A Road Network Traffic State Identification Method Based on Macroscopic Fundamental Diagram and Spectral Clustering and Support Vector Machine

Abstract

Accurate identification of road network traffic status is the key to improve the efficiency of urban traffic control and management. Both data mining method and MFD-based methods can divide the traffic state of road network, but each has its own advantages and disadvantages. The data mining method is oriented to traffic data with high efficiency, but it can only discriminate traffic status from microlevel, while the MFD of road network can discriminate traffic status from macrolevel, but there are still some problems, such as the fact that the discriminant method of equivalence points based on MFD lacks theoretical support or that traffic status could not be subdivided. If data mining methods and road network’s MFD are combined, the accuracy of road network traffic state identification will be greatly improved. In addition, the research shows that the combination of unsupervised learning clustering analysis method (such as spectral clustering algorithm) and supervised learning machine algorithm (such as support vector machine algorithm (SVM)) is more accurate in traffic state identification. Therefore, a traffic state identification method based on MFD and spectral clustering and SVM is proposed, combining the advantages of spectral clustering algorithm and SVM algorithm. Firstly, spectral clustering algorithm is used to classify the traffic state of road network’s MFD. Secondly, SVM multiclassifier is trained with the partitioned road network’s MFD parameters, and the accuracy evaluation method of classification results based on obfuscation matrix is given. Finally, the connected-vehicle network simulation platform is built for empirical analysis. The results show that the classification results of spectral clustering algorithm are closer to the theoretical values, compared with K-means algorithm, and the accuracy of SVM multiclassifier is 96.3%. It can be seen that our algorithm can identify the road network traffic state more effectively from the macrolevel.

Full text

Research Article
A Road Network Traffic State Identification
Method Based on Macroscopic Fundamental Diagram
and Spectral Clustering and Support Vector Machine
Xiaohui Lin
Institute of Rail Trac, Guangdong Communication Polytechnic, Guangzhou, China
Correspondence should be addressed to Xiaohui Lin; linxh@.com
Received 18 December 2018; Revised 27 March 2019; Accepted 10 April 2019; Published 21 April 2019
Academic Editor: Alexander Paz
Copyright ©  Xiaohui Lin. is is an open access article distributed under the Creative Commons Attribution License, which
permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Accurate identication of road network trac status is the key to improve the eciency of urban trac control and management.
Both data mining method and MFD-based methods can divide the trac state of road network, but each has its own advantages and
disadvantages. e data mining method is oriented to trac data with high eciency, but it can only discriminate trac status from
microlevel, while the MFD of road network can discriminate trac statusf rom macrolevel, but there are still some problems, such as
the fact that the discriminant method of equivalence points based on MFD lacks theoretical support or that trac status could notb e
subdivided. If data mining methods and road network’s MFD are combined, the accuracy of road network trac stateidentication
will be greatly improved. In addition, the researchshows that the combination of unsupervised learning clustering analysis method
(such as spectral clustering algorithm) and supervised learning machine algorithm (such as support vector machine algorithm
(SVM)) is more accurate in trac state identication. erefore, a trac state identication method based on MFD and spectral
clustering and SVM is proposed, combining the advantages of spectral clustering algorithm and SVM algorithm. Firstly, spectral
clustering algorithm is used to classify the trac state of road network’s MFD. Secondly, SVM multiclassier is trained with the
partitioned road network’s MFD parameters, and the accuracy evaluation method of classication results based on obfuscation
matrix is given. Finally, the connected-vehicle network simulation platform is built for empirical analysis. e results show that
the classication results of spectral clustering algorithm are closer to the theoretical values, compared with K-means algorithm,
and the accuracy of SVM multiclassier is .%. It can be seen that our algorithm can identify the road network trac state more
eectively from the macrolevel.
1. Introduction
e trac state of road network objectively reects the trac
operation of road network, which is the key to improve the
eciency of urban trac control and management. Trac
state identication method of road network has always been
a research hotspot in the eld of intelligent transportation
system (ITS). Generally, it can be divided into two categories:
the methods based on data mining and the methods based on
trac ow fundamental diagram.
1.1. e Methods Based on Data Mining. e methods based
on data mining are to use machine learning algorithms
such as neural network, deep learning, clustering algorithm,
support vector machine, and Bayesian method to mine
data, so as to automatically identify the trac state of the
road network. For example, Mehdi () et al. [] used K-
means, fuzzy c-means (FCM), clustering large applications
(CLARA), and other three clustering methods to classify
expressway trac ow. e results showed that K-means
clustering results are most consistent with highway capacity
manual (HCM) classication. Montazeri-Gh () et al. []
used K-means algorithm to classify data sets such as average
speed, acceleration, and percentage of idle time collected by
oating cars, so as to discriminate the actual road network
trac state. Xia () et al. [] used Bayesian algorithm
to identify highway trac state based on trac ow, speed,
and occupancy data. Antoniou () et al. [] proposed a
Hindawi
Mathematical Problems in Engineering
Volume 2019, Article ID 6571237, 10 pages
https://doi.org/10.1155/2019/6571237

Mathematical Problems in Engineering
location trac state estimation method based on dynamic
data driving, which used machine learning algorithm to
cluster and classify trac ow data. Yang () et al. [] used
FCM clustering method to discriminate the trac state of
expressway based on the change of speed of big and small
cars. Bing () et al. [] used projection pursuit technique
and dynamic clustering method to construct projection
index function between trac parameters and trac state in
order to improve the accuracy of trac state discrimination.
e projection direction of projection index function was
optimized by using thehybrid frog leaping algorithm. Finally,
the threshold of trac state discrimination was calibrated
by simulation data. Zhang () et al. [] took speed,
trac ow, and trac density as data sets and dened the
relational relationship between multidimensional attribute
information based on grey relational analysis and rough
set theory, established the grey relational clustering model,
and then introduced the grey relational membership ranking
algorithm (GMRC) to discriminate the clustering priority,
so as to analyze the degree of road network congestion.
Shang () et al. [] constructed a trac state discrim-
ination model based on spectral clustering and stochastic
subspace integration K-nearest neighbor (RS-KNN) in order
to improve the accuracy of urban expressway trac state
discrimination.
1.2. e Methods B ased on Trac Flow Fundamental Diagram.
e methods based on trac ow fundamental diagram
are to use the relationship between trac ow and density,
which presents a single peak parabola (called fundamental
diagram) to distinguish the trac state of the road network
[]. According to the fundamental diagram, the trac state
of the road network can be divided into two-phase trac
ow, i.e., congestion ow and noncongestion ow. Kerner
() et al. [, ] divided the trac state of the road
network into three phases: free ow, synchronous ow, and
wide moving congestion according to the measured data
based on the two-phase trac ow. Guan () et al. []
divided trac ow into four steady-state phases: free ow,
harmonic ow, synchronous ow, and congestion based on
the analysis of the general distribution characteristics of
trac ow speed and density in urban expressway network.
Trac state identication based on fundamental diagram has
been developing slowly. With the revelation of macroscopic
fundamental diagram (MFD), some scholars used MFD to
discriminate road network trac from macroscopic level. For
example, Wang () et al. [] proposed a trac condi-
tion discrimination method based on equal points of MFD
parameters (referred to as “MFD equal points discrimination
method”). is method determined the road network’s MFD
through simulation data and divided the trac state of the
road network into ve congestion levels by equal points, i.e.,
free ow, stable ow, unstable ow, restricted ow, and forced
ow. However, it directly divided trac status by equal points,
which lacked theoretical support. Zhu () et al. [] used
the measured and simulated data to establish the actual road
network’s MFD and calibrated the trac ow parameters
of the road network and then studied the dierence of the
distribution of average trac ow and average density in the
periodoftime,soastodeterminethetracstateoftheroad
network, i.e., free ow, congestion ow, and oversaturated
ow. However, the three trac conditions cannot be further
subdivided. Xu () et al. [] divided the trac state of the
road network into free ow, cumulative ow, and congestion
ow according to the observed MFD. However, there are only
three trac conditions. Yue () et al. [] established the
actual road network’s MFD model with the help of trac
data of remote trac detectors and designed the macrotrac
state index of expressway based on speed mileage distribution
and divided the trac state of expressway into ve grades,
including smooth, basic smooth, mild congestion, moderate
congestion, and congestion. However, this method only
discussed and veried thefeasibility of expressway trac state
discrimination, and it did not discuss whether it was suitable
for the trac state division of the whole road network.
Ding () et al. [] estimated the MFD of expressway
network based on oating car detection data and divided
the expressway network into ve states initially according to
the MFD equal points discrimination method []. Finally,
the state parameters of the network are further modied by
clustering algorithm according to the real-time data of the
network. Similarly, it directly divided trac status by equal
points, which lacked theoretical support.
However, both data mining method and MFD-based
methods can divide the trac state of road network, but
each has its own advantages and disadvantages. e data
mining method is oriented to trac data with high eciency,
but it can only discriminate trac status from microlevel,
while the MFD of road network can discriminate trac
status from macrolevel, but there are still some problems,
such as the fact that the discriminant method of equivalence
points based on MFD lacks theoretical support [, ] or
that trac status could not be subdivided [, ] or that the
application scope of the method is limited []. If data mining
methods and MFD can be combined, the accuracy of road
network trac state identication will be greatly improved.
With the rapid development of large data mining algorithms,
K-means, FCM, spectral clustering, and other clustering
analysis methods have emerged, and they have been widely
used in trac state discrimination. At the same time, super-
vised learning machine algorithms, represented by articial
neural network (ANN) and support vector machine (SVM),
are also applied in trac condition discrimination. Recent
studies have shown that the combination of clustering anal-
ysis method and supervised learning machine algorithm is
more accurate in trac state identication [, ]. Clustering
analysis provides necessary prior information for supervised
learning algorithm, and supervised learning algorithm can
ensure the real-time trac status discrimination []. Among
them, spectral clustering is a new clustering method based
on spectral graph theory. It has been widely used in speech
recognition, video segmentation, image segmentation, VLSI
design, web page partitioning, text mining, and so on, but
its application in the eld of transportation has just begun.
SVM method, which has a rigorous mathematical basis, has
become a hot technology in the elds of clustering anal-
ysis, pattern recognition, state discrimination, prediction,

Mathematical Problems in Engineering 
and regression analysis and has attracted wide attention of
scholars at home and abroad. Spectral clustering algorithm
and SVM algorithm have been widely used in many elds
because of their strong mathematical theory support, and
many examples have proved their good application eect.
erefore, in view of the fact that the discriminant method
of equivalence points of MFD lacks theoretical support and
trac status could not be subdivided, this paper proposes
a road network trac state identication method based on
MFD and spectral clustering and SVM, combining the advan-
tages of spectral clustering algorithm and SVM algorithm. Its
basic ideas are as follows.
Firstly, FCD method is used to estimate road network’s
MFD and then spectral clustering algorithm is used to classify
road network’s MFD. e trac state of the road network
is divided into four trac states, i.e., smooth, stationary,
congested, and oversaturated. en, SVM multiclassier
is trained with the divided MFD parameters of the road
network, and the accuracy of the classication results is
evaluated by the confusion matrix. Finally, the core road
network intersection group of Guangzhou is taken as a
research area. e microscopic trac simulation model is
built up by using the Vissim trac simulation soware, and
the validity of the algorithm is validated. e specic process
is shown in Figure .
2. Traffic State Identification
Method Based on MFD
e concept of MFD was rst proposed by Godfrey ()
[], but its theoretical principle was not revealed by Daganzo
and Geroliminis [, ] until . ese two scholars believe
that MFD is an inherent attribute of road network, which
objectively reects the general relationship between weighted
tracowandweightedtracdensityofroadnetwork.If
the oating car is evenly distributed in the road network and
itscoverageisknown,thentheroadnetwork’sMFDcanbe
estimated by using the oating car data (FCD). e formula
is as follows []:
𝑤=∑𝑚󸀠
𝑗=1 󸀠
𝑗
∗∗∑𝑛
𝑖=1 𝑖
()
𝑤=∑𝑚󸀠
𝑗=1 󸀠𝑗
∗∗∑𝑛
𝑖=1 𝑖
()
where 𝑤and 𝑤are the weighted trac density (veh/km)
and the weighted trac ow (veh/h)oftheroadnetwork
obtained by the FCD estimation method, respectively; is
the ratio of oating cars; is the acquisition cycle(); is total
number of sections of the road network; 𝑖is the length of road
section ();󸀠is the number of oating cars during the
acquisition cycle (V); 󸀠𝑗is the driving time of the -th
oating car during the acquisition cycle ();and󸀠𝑗is the
driving distance of the j-th oating car during the acquisition
cycle ().
Road network’s MFD can monitor the trac state of the
road network from the macrolevel, as shown in Figure .
Estimation of Road Network’s
MFD by FCD Method
Classification of Road Network’s
MFD by Spectral Clustering
Method
Training SVM classifier based on
MFD partition result of road
network
Evaluating the accuracy of SVM
classifier by using obfuscation
matrix
e end
e start
Algorithmic validation by building
microsimulation model
F : e basic research ideas.
qw
qw
c
qw
i
kw
ikwkw
c
0
e weighted traffic density, kw(veh/km)
e w eighted traffic flow, qw(veh/h)
F : e schematic diagram of road network’s MFD.
As shown in Figure , when the number of vehicles in the
road network is less, the weighted trac density and weighted
trac ow of the road network are small. With the increase
of vehicles in the road network, the weighted trac density
of the road network increases, and the weighted trac ow
increases with the increase of the weighted trac density.
At this time, the trac state of the road network is dened
as smooth state. With the continuous increase of trac ow
in the road network, the weighted trac density and the
weighted trac ow in the road network are also rising, but
the trac ow in the road network is relatively smooth. At
this time, the trac state of the road network is dened as

Mathematical Problems in Engineering
a stable state. When the trac ow keeps entering the road
network, the weighted trac density of the road network rises
again, and the trac ow in the road network will interfere
with each other. e weighted trac ow of the road network
will continue to increase with the weighted trac density of
the road network. When the weighted trac density of the
road network continues to rise to a certain range, the change
of the vehicle speed in the road network will be unstable.
e trac ow of the road network reaches the maximum,
and the trac state of the road network is dened as the
congestion state. When vehicles continue to pour into the
road network, the weighted trac density of the road network
continues to increase, the speed of the road network and the
weighted trac ow continue to decline, the trac demand
has exceeded the supply capacity of the road network, the
eciency of the trac operation has been declining, and
the road network has entered a state of oversaturation. At
this time, the trac state of the road network is dened as
oversaturated state. As the trac ow continues to increase,
the trac density continues to increase, reaching the road
network congestion density, the speed and trac ow of the
road network are close to zero, and the whole road network
is paralyzed.
According to the road network’s MFD, the trac state of
the road network is divided into four grades: smooth, stable,
congested, and oversaturated. In order to quantify the trac
state of the road network, Wang () et al. [] analyzed
the relationship among ow ,density, and speed based
on the road network’s MFD and solved the extreme value of
the road network operation index. e critical point between
steady ow and unstable ow is determined as 𝑐=(2/3)𝑓,
𝑐=(1/3)𝑗,where𝑐is the critical velocity, 𝑐is the critical
density, 𝑓is the free ow velocity, and 𝑗is the blocking
density, and then the trac state of the road network is
divided into ve grades directly according to the equivalence
of velocity and density. e trac state of the road network is
free ow, stable ow, unstable ow, restricted ow, and forced
ow. e corresponding evaluation indicators are shown in
Table .
In theory, it is feasible to divide the trac state of the
road network into ve grades according to the trac density
or speed of the road network. However, this method directly
divides the trac density or speed of the road network by
equal points, lacking theoretical support, and whether it is
reasonable needs further verication.
3. Road Network Traffic State Identification
MethodBasedonMFDandSpectrum
Clustering and SVM
3.1. e Division Process of Road Network’s MFD Based on
NJW Spectral Clustering Algorithm. Spectral clustering (SC)
algorithm is a research hotspot in the eld of machine
learning. It is a point-to-point clustering algorithm based
on spectral graph theory, which transforms the data clus-
tering problem into the optimal graph partition problem.
SC algorithm is suitable for spatial clustering problems with
arbitrary shapes, compared with typical clustering algorithms
such as K-means clustering and FCM clustering, and it can
obtain global optimal solutions. e graph theory based on
partition criterion is most closely related to spectral clustering
results. e common partition criteria are mini cut, average
cut, normalized cut, min-max cut, ratio cut, MN cut, and so
on. SC algorithm can be divided into two categories: two-
way SC algorithm and multiway SC algorithm according to
the partition criterion. Among them, two-way SC algorithm
includes PF algorithm, SM algorithm, SLH algorithm, KVV
algorithm, M cut algorithm, and so on. Multiway SC algo-
rithm includes Ng-Jordan-Weiss (NJW) algorithm [] and
MS algorithm; NJW algorithm has the best eect, compared
with the application eect of various SC algorithms. e basic
idea of NJW algorithm is to calculate the similarity matrix
of sample data sets rst and then transform the similarity
matrix into Laplace matrix and then construct a new vector
space by using the eigenvectors corresponding to the rst 
largest eigenvalues of Laplace matrix and build a one-to-one
construction matrix corresponding to the original data in
the new space. Finally, cluster the construction matrix by
using K-means algorithm []. erefore, this paper will use
NJW algorithm to divide road network’s MFD; the specic
processisasfollows.
() It needs to dene the sample data set and then
determine the number of clusters ,K= (i.e., smooth state,
stable state, congestion state, and oversaturated state); the
formula is as follows:
=𝑖|=1,2,..., ()
𝑖=𝑖1,𝑖2()
where is the sample data set; 𝑖is the i-th scatter point on
road network’s MFD; 𝑖1 is the i-th weighted trac density of
road network; and 𝑖2 is the i-th weighted trac ow of road
network.
() Normalization of sample data: the formula is as
follows: 󸀠
𝑖𝑗 =𝑖𝑗 −𝑗mi n
𝑗max −𝑗min
()
where 𝑗max and 𝑗min are the maximum and minimum
values of the j-th eigenvector, respectively; 𝑖𝑗 is the initial
value of the rst i-th element of the j-th eigenvector; and 󸀠
𝑖𝑗
is the normalized value of normalization of the i-th element
of the j-th eigenvector.
() To calculate the similarity matrix A, the formula is as
follows:
𝑖𝑗 =






exp −𝑖−𝑗2
22,  =
0, = ()
where 𝑖−𝑗is the Euclidean distance between sample 𝑖
and sample 𝑗and is the standard deviation of samples; the
value is . in this algorithm.
() To calculate the Laplace matrix ,theformulaisas
follows: =−1/2−1/2 ()

Mathematical Problems in Engineering 
T : e identication of trac state and the classication of congestion level.
Free ow steady ow unsteady ow constrained ow forced ow
Density [0,1/6)𝑗[1/6,2/6)𝑗[2/6,4/6)𝑗[4/6,5/6)𝑗[5/6,1]𝑗
Speed [1,5/6)𝑓[5/6,4/6)𝑓[4/6,2/6)𝑓[2/6,1/6)𝑓[1/6,0]𝑓
where is the diagonalization matrix of similar matrix ,
which satises the following conditions:
𝑖𝑗 =
𝑗𝑖𝑗.()
() e rst maximum eigenvalues (1,2,...,𝑘)
and corresponding eigenvectors (1,2,...,𝑘)of Laplacian
matrix are calculated. e eigenvectors are arranged in
descending order according to the size of eigenvalues, and
the matrix U is constructed, which is expressed as =
{1,2,...,𝑘}∈𝑛×𝑘.
() To normalize the row vector of matrix U to get matrix
Y, the formula is as follows:
𝑖𝑗 =𝑖𝑗
∑𝑗2
𝑖𝑗 ()
() To take every row vector 𝑖𝑗 ∈
𝑘(=1,2,...,)
in the Y matrix as a point, K-means algorithm is used to
cluster 𝑖, and then it gets K clustering, which are expressed
as 1,2,...,𝑘.
() Output clustering results, which are expressed as
1,2,...,𝑘,𝑖={|𝑗∈𝑖}.
3.2. Design of SVM Multiple Classiers. SVM was proposed
by Cortes and Vapnik in , which is mainly used to
solve the problem of data classication. is method has
strict theoretical basis and belongs to supervised machine
learning method. It has been widely used in many elds,
such as pattern recognition, data classication, data mining,
computational intelligence, prediction and analysis, trac
condition identication, trac sign recognition, vehicle type
recognition, trac demand prediction, trac accident sever-
ity, pedestrian detection, and so on.
SVM multiclassier is implemented by the LIBSVM
soware package developed by Professor Lin Chih-Jen of
Taiwan University. is soware package belongs to One-
Versus-One SVMs, whose basic principle is to combine 
samples in pair arbitrary combinations, design a SVM for
each combination sample, and form k∗(k-1)/2 SVMs. When it
classies an unknown sample, each SVM decides the category
of the unknown sample, votes on the corresponding category,
and nally decides that the category of the unknown sample
is the category with the most votes. e basic idea of each
SVM classier is to nd an optimal hyperplane and segment
thesampledataaccordingtopositiveandnegativeexamples
to maximize the classication margin. e algorithm ow is
as follows [].
It assumes that there is a training sample set {𝑖,𝑖|=
1,2,...,},∈𝑛,∈{1,−1},whereis the number of
samples and is the dimension of .
() e training sample set is linearly separable, that is,
thereexistsaplanewhichcandividethetrainingsample
into positive and negative categories. is plane is called
hyperplane, and its classication function formula is as
follows: ()=𝑇+=0 ()
where istheslopeofthehyperplaneand𝑇is the trans-
position of the slope; is a constant; is a multidimensional
vector.
At this time, the classication interval is 2/.When
is the smallest, the classication interval is the largest.
e problem is transformed into a minimization problem
for easy solution. e objective function and constraints are
established as follows:
min 2
2
.. 𝑖𝑖+−1≥0, =1,2,..., ()
() When the training sample set is linearly inseparable,
it needs to introduce the kernel function K to map the low-
dimensional sample set to the high-dimensional one, so that
the results calculated in the low-dimensional space are the
same as those calculated in the high-dimensional space. en
the linearly inseparable is transformed into linearly separable.
Its classication function formula is as follows:
()=𝑙

𝑖=1𝑖𝑖,𝑖+=0 ()
where is a kernel function. e common kernels are
polynomial kernels, Gauss kernels, linear kernels, string
kernels, etc.; 𝑖is the Lagrange coecient.
ere may be data points that are far from the normal
position or the outlier data points of Category  are mixed in
Category  area. In order to deal withthis situation, individual
data points are allowed to deviate from the hyperplane
to some extent; i.e., nonnegative relaxation variable 𝑖is
introduced. e original objective function and constraints
are transformed into
min 2
2+𝑙

𝑖=1𝑖
.. 𝑖𝑖+≥1−𝑖, =1,2,..., ()
where is the penalty coecient, indicating the importance
of the loss caused by outlier sample data points. e smaller
the value, the smaller the penalty for misclassication and
the smaller the loss to the objective function.

Mathematical Problems in Engineering
T : e confusion matrix of the classication results of SVM multiple classiers.
e predicted value
e actual value   ...  e total line
𝑥11 𝑥12 ... 𝑥1𝑛 𝑥1+
𝑥21 𝑥22 ... 𝑥2𝑛 𝑥2+
... ... ... ... ... ...
𝑥𝑛1 𝑥𝑛2 ... 𝑥𝑛𝑛 𝑥𝑛+
e total column 𝑥+1𝑥+2... 𝑥+𝑛
3.3. e Accuracy Evaluation of SVM Multiple Classiers. e
test classication results of the SVM classier are transformed
into the confusion matrix, as shown in Table .
According to the confusion matrix, the classication
accuracy of SVM multiclassier can be evaluated from ve
evaluation indicators: accuracy, recall, omission, prediction,
and commission.
(1) Accuracy. e accuracy rate is the correct ratio in all test
samples; the formula is as follows:
Accuracy =𝑛

𝑘=1𝑘𝑘
()
(2) Recall. e actual recall rate refers to the proportion
of the correct predicted value of the actual category to
the total number of the actual categories in the i-th actual
classication; the formula is as follows:
Re𝑖=𝑖𝑖
𝑖+ ()
(3) Omission. e actual omission rate refers to the pro-
portion of the actual category value to the total number of
the actual category value in the i-th actual classication; the
formula is as follows:
𝑖=𝑖+ −𝑖𝑖
𝑖+ ()
(4) Precision. e prediction accuracy rate is the proportion
of the correct value of the prediction to the total number
of samples of the prediction category in the j-th prediction
category; the formula is as follows:
Precision𝑗=𝑗𝑗
+𝑗 ()
(5) Commission. e commission refers to the ratio of the
value of the error prediction to the total number of samples
in the j-th prediction category; the formula is as follows:
commission𝑗=+𝑗 −𝑗𝑗
+𝑗 ()
4. Empirical Analysis
4.1. Experimental Platform Construction. e intersections
of Tianhe District core road network in Guangzhou are
chosen as the experimental area [], as shown in Figure .
A microtrac simulation platform for connected-vehicle
network is built by using VISSIM simulation soware and
based on the road network layout, the actual road lane
layouts, the intersection plane layout, the trac ow data, the
intersection signal control schemes, the trac organizations,
and other information.
e MFD estimation accuracy of road network can
reach % when the coverage of networked vehicles reaches
% aer many simulations. erefore, the coverage rate of
networked vehicles is set to %, and the related data of each
networked vehicle are read every  seconds. e statistical
period of data is  seconds, and the simulation time is
 seconds. e simulation results of the online vehicle
data le (∗. fzp) are imported into EXCEL le, and the FCD
estimation method is realized by VBA macroprogramming.
Finally  sets of the weighted trac ow (𝑤)andthe
weighted trac density (𝑤)are obtained, and the MFD of
the simulation network is drawn, as shown in Figure .
e data points of road network’s MFD are tted by
function, and the critical weighted trac density (𝑐)and the
critical weighted trac ow (𝑐)arecalculated,asshownin
Table .
4.2. Analysis of Experimental Results
(1) e Partition Result of Road Network’s MFD Based on
NJW Spectral Clustering Algorithm.eNJWalgorithmis
programmed in Matlab soware. e parameter of the road
network’s MFD is input into the program, and the result of
trac state division is output, as shown in Figure . In order
to better analyze the eect of spectral clustering algorithm,
K-means algorithm is selected as a comparison to cluster the
MFD parameters of road network, as shown in Figure .
As shown in Figures  and , the partition result of road
network’s MFD based on K-means algorithm only considers
the size of MFD parameters butdoes not consider the specic
location of MFD scatters. It incorrectly incorporates part
of the congestion scatters into the oversaturated state and
individual oversaturated scatters into the congested state,
while the partition result of road network’s MFD based on
spectral clustering is more reasonable. It can distinguish
trac conditions into four better states, i.e., smooth, station-
ary, congested, and oversaturated. e scope of trac state
partition of the two clustering methods is obtained by Figures
 and . At the same time, according to the MFD tting
function of the whole road network in Table , the equal

Mathematical Problems in Engineering 
T : e tting function of MFD.
Fitting formula 𝑐(V/) 𝑐(V/)
y= .x3-.x
2+ .x - . . 
A1 A2 A3 A4 A5
C2
B1
B3
C4 C5 C7
C8 C9
D1
F9
D2
E1 E2
E3 E4 E6 E7 E8
E9
E10
E11
F1 F2 F3 F4 F5 F11
F6
G1 G2
H2 H3 H5
H6
H1 H4
I1
I2
I3
I5
B4 B5 B6 B7
C1 C6
D3 D4 D5 D6
E12
E13 E14
F7 F8
F10 F12
G3
I4
E5
E15
B2
5698
3159
1876
254
2643
1932
1872
2501
176
2379
5720
784 1091 2603 213 252 Unit: veh/h
G4
C3
F : Road network layout diagram of vehicle networking simulation platform.
3.5
3
2.5
2
1.5
1
0.5
0
1500 1000 500 0 0 20 40 60 80 100
T (s)
Ｋ
Ｑ
(veh/h)
Ｅ
Ｑ
(veh/km)
×104
F : e D diagram of simulation road network’s MFD.
value of trac state partition of the road network is calculated
by using MFD equal points discrimination method [], as
shown in Table .
As shown in Table , compared with the K-means-based
trac state partition results, the result of road network
trac state partition based on spectral clustering is close
to the equal value. It shows that the results of spectral
clustering algorithm and equivalence method are feasible, but
smooth
stationary
congestion
supersaturatio
n
1400
1200
1000
800
600
400
200
0010 20 30 40 50 60 70 80 90
qw(eℎ/ℎ)
kw(eℎ/km)
X: 14.09
Y: 686.5
X: 19.77
Y: 938.4
X: 40.88
Y: 1058
F : e division results of road network’s MFD based on
spectral clustering.
the equivalence method is directly divided by equivalence
points. It is too idealized and lacks theoretical support. e
spectral clustering algorithm has detailed and reliable theory
as support, and it is more scientic.
(2) SVM Multiclassier Training. According to the above
results of road network trac state partition based on spectra l
clustering,  sets of parameters of road network’s MFD are

Mathematical Problems in Engineering
T : e scope of trac state parameters.
Trac state Partition based on K-means algorithm Partition based on spectral clustering algorithm Equal value
Smooth [0,12.26) [0,14.09) [0,10.83)
Stationary [12.26,16.9) [14.09,19.77) [10.83,21.67)
Congestion [16.9,20.69) [19.77,40.88) [21.67,43.33)
Oversaturated [20.69,𝑗) [40.88,𝑗) [43.33,𝑗)
T : e confusion matrix and the accuracy evaluation index of the classication results by SVM multiclassiers.
predicted value
Actual Value     total recall omission
      .% .%
      .% .%
      .% .%
      .% .%
total      .% .%
precision .% .% .% .%
commission .% .% .% .%
smooth
stationary
congestion
X: 20.69
Y: 975.8
supersaturation
1400
1200
1000
800
600
400
200
00 102030405060708090
qw(eℎ/ℎ)
kw(eℎ/km)
X: 16.9
Y: 814.8
X: 12.26
Y: 596.2
F : e division results of road network’s MFD based on K-
means.
taken as sample data. Four grades of trac state (smooth,
stationary, congestion, and oversaturated) are expressed by
numbers , , , and , respectively. e weighted trac
density of odd samples is used as training set, and the trac
state corresponding to odd samples is classied as train group.
e weighted trac density of even samples is used as test
set, and the trac state corresponding to even samples is the
actual trac state of test set (test group). A multiclassier of
SVM is implemented in Matlab soware. e kernel function
chooses Gauss (RBF) kernel function:exp(−|−|2),where
r value is  and penalty coecient is . e classication
results of the classiers are shown in Figure .
(3) Accuracy Evaluation of SVM Multiclassier. e classi-
cation result of the classier is sorted out into confusion
matrices, and the accuracy evaluation indexes of the classier
are calculated, as shown in Table .
the classification of the actual test sets
the classification of the predictive test sets
20 40 60 80 100 120 1400
the ample size
1
1.5
2
2.5
3
3.5
4
the class labels
F : e classication results of SVM multiclassier.
AsshowninTable,itcanbeseenthattheprediction
accuracy of Category  is %, the actual recall rate is
.%, the prediction accuracy of Category  is .%, the
actual recall rate is .%, the prediction accuracy of Category
 is .%, the actual recall rate is .%, the prediction
accuracy of Category  is .%, and the actual recall rate
is %. From the overall prediction results, the accuracy of
SVM multiclassier is .%. erefore, the results of SVM
multiclassier are ideal.
5. Conclusion
In view of the fact that the discriminant method of equiv-
alence points of MFD lacks theoretical support and trac
status could not be subdivided, this paper proposes a road

Mathematical Problems in Engineering 
network trac state identication method based on MFD
and spectral clustering and SVM, combining the advantages
of spectral clustering algorithm and SVM algorithm. Based
on the results of empirical analysis, this paper draws the
following conclusions:
() Spectral clustering-based trac state partition results
are closer to the theoretical values, compared with K-means-
based trac state partition results.
() e accuracy of SVM multiclassier is up to .%; it
can be seen that the classication results are ideal.
() is paper combines the advantages of spectral
clustering algorithm and SVM algorithm, which can iden-
tify the trac state of road network more eectively
and automatically from the macrolevel on the basis of
MFD.
() It is noteworthy that this paper estimates the road
network’s MFD by using the data of the simulation environ-
ment of the networked vehicle and assumes that the coverage
rateofthenetworkedvehicleisashighas%andisevenly
distributed in the road network, but, in the actual road
network, it is impossible to obtain such a high coverage rate
of the networked vehicle, and there is an uneven distribution
of the networked vehicle. erefore, in practical application,
a large amount of trac data is needed to accurately estimate
road network’s MFD.
Data Availability
e data used to support the ndings of this study are
available from the corresponding author upon request.
Conflicts of Interest
e author declares that there are no conicts of interest.
Acknowledgments
is paper is jointly funded by Natural Science Founda-
tion of Guangdong Province (A), Guangdong
Province higher education outstanding young teachers train-
ing program in  (YQ), special innovative research
projects of Guangdong Provincial Department of Education
in  (GKTSCX), key scientic research projects
of Guangdong Communication Polytechnic in  (--
), special fund project for Guangdong university students’
science and technology innovation in  (pdjhb),
and Guangdong science and technology project in 
(A).
References
[] M. Azimi and Y. Zhang, “Categorizing freeway ow conditions
by using clustering methods,” Transportation Research Record:
Journal of the Transportation Research Board,vol.,no.,pp.
–, .
[] M. Montazeri-Gh and A. Fotouhi, “Trac condition recogni-
tion using the k-means clustering method,” Scientia Iranica,vol.
, no. , pp. –, .
[] J. Xia, W. Huang, and J. Guo, “A clustering approach to online
freeway trac state identication using ITS data,” KSCE Journal
of Civil Engineering,vol.,no.,pp.–,.
[] C. Antoniou, H. N. Koutsopoulos, and G. Yannis, “Dynamic
data-driven local trac state estimation and prediction,” Tran s -
portation Research Part C: Emerging Technologies,vol.,pp.
–, .
[] Q. F. Yang, M. H. Ma, S. D. Liang et al., “Freeway trac
state identication based on toll data,” Journal of South China
University of Technology (Natural Science Edition),vol.,no.
, pp. –, .
[] Q. Bing, B. Gong, Z. Yang, C. Lin, and X. Qu, “Trac state
identication for urban expressway based on projection pursuit
dynamic cluster model,” Xinan Jiaotong Daxue Xuebao/Journal
of Southwest Jiaotong University,vol.,no.,pp.–,
.
[]Y.Zhang,N.Ye,R.Wang,andR.Malekian,“Amethodfor
trac congestion clustering judgment based on grey relational
analysis,” ISPRS International Journal of Geo-Information,vol.,
no.,p.,.
[] Q.Shang,C.Y.Lin,Z.S.Yangetal.,“Tracstateidentication
for urban expressway based on spectral clustering and RS-
KNN,” Journal of South China University of Technology (Natural
Science Edition),vol.,no.,pp.–,.
[] W. Wei, Analytical Method of Trac Condition Characteristic
and Congestion Propagation Rules Based on Practical Measured
Data, Beijing Jiaotong University, .
[] B.S.Kerner,S.L.Klenov,andD.E.Wolf,“Cellularautomata
approach to three-phase trac theory,” Journal of Physics A:
Mathematical and General,vol.,no.,pp.–,.
[] B. S. Kerner, “ree-phase trac theory and highway capacity,”
Physica A: Statistical Mechanics and Its Applications, vol. , no.
,pp.–,.
[] W. Guan and S. He, “Phase identication of urban freeway
trac based on statistical properties,” Journal of Transportation
Systems Engineering and Information Technology,vol.,no.,
pp.–,.
[] F. J. Wang, W. Wei, and D. H. Wang, “Urban road network
trac state identication andmonitoring based on macroscopic
fundamental diagram,” in Proceedings of the presented atthe 7nd
Annual Conference of ITS China,Beijing,China,.
[] L. Zhu, L. Yu, and G. H. Song, “MFD-based investigation into
macroscopic trac state of urban networks and its inuencing
factors,” Journal of South China University of Technology (Natu-
ral Science Edition),vol.,no.,pp.–,(Chinese).
[]F.Xu,Z.He,Z.Sha,W.Sun,andL.Zhuang,“Tracstate
evaluation based on macroscopic fundamental diagram of
urban road network,” Procedia - Social and Behavioral Sciences,
vol.,no.,pp.–,.
[   ] Y. Y. Yue , L . Yu , L . Z h u e t al . , “ M a c r o s c o pi c m o d e l f o r
evaluating trac conditions on the expressway based on speed-
specic VKT distributions,” Journal of Transportation Systems
Engineering and Information Technology,vol.,no.,pp.–
, .
[] H.Ding,L.Y.Zhu,C.B.Jiangetal.,“Tracstateidentication
for citie s freeway networ k based on M FD,” Journal of Chongqing
Jiaotong University (Natural Science),pp.–,.
[] C. Deng, F. Wang, H. Shi, and G. Tan, “Real-time freeway trac
state estimation b ased on cluster analysis and multicla ss support
vector mach ine,” in Proceedings of the International Workshop on
Intelligent Systems and Applications, ISA ’09, China, .

 Mathematical Problems in Engineering
[] J. W. Godfrey, “e mechanism of a trac network,” Trac
Engineering & Control,vol.,no.,pp.–,.
[] C. F. Daganzo, “Urban gridlock: macroscopic modeling and
mitigation approaches,” Transportation Research Part B: Meth-
odological,vol.,no.,pp.–,.
[] N. Geroliminis and C. F. Daganzo, “Existence of urban-scale
macroscopic fundamental diagrams: some experimental nd-
ings,” Transportation Research Part B: Methodological,vol.,
no.,pp.–,.
[   ] A . S . N a g l e a n d V. V. G a y a h , “A c c u r a c y o f n e t w o r k w i d e
trac states estimated from mobile probe data,” Transportation
Research Record Journal of the Transportation Research Board,
vol. , no. , pp. –, .
[] A. Y. Ng, M. I. Jordan, and Y. Weiss, “On spectral clustering:
analysis and an algorithm,” in Advances in Neural Information
Processing Systems, vol. , MIT Press, .
[] D.Wang,C.Lu,W.Jiangetal.,“StudyonPSO-baseddecision-
tree SVM multi-class classication method,” Journal of Elec-
tronic Measurement and Instrumentation,vol.,no.,pp.–
, .
[] X. Lin, J. Xu, and W. Zhou, “A dynamic partitioning method for
the multilayer boundary for urban oversaturated homogeneous
trac networks based on macroscopic fundamental diagrams
in connected-vehicle network,” Advances in Transportation
Studies, in press.