002205442530000024
Figure FDA0002205442530000025
Figure FDA0002205442530000026
Figure FDA0002205442530000027
wherein
Figure FDA0002205442530000028
An estimate representing the (i, j, k) th element in tensor A;
Figure FDA0002205442530000029
the tensor outer product is represented. The numerical values of the variables can be updated in each iteration process by the updating formula, and finally, the locally optimal estimation tensor is obtained
Figure FDA00022054425300000213
Closest to tensor a.
(3) The iterative update process first needs to initialize each core tensor and factor matrix, and assigns smaller values to its elements. Then, the updating formula is used for calculating the updating value of each variable, so that a new core tensor and a factor matrix can be obtained, and a new estimated tensor can be obtained
Figure FDA00022054425300000210
Estimating tensor after certain iteration
Figure FDA00022054425300000212
The update terminates after the error between the tensor A and the tensor A is gradually reduced to be less than epsilon. At this time, the estimated tensor is obtained
Figure FDA00022054425300000211
I.e. the tensor after completion, in which the element values are the corresponding estimated travel times.
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CN112116810A (en) * 2020-09-07 2020-12-22 东南大学 Whole road network segment travel time estimation method based on urban road checkpoint data
CN112182395A (en) * 2020-10-10 2021-01-05 深圳市万佳安物联科技股份有限公司 Financial service personalized recommendation device and method based on time sequence
CN112820104A (en) * 2020-12-31 2021-05-18 北京航空航天大学 Traffic data completion method based on space-time clustering tensor decomposition

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106997389A (en) * 2017-03-30 2017-08-01 浙江鸿程计算机系统有限公司 Recommend method in a kind of tourist attractions based on many data sets and collaboration tensor resolution
CN107992536A (en) * 2017-11-23 2018-05-04 中山大学 Urban transportation missing data complementing method based on tensor resolution
CN109308804A (en) * 2018-08-08 2019-02-05 北京航空航天大学 Hourage estimation method based on tensor resolution
CN109829588A (en) * 2019-02-13 2019-05-31 苏州大学 Tensor trajectory path planing method based on context
CN110119482A (en) * 2019-05-13 2019-08-13 杭州电子科技大学 Based on the crowd of POI and multi-source mobile data collection trip mode visible analysis method

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106997389A (en) * 2017-03-30 2017-08-01 浙江鸿程计算机系统有限公司 Recommend method in a kind of tourist attractions based on many data sets and collaboration tensor resolution
CN107992536A (en) * 2017-11-23 2018-05-04 中山大学 Urban transportation missing data complementing method based on tensor resolution
CN109308804A (en) * 2018-08-08 2019-02-05 北京航空航天大学 Hourage estimation method based on tensor resolution
CN109829588A (en) * 2019-02-13 2019-05-31 苏州大学 Tensor trajectory path planing method based on context
CN110119482A (en) * 2019-05-13 2019-08-13 杭州电子科技大学 Based on the crowd of POI and multi-source mobile data collection trip mode visible analysis method

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
KUN TANG，SHUYAN CHEN，AEMAL J. KHATTAK: "Personalized travel time estimation for urban road networks: a tensor-based context-aware approach", 《EXPERT SYSTEMS WITH APPLICATIONS》 *
YILUN WANG;YU ZHENG;YEXIANG XUE: "Travel Time Estimation of a Path using Sparse Trajectories", 《SIGKDD EXPLORATIONS》 *
邴其春: "城市快速路交通状态评估与预测关键技术研究", 《中国博士学位论文全文数据库 工程科技II辑》 *

Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112116810A (en) * 2020-09-07 2020-12-22 东南大学 Whole road network segment travel time estimation method based on urban road checkpoint data
CN112182395A (en) * 2020-10-10 2021-01-05 深圳市万佳安物联科技股份有限公司 Financial service personalized recommendation device and method based on time sequence
CN112182395B (en) * 2020-10-10 2023-08-29 深圳市万佳安物联科技股份有限公司 Financial service personalized recommendation device and method based on time sequence
CN112820104A (en) * 2020-12-31 2021-05-18 北京航空航天大学 Traffic data completion method based on space-time clustering tensor decomposition
CN112820104B (en) * 2020-12-31 2022-05-31 北京航空航天大学 Traffic data completion method based on spatio-temporal clustering tensor decomposition

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