CN108492561B - Road network traffic state space-time characteristic analysis method based on matrix decomposition - Google Patents

Road network traffic state space-time characteristic analysis method based on matrix decomposition Download PDF

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CN108492561B
CN108492561B CN201810300722.7A CN201810300722A CN108492561B CN 108492561 B CN108492561 B CN 108492561B CN 201810300722 A CN201810300722 A CN 201810300722A CN 108492561 B CN108492561 B CN 108492561B
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孔德慧
巩林昊
张勇
汪洋
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Beijing University of Technology
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    • G08—SIGNALLING
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    • G08G1/00—Traffic control systems for road vehicles
    • G08G1/01—Detecting movement of traffic to be counted or controlled
    • G08G1/0104—Measuring and analyzing of parameters relative to traffic conditions
    • G08G1/0125—Traffic data processing
    • G—PHYSICS
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    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G1/00—Traffic control systems for road vehicles
    • G08G1/01—Detecting movement of traffic to be counted or controlled
    • G08G1/0104—Measuring and analyzing of parameters relative to traffic conditions
    • G08G1/0108—Measuring and analyzing of parameters relative to traffic conditions based on the source of data
    • G08G1/0112—Measuring and analyzing of parameters relative to traffic conditions based on the source of data from the vehicle, e.g. floating car data [FCD]

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Abstract

The invention discloses a road network traffic state space-time characteristic analysis method based on matrix decomposition, which can visually reflect the change characteristics of the road network traffic state in time and space and can find areas with easy congestion and areas with fast evacuation of a road network. The method comprises the following steps: (1) constructing a time-space data matrix of road network traffic; (2) considering noise factors and time sequence similarity characteristics, and performing non-negative matrix decomposition on a space-time data matrix of the road network; (3) performing clustering analysis on the spatial pattern matrix; (4) and (3) road network traffic state space-time characteristic analysis based on spatial mode classification.

Description

Road network traffic state space-time characteristic analysis method based on matrix decomposition
Technical Field
The invention belongs to the technical field of intelligent traffic, and particularly relates to a road network traffic state space-time characteristic analysis method based on matrix decomposition.
Background
The accurate analysis of the urban road traffic state is the key to mastering the urban traffic running condition. With the rapid advance of social economy, the problems of traffic jam and the like become more severe, and the serious road jam problem brings many negative problems, such as increased fuel consumption, time waste of trip personnel, environmental pollution and the like, which hinder the development of cities and influence the daily life of people. Therefore, it is urgent to solve the problem of traffic congestion. The accurate control of the urban road traffic state is one of effective measures for relieving the current traffic problem, and the traffic flow of the traffic road can be shunted and induced by the implementation of the effective relieving measures.
Most of the previous researches on urban road traffic states are concentrated on a single intersection or some road sections, and the intersections, expressways or main roads are analyzed from a microscopic mesoscopic level by adopting simulation data, induction coil data, license plate identification data and the like through microscopic simulation, statistical model construction and data-driven related algorithms. In recent years, with the rapid development of communication technology, floating car data of traffic flow parameters are returned at certain time intervals by using vehicle-mounted GPS equipment, the coverage range of time and space dimensions is wide, the method has strong applicability to grasping urban road network traffic states from a macroscopic level, provides good data support for road network level research, and gradually becomes a main and widely applied data source in large-scale road network research. However, the traffic state of the urban road network constantly changes in space along with time, high dynamics, randomness and complexity are presented, the obtained traffic flow time-space data has the characteristics of multi-source, multi-dimension, mass, multi-scale and multi-time equality, and meanwhile, a new challenge is brought to the analysis of the traffic state of the large-scale road network.
Aiming at the analysis problem of the massive high-dimensional large-scale road network traffic data, a data-driven method is partially researched and utilized, and the high-dimensional road network traffic state data are simplified on the basis of keeping enough information of a road network, so that the space-time evolution characteristic of the traffic state is mined. However, the analysis of the compact space at present focuses on the expression of the traffic state of the road network and the time evolution law of the traffic state, and the dimension reduction process of the road network traffic data can be rarely optimized by simultaneously combining the time structure and the space structure, so that the ability of interpreting the space-time characteristics of the road network traffic state is lacked to a certain extent.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the method can be used for exploring the operation rule of the road network traffic state on time and space by visually reflecting the change characteristics of the road network traffic state on time and space.
The technical solution of the invention is as follows: the road network traffic state space-time characteristic analysis method based on matrix decomposition comprises the following steps:
(1) constructing a time-space data matrix of road network traffic;
(2) considering noise factors and time sequence similarity characteristics, and performing non-negative matrix decomposition on a space-time data matrix of the road network;
(3) performing clustering analysis on the spatial pattern matrix;
(4) and (3) road network traffic space-time characteristic analysis based on spatial mode classification.
According to the invention, from a macroscopic view, a large-scale road network is considered as a whole to be analyzed, the limitation of large-scale road network traffic state data volume and high dimension on an analysis means is overcome, the dimension reduction processing is carried out on the road network traffic data by using an improved matrix decomposition algorithm, and the calculation complexity is reduced while sufficient space-time information is kept. Compared with the traditional analysis method, the analysis of the road network traffic state of the invention simultaneously achieves the purpose of digging the traffic operation rule under the influence of time and road space characteristics, thereby being beneficial to a traffic manager to carry out macroscopic regulation and control on a large-scale road network and also being beneficial to implementing a corresponding congestion management method.
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FIG. 1 is a flow chart of a road network traffic state space-time characteristic analysis method based on matrix decomposition according to the invention.
Detailed Description
The invention discloses a road network traffic data completion method based on a self-adaptive space-time constraint low-rank algorithm, which comprises the following steps of:
(1) constructing a time-space data matrix of road network traffic;
(2) considering noise factors and time sequence similarity characteristics, and performing non-negative matrix decomposition on a space-time data matrix of the road network;
(3) performing clustering analysis on the spatial pattern matrix;
(4) and (3) road network traffic space-time characteristic analysis based on spatial mode classification.
The present invention will be further described with reference to the following examples and the accompanying drawings.
(1) Space-time data matrix for constructing road network traffic data
The taxi GPS data of a road network in the four-ring range of Beijing city is selected as a research object, the road network comprises 9044 road sections, and the time-space change characteristics of the traffic state of the whole road network in one working day are researched.
And (3) establishing a space-time data matrix M of the road network by using road speed data returned by the taxi provided with the GPS equipment and taking continuous time intervals in one day as rows M and each road section n of the road network as columns.
(2) Non-negative matrix factorization of road network space-time data matrix
The abnormal events are inevitable to occur in the road network operation process, which is expressed as sparse noise in the road network data matrix constructed by the invention, so that the part of noise is considered to be added into a non-negative matrix decomposition model here:
Figure BDA0001619702470000041
s.t.M＝UTV+E，Uij≥0，Vij≥0 (7)
and expressing a matrix U obtained by the non-negative matrix decomposition model as a time weight coefficient matrix, expressing a matrix V as a space mode matrix, and expressing a matrix E as sparse noise together with the abnormal events.
In addition, considering the case that the sampling time interval before and after the data is short, we can consider that the weight coefficient acting at the time t +1 is close to the weight coefficient acting at the time t in the time weight coefficient matrix U, so as to perform difference processing on the data at the time points adjacent to the time weight coefficient U, introduce the F-norm to perform error measurement on the difference term, and finally define the improved non-negative matrix decomposition model as the following form:
Figure BDA0001619702470000042
s.t.M＝UTV+E，Uij≥0，Vij≥0 (1)
wherein the content of the first and second substances,
Figure BDA0001619702470000043
is a linear decomposition of the nuclear norm,
Figure BDA0001619702470000044
for time-differential error terms, λ1,λ2Are balance parameters respectively. The matrix T is formed by Rm×(m-1)Is a Toeplitz matrix with diagonal elements and upper and lower layer elements of-1 and 1, respectively, for time varying patternsAnd (3) performing smooth differential constraint on the factor matrix, wherein the form is as follows:
Figure BDA0001619702470000045
solving the formula (1) by using an augmented Lagrange algorithm, removing constraint of the formula (1), introducing an auxiliary variable, making S equal to U, and writing the formula (1) as:
Figure BDA0001619702470000046
s.t.Uij≥0，Vij≥0 (2)
the augmented Lagrange multiplier function of the structural formula (2) is:
Figure BDA0001619702470000051
s.t.Uij≥0，Vij≥0 (3)
wherein A is1Is a Lagrangian multiplier, α>0 is the weight of the error term.
Equation (3) can be broken down into three subproblems, namely equations (4), (5), (6):
Figure BDA0001619702470000052
s.t.Uij≥0，Vij≥0 (4)
Figure BDA0001619702470000053
Figure BDA0001619702470000054
problems (4), (5), (6) are solved separately as follows:
1) equation (4) is a conventional non-negative matrix decomposition problem, and in the case that the noise matrix E follows a gaussian distribution, E is M-UTV, then the maximum can be obtainedThe likelihood function is:
Figure BDA0001619702470000055
after taking the logarithm, the log-likelihood function is obtained as
Figure BDA0001619702470000056
The following objective function value is only required to be the minimum to maximize the value of the log-likelihood function.
Figure BDA0001619702470000058
The loss function is a 2-norm loss function, which is a metric based on euclidean distance. And because of
Figure BDA0001619702470000057
Wherein i is 1,2, …, m; j is 1,2, … n; k is 1,2, …, r, then can be obtained
Figure BDA0001619702470000061
For the same reason have
Figure BDA0001619702470000062
The iteration was then performed using a gradient descent method, with the following results
Figure BDA0001619702470000063
Vkj＝Vkj-α2·((UM)kj-(UUTV)kj) (15)
Is selected here
Figure BDA0001619702470000064
Then the final result is an iteration of
Figure BDA0001619702470000065
Figure BDA0001619702470000066
According to the multiplicative iteration rule, the result is guaranteed to be positive in each step, and the solution of the problem can be obtained after iteration is continued.
2) To solve the problem (5)
Figure BDA0001619702470000067
By taking the derivative of equation (5) and making the derivative 0, we can obtain:
Figure BDA0001619702470000068
and calculating to obtain:
S＝(αU-A1)·(2λ1TTT+αE)-1(19)
3) to problem (6)
Figure BDA0001619702470000069
Let J be M-UTV，
Figure BDA00016197024700000610
Iteratively updating E by equation (6) to obtain a closed solution:
E＝sign(J)max{|J|-η,0} (20)
wherein the content of the first and second substances,
Figure BDA0001619702470000071
(3) performing cluster analysis of spatial pattern matrices
And (3) implementing the spatial mode matrix V obtained by decomposition in the step (2) to represent a spatial characteristic attribute of the traffic state of the four-ring road network in Beijing City, selecting the loop and part of highway sections in the space of the matrix V, and performing cluster analysis on the section matrixes by adopting a K-means clustering algorithm to obtain several clusters of the traffic state attribute of the road network on the spatial level, wherein the result obtained when the number of the selected clusters is 5 has the best distinguishability.
(4) Road network traffic space-time characteristic analysis based on spatial mode classification
Based on the nonnegative matrix decomposition and clustering algorithm process, 5 kinds of clusters of spatial road sections are obtained, visual expression can be performed on the basis of time change according to the longitude and latitude of the road sections in the taxi GPS data in the space and the speed of each time interval in the whole day, the speed change rule of the road sections with different spatial characteristic attributes of the road network is obtained, and the influence of the different spatial characteristic attributes of the road network on the traffic state of the road network is contrastively analyzed.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention in any way, and all simple modifications, equivalent variations and modifications made to the above embodiment according to the technical spirit of the present invention still belong to the protection scope of the technical solution of the present invention.

Claims (2)

1. A road network traffic state space-time characteristic analysis method based on matrix decomposition is characterized in that a road network traffic space-time data matrix is established by using floating car GPS data of a road network, the space-time data matrix is divided into two parts of time weight and a space mode through an improved nonnegative matrix decomposition algorithm, and the space-time characteristic of the road network traffic state is discovered through cluster analysis, and the method comprises the following steps:
(1) constructing a time-space data matrix of road network traffic;
(2) carrying out non-negative matrix decomposition on the road network space-time data matrix;
(3) performing clustering analysis on the spatial pattern matrix;
(4) analyzing road network traffic space-time characteristics based on spatial mode classification;
wherein, the step (2) carries out nonnegative matrix decomposition on the time-space data matrix under the condition of considering noise factors and time sequence similarity characteristics, and the nonnegative matrix decomposition is a formula (1)
Figure FDA0002437695390000011
s.t.M＝UTV+E，Uij≥0，Vij≥0 (1)
Wherein, M ═ M1,m2,…,mn]∈Rm×nThe method comprises the steps that a road network real data matrix containing noise is obtained, M is the number of continuous time intervals, n is the number of road sections, and M and n are the dimensionality of a variable M; u ═ U1,u2,…,um]∈Rr×mThe weight coefficient matrix is expressed as a time weight coefficient matrix, each column of the time weight coefficient matrix is regarded as a weight coefficient based on time, and the influence degree on the operation speed of the road network is expressed; v ═ V1,v2,…,vn]∈Rr×nExpressed as a spatial mode matrix, each column of which is regarded as the mode distribution of different road sections on the space; the matrix E is a noise matrix and represents sparse noise caused by abnormal events in real data of the road network;
Figure FDA0002437695390000012
is a linear decomposition of the nuclear norm,
Figure FDA0002437695390000013
for time-differential error terms, λ1,λ2Respectively representing each balance parameter; the matrix T is formed by Rm×(m-1)The Toeplitz matrix is a Toeplitz matrix, the upper and lower layer elements of the diagonal element of the matrix are respectively-1 and 1, and the Toeplitz matrix is used for performing smooth differential constraint on a time-varying mode factor matrix and has the following form:
Figure FDA0002437695390000021
2. the method for analyzing road network traffic state space-time characteristics based on matrix decomposition as claimed in claim 1, wherein: solving the formula (1) by using an augmented Lagrange algorithm, removing constraint of the formula (1), introducing an auxiliary variable, making S equal to U, and writing the formula (1) as:
Figure FDA0002437695390000022
s.t.Uij≥0，Vij≥0 (2)
the augmented Lagrange multiplier function of the structural formula (2) is:
Figure FDA0002437695390000023
s.t.Uij≥0，Vij≥0 (3)
wherein A is1Is a Lagrangian multiplier, α>0 is the weight of the error term;
equation (3) can be broken down into three subproblems, namely equations (4), (5), (6):
Figure FDA0002437695390000024
s.t.Uij≥0，Vij≥0 (4)
Figure FDA0002437695390000025
Figure FDA0002437695390000026
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