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AAAAFittingFittingFittingFittingAAAApproachpproachpproachpproach totototoMendMendMendMendDefectiveDefectiveDefectiveDefective UrbanUrbanUrbanUrbanTrafficTrafficTrafficTraffic FlowFlowFlowFlow InformationInformationInformationInformationBasedBasedBasedBased ononononSARBFSARBFSARBFSARBFNeuralNeuralNeuralNeuralNetworksNetworksNetworksNetworks

NingNingNingNing ChenChenChenChen,,,, WeibingWeibingWeibingWeibing WengWengWengWeng andandandand XingXingXingXing XuXuXuXu

SchoolSchoolSchoolSchool ofofofof MechanicalMechanicalMechanicalMechanical andandandand AutomotiveAutomotiveAutomotiveAutomotive EngineeringEngineeringEngineeringEngineering,,,, ZhejiangZhejiangZhejiangZhejiang UniversityUniversityUniversityUniversity ofofofof ScienceScienceScienceScience andandandand TechnologyTechnologyTechnologyTechnologyHangzhouHangzhouHangzhouHangzhou,,,, 310023310023310023310023,,,, P.R.ChinaP.R.ChinaP.R.ChinaP.R.China

AbstractAbstractAbstractAbstractData-defectives are always occurred during collecting urbantraffic flow information due to all kinds of sensors’ failures. Tomend the defective urban traffic flow information data, a newapproach named SARBF neural network fitting is presented. Itcombines analysis based on spatial autocorrelation and RBFneural network fitting method. The complete data is determinedto mend the defective data according to the spatialautocorrelation of traffic grid. Not only the mending precision isimproved and also the limitation of regression analysis is avoidedby using RBF neural network. Finally, the experiment to mendthe defective traffic flow data in Hangzhou City is shown that themethod is practicable.Keywords:Keywords:Keywords:Keywords: Defective-data Mending, Spatial Auto-correlation，SARBF Neural Network, Fitting Approach, Urban Traffic FlowInformation

1.1.1.1. IntroductionIntroductionIntroductionIntroduction

At present, most of the traffic flow data are collected bythe loops buried closely to the intersections of urbanarteries in China. However, there is data-defectiveoccurred frequently because of the sensor failure whileconstructing road, transmitting signal or processing data. Itis impeded to process and analysis traffic data by the issue.Consequently, it is demanded imperatively to mend thedefective data[1]. There exists research on mendingmethods including the cluster analysis[2], principalcomponent analysis[3], stepwise regression analysis[4],EM(expectation maximization), DA(data augmentation)[5][6], predicting on grey system theory[7] and artificialneural network [8] , etc.

There have been both principle guidelines among thesemethods. Firstly, some methods such as cluster analysis,principal component analysis, stepwise regression analysis,EM, DA merely focus on the relationship of the historicaltraffic data between the data-defective intersection and thedata-complete intersections, but pay little attention to theirspatial autocorrelation of these intersections in the wholetraffic grid. Secondly, other methods such as trafficprediction based on grey system and the artificial neuralnetwork concentrate on the historical data just from thedata-defective intersection, without considering the data of

other intersections’ effect in the traffic grid, which leads tothe reflecting disability of the peripheral-zone real-timetraffic change to mend the defective data of a sensor-failure intersection.

On the methods of cluster analysis, principal componentanalysis, stepwise regression analysis, EM, DA, thedefective data are mended by the relation between thehistorical data from the data-defective intersection and thecomplete traffic flow data in other intersections, withoutconsidering the spatial autocorrelation of the intersectionsin the traffic grid. On the methods of predicting on greysystem theory and artificial neural network, the defectivedata is mended by predicting with the historical data fromthe data-defective intersection, without considering thedata of other intersections’ effect in the traffic grid, so thereal-time influence of the traffic flow breakdown can’t bereflected on the defective data mending.

Therefore, here is proposed a new neural network fittingapproach named SARBF, abbreviated from SpatialAutocorrelation and Radical Basis Function, to mend thedefective data. The approach is composed of spatialautocorrelation based analysis method[9] and RBF neuralnetwork fitting method[10][11]. In our research, the precisionand calculating speed for mending the defective data isimproved by fully using the traffic flow data both from thehistorical data of a data-defective intersection and its auto-correlated data-complete intersections.

2.2.2.2. AlgorithmAlgorithmAlgorithmAlgorithm DesignDesignDesignDesign ofofofof SARBFSARBFSARBFSARBF NeuralNeuralNeuralNeuralNetworksNetworksNetworksNetworks FittingFittingFittingFittingMethodMethodMethodMethod

Our research focuses on mending all the defective data ofeach transportation intersection in urban area. As shown inFig.1, by the analysis of the historical records, there areboth salient features concerning traffic flow data.

1) TheTheTheThe timetimetimetime periodicperiodicperiodicperiodic characteristic.characteristic.characteristic.characteristic. It is evident that thetraffic flow data of each intersection changes periodically.

IJCSI International Journal of Computer Science Issues, Vol. 10, Issue 2, No 2, March 2013 ISSN (Print): 1694-0814 | ISSN (Online): 1694-0784 www.IJCSI.org 150

Copyright (c) 2013 International Journal of Computer Science Issues. All Rights Reserved.

(a) Intersection A

(b) Intersection B

Fig. 1 Two adjacent intersections traffic flow data.

For example, Fig.1 shows the changes of the traffic flowdata collected at two intersections during one whole weekin Hangzhou city.

2) TheTheTheThe spatialspatialspatialspatial correlation.correlation.correlation.correlation. There is correlation of thetraffic flow data among the proximity intersections,because the change regularity of the adjacent intersectionsis usually very similar.

According to the SARBF neural network fitting method,the defective data can be mended resorting to processingthe complete data from other intersections. Prior tomending the defective data by means of the neural network,the data-complete corresponding intersections should beselected firstly to improve the mending speed. As shown

in Fig.1, the data-complete intersections can be selected bythe spatial autocorrelation of the intersections from thetraffic grid.

Further more, the defective data can be mended in terms ofRBF neural network fitting method based on the historicalrecords of the selected data-complete intersections and theoccurred data-defective intersections. The algorithm flowis shown in Fig.2.

Spacial informationdatabase

Find out the intersections withdefective data

Historical trafficflow database

Ensure this intersection’s complete data to mendthe defective traffic flow information

Calculating the value of Moran Index betweenintersection A and another one

Making each intersection’s historical traffic flowdata as training sample

RBF neural network’s learning

RBF neural network’s fitting

0I ≥

Y

Fig. 2 Diagram of SARBF neural networks fitting method

2.1 Spatial Auto-correlation Analysis

The first step of the SARBF neural networks fittingmethod for mending defective traffic flow data is to seekfor the relating data-complete intersections, which is thebasis to establish a neural network model. The urbantraffic grid is an organic whole with the intersections beingconnected by sections. The traffic flow of most adjacentintersections is closely related because of their similarityof the travelers’ regularity and travel-mode. The data-complete intersections which are strongly correlated to thedata-defective intersection can be chosen by Moran’s Ispatial autocorrelation analysis method at the benefit ofreducing data redundancy.



The spatial autocorrelation in urban traffic flow reflectstheir correlative degree among the different intersectionsin the traffic grid. The spatial autocorrelation theory tell usthat the closer, the more similar between both objects. Thejudging procedure by the Moran’s I spatial autocorrelationis as follows:

1) Generate a data table with the position of every nodeand their connections in the traffic grid by GIS software.The intersections are numbered from 1 to n.

2) Find out the data-defective intersection No.i from thetraffic flow database, then building a spatial adjacencymatrix ijW .

If the intersection No.j is close to intersection No.i, then1ijW = , else 0ijW = .

Meanwhile i j≠ , 0iiW = .

3) Calculating the decision index I for the spatialautocorrelation:

1 1

2

1 1 1

( )( )

1 ( )

n n

ij i ji j

n n n

ij ii j i

W X X X XI

W X Xn

= =

= = =

× − −=

× −

∑∑

∑∑ ∑(1)

In which, ijW is expressed as spatial adjacency matrix, iXis the traffic flow data from the intersection No. i, and jXis the traffic flow data from the intersection No. j.

4) Determine the corresponding data-completeintersections on the value I. The value range of I comefrom the Moran’s I formula is between -1 to 1. It is calledpositive correlation if 0I > . In contrast, it is negativecorrelation if 0I < . The greater value I is, the higherspatial correlation it is between both intersections.Simultaneously, the lower value I is, the weaker spatialcorrelation it is between both intersections. The spatialdistribution would be at random, when I tends to be 0.

2.2 RBF Neural Network Fitting

Because of the random variation of the traffic flow, therelation between both intersections is always nonlinear.However, it can be pursued easily by RBF neural networkmethod.

The radical basis function neural network, i.e. RBFnn, is afeed-forward neural network model with the capacity oflocal approximation, which can be used in mending the

defective traffic data. The weight from input layer tohidden layer is 1 all the time, only the weight from hiddenlayer to output layer is adjustable. The radial basisfunction has a local response to the input signal, and thelarge output would be produced when the input signalcloses to the central range of the radial basis function.

Generally, the Gaussian kernel function is selected as thetransform mode in the hidden layer due to its preferentialproperties as simplicity, radial symmetry, smoothness andaccurate analyses, the form show as:

2

2( ) exp2

cc

x xG x x

σ

⎧ ⎫−⎪ ⎪− = −⎨ ⎬⎪ ⎪⎩ ⎭

(2)

In which, cx is the center of kernel function; σ is the widthparameter of kernel function which controls the radialaction sphere and could be determined by k-meansclustering algorithm; “ . ”is norm which usually takesEuclidean norm.

The RBF network of multi-parameter input and single itemoutput is designed to mend the defective data. Meanwhile,the historical traffic data of the data-defective intersectionand the corresponding data-complete intersections turns tobe training samples. The weight vector W of the hiddenlayer to output layer can be obtained by interpolationalgorithm when cx is determined, because the input vectormust be mapped to the hidden layer.

3333.... CASECASECASECASE STUDYSTUDYSTUDYSTUDY

Currently, the urban traffic flow data in urban Hangzhou isusually collected by SCATS system with loops. Thedeployment situation of SCATS system in Xihu ward ofHangzhou city is shown in Fig.3. The GIS applicationplatform is developed by Map-info system. Besides, thetraffic flow data is collected in 5 minutes interval. Here thedefective traffic flow data is occurred because of the loopsfailure, which could be mended by using the SABRFneural network fitting method.



Fig. 3 The deployment of SCATS in Xihu ward of Hangzhou.

Take the Wensan-Xueyuan east intersection encoded 871as an example, in which the digit 87 stands for 87thintersection and the digit 1 means the east direction. It isobvious the defective data was occurred as shown in thetable. There is some traffic flow data in Xihu ward asshown in table 1. The first row data in table I is theintersection number, in which the last number “1”, “3”,“5”, and “7”stands for the directions of East, South, Westand North separately. In addition, the character “/”represents for defective data.

Table 1: Part of traffic flow data in Xihu district

time … 451 871 891 923 455 …

07:05 … 56 / 95 44 71 …

07:10 … 47 / 92 85 99 …

07:15 … 24 / 109 77 68 …

07:20 … 84 / 78 86 74 …

07:25 … 26 / 85 84 55 …

… … … … … … … …

time … 451 871 891 923 455 …

The intersections information table can be acquired byMap-info system to build the spatial weight matrix shownas formula (3).

... ... ... ... ... ... ...

... 0 0 0 0 0 ...

... 0 1 1 1 0 ...

... 0 1 1 0 ...

... 0 1 1 1 0 ...

... 0 0 0 0 0 ...

... ... ... ... ... ... ...

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

⋱ (3)

The next step is to hunt for the corresponding data-complete intersections to mend the defective data of theWensan-Xueyuan east intersection by calculating theMoran’s I-value from the prospective relevantintersections such as Wener-Xueyuan intersection,Wensan-Jiaogong intersection, and so on. The trainingsamples for the established Neural Network modeloriginate from the historical flux data of the variousintersections including not only the data-defectiveintersection but also data-complete intersections. It isconcluded that the regularity of traffic flow usually varieswith different periods by analyzing the historical data.Thus in order to guarantee the mending outcome precision,the training samples should belong to the different periods.Meanwhile, it is important to distinguish the different kindof time segment for the RBF neural networks mendingmodel. The time segments may be short ones or long onesThe long ones can be further divided into several typessuch as Spring Festival period i.e. the holiday of Chineselunar new year, other legislated festival period such as TheLabor Day, The National Day, or New Year’s Day,weekends, normal time from Tuesday to Thursday, specialtime such as Monday and Friday. Similarly, the short onescan be divided into morning rush hour, evening rush hourand others.

To mend the defective data using RBF neural networkfitting method, it is primary to determine which timesegment the defective data locates. Only after thedetermination could the defective data be mendedresorting to the corresponding neural network model. Forexample, if the defective data of the intersection encoded871 occurred in December 1st , Saturday in 2012, Itdemands to establish three different neural network modelsusing the historical traffic data in different time segmentsthat is morning rush hour, evening rush hour and others onSaturday. The mending traffic flow data are shown in table2.

The MATLAB software, a popular calculating toolkitsystem can help us to realize the computing process tomend the defective data in terms of RBF neural networkfitting method[12-14]. During the process, the traffic flowdata of the data-complete intersections being correlated tothe data-defective intersection is taken as input vector, andthe traffic flow data of the data-defective intersection istaken as object vector. It is proposed that the GOAL of themean square error is 0, and SPREAD index is 1 in thisalgorithm. The mean square error of network output willbe decreasing continuously by automatically increasing theradial nerve, and the training of the network will be keptuntil the error attains to the GOAL.



It is the time to use it after the neural network beingtrained. The defective data can be mended by the belowsimulation function of the Matlab software:

si ( , )y m net P= (4)

To demonstrate the advantage of our proposed method, itis compared with another data mending method, regression

analysis abbreviated RA. The comparing result is shown intable 3 .

The table tells the relative error with the RBF neuralnetwork fitting method is about 5%, while the result withregression analyzing method is above 10%. It is apparentthat the mending precision with the RBF neural networkfitting method is much higher.

Table 2: Mending result（2012.12.1）

Period Real data/cars Mending result /cars Relative error%

12:00~12:05 48 51 6.25

12:05~12:10 70 60 14.3

12:15~12:20 60 49 18.3

12:20~12:25 53 58 9.43

12:25~12:30 65 76 16.9

12:30~12:35 38 40 5.26

12:35~12:40 58 66 13.8

12:45~12:50 82 90 9.75

12:50~12:55 60 68 3.33

Table 3: Comparing result（2012.12.1）

Period Real data/cars Mending result /cars Relative error%

RA RBF RA RBF

07:00~07:05(AM) 100 82 95 18.0 5.0

08:00~08:05(AM) 168 192 159 14.0 5.4

08:50~08:55 (AM) 161 189 154 17.4 4.3

09:10~09:15 (AM) 193 219 183 13.5 5.2

07:00~07:05(PM) 146 120 139 17.8 4.8

08:00~08:05(PM) 108 92 103 14.8 4.6

08:50~08:55 (PM) 101 85 97 15.8 4.0

09:10~09:15 (PM) 99 84 95 15.2 4.0

4444.... SummarySummarySummarySummary

In our research and experiment, the SARBF neuralnetwork fitting method is proved to enable speedingprocess to mend defective traffic flow data by selectingrelevant historical data as training samples for neuralnetwork by means of spatial autocorrelation analysis.Furthermore, the mending precision can be also improvedby RBF neural network method comparing with traditionalregression analyzing method. Besides, the mending

experiment has given us an acceptable mending precisionpractically in XiHu ward of Hangzhou city.

AcknowledgmentsAcknowledgmentsAcknowledgmentsAcknowledgments

This work is partially supported by the National NaturalScience Foundation of China (Grant No.61273240), andthe Key Project of Chinese Ministry of Education (GrantNo.211070), and Zhejiang Provincial Natural ScienceFoundation of China (Grant No. LY12F03024), and theProject of International S＆ T Cooperation Program ofChina (Grant No. 2013DFA31920), as well as the National



High-tech R&D Program of China (863 Program, underGrant No. 2012AA101704).

Thanks for the suggestions and helps from Miss BingjingXiang to process all kinds of traffic data involved in thefigures and tables in this paper.

Thanks for the technical supporting from ZhejiangProvincial Key Laboratory for Food Logistics Technologyand Equipment (under cultivation).

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[2] He. Zhang, Zhaosheng. Yang, and Yiwu. Li, “Study onforecast of traffic volume at non-detector intersections”,Journal of Highway and Transportation Research andDevelopment, Vol. 29, No. 1, 2012, pp. 91-95.

[3] Zhaosheng. Yang, He. Zhang, Juan. Li, “Step-by-stepregression used in traffic flow prediction of non-detector roadintersections”, Journal of Jilin University (Engineering andTechnology Edition), Vol. 42, No. 4, 2012, pp. 16-19.

[4] He. Zhang, “Application of cluster analysis and stepwiseregression in predicting the traffic volume of lanes,” Journalof Southeast University (English Edition), Vol. 21, No. 3,2005, pp. 359-362.

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Dr.Dr.Dr.Dr. NingNingNingNing ChenChenChenChen received the Ph.D. degree in mechanicalengineering from Zhejiang University in 2004. Currently, he is anAssociate Professor at Zhejiang University of Science andTechnology, and the fellow of Chinese Association on MechanicalEngineering. His research interests include Intelligent TransportSystem(ITS) and Logistics Engineering. He has published 33papers around mechanical engineering, transportation engineering,and logistics engineering. His work has been supported by theNational Natural Science Foundation of China as well as otheracademic originations.

Dr.Dr.Dr.Dr. WeibingWeibingWeibingWeibing WengWengWengWeng received the Ph.D. degree in LogisticsEngineering from Dortmund University of Technology in 2011.Currently, he is an assistant professor at Zhejiang University ofScience and Technology. His interests are in logistics technologiesand equipments.

Dr.Dr.Dr.Dr. XingXingXingXing XuXuXuXu received the Ph.D. degree in mechanical engineeringfrom Zhejiang Sci-Tech University in 2013. Currently, he is anassistant professor at Zhejiang University of Science andTechnology. His interests are in urban transportation systemcontrol design and information processing.



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