TRAFFIC FATALITIES PREDICTION BASED ON SUPPORT VECTOR MACHINE

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1 ARCHIVES OF TRANSPORT ISSN (prnt): Volume 39, Issue 3, 016 e-issn (onlne): DOI: / TRAFFIC FATALITIES PREDICTION BASED ON SUPPORT VECTOR MACHINE Tng L 1, Yunong Yang 1, Yonghu Wang 1, Chao Chen, Jnbao Yao 3 1 Dalan Martme Unversty, Transportaton Management College, Dalan, PR Chna Dalan Unversty of Technology, Automotve Engneerng College, Dalan, PR Chna 3 Bejng Jaotong Unversty, School of Cvl Engneerng and Archtecture, Bejng, PR Chna 3 e-mal: bao_yaojn@163.com To effectvely predct traffc fataltes and promote the frendly development of transportaton, a predcton model of traffc fataltes s establshed based on support vector machne (SVM). As the predcton accuracy of SVM largely depends on the selecton of parameters, Partcle Swarm Optmzaton (PSO) s ntroduced to fnd the optmal parameters. In ths paper, small sample and nonlnear data are used to predct fataltes of traffc accdent. Traffc accdent statstcs data of Chna from 1981 to 01 are chosen as expermental data. The nput varables for predctng accdent are hghway mleage, vehcle number and populaton sze whle the output varables are traffc fatalty. To verfy the valdty of the proposed predcton method, the backpropagaton neural network (BPNN) predcton model and SVM predcton model are also used to predct the traffc fataltes. The results show that compared wth BPNN predcton model and SVM model, the predcton model of traffc fataltes based on PSO-SVM has hgher predcton precson and smaller errors. The model can be more effectve to forecast the traffc fataltes. And the method usng partcle swarm optmzaton algorthm for parameter optmzaton of SVM s feasble and effectve. In addton, ths method avods overcomes the problem of over learnng n neural network tranng progress. Key words: traffc accdent; support vector machne (SVM); Partcle Swarm Optmzaton (PSO); predcton model; optmal parameters. 1. Introducton 1.1. Background In recent years, road nfrastructure constructon of Chna has mproved constantly. Vehcle number and hghway mleage ncrease accordngly. Ths drves the development of economy, but also produces some negatve effects,.e. road traffc accdents occur frequently. In traffc accdents, the traffc fatalty s the most harmful, and become a menace to our lfe. It has become a severty socetal problem we should pay full attenton to. However, the traffc fatalty has randomness whch s affected by the factors such as drver and passenger characterstcs, vehcles types, traffc condtons, as well as geometrc desgn characterstcs, etc. However, the complex relatonshp between traffc fataltes and varous nfluencng factors s nonlnear. As some factors generate nfluence on one another, t s hard to use only one factor to fully explan traffc fataltes. Therefore, t s necessary to summarze and analyze the data about traffc safety. The development trend of traffc fataltes under the exstng road traffc condtons can be predcted by fndng out the nherent law of accdent. For makng plan and decson of road traffc safety, predcton of traffc fataltes has practcal sgnfcance. 1.. Lterature revew Currently, many methods n traffc accdent predcton are used, the applcaton condtons and modelng mechansm of whch are dfferent. Bnomal regresson, Bayesan approach, backpropagaton neural network models and some new methods are used to ft the accdent data. Pamuła (01) presented a method of classfcaton of tme seres of traffc flow. Nowakowska (01) ponted hghlght road traffc accdent patterns n the context of nterrelatons between road characterstcs and a traffc safety threat. Ghasemlou et al. (015) amed to predct the crash severty wth the traffc njury data by mplementng the Artfcal Neural Networks (ANN), Regresson Trees (RT) and Multple Lnear Regresson modellng (MLRM) method. Mtas et al. (013) researched the traffc securty level. Poch et al. (1996) estmated a negatve bnomal regresson of the frequency of 1

2 Tng L, Yunong Yang, Yonghu Wang, Chao Chen, Jnbao Yao Traffc fataltes predcton based on support vector machne accdents at ntersecton approaches. Clarke et al. (1998) employed a machne learnng method to create decson trees. The characterstcs of accdents that resulted n njury or n damage only are dstngushed. Abdel-Aty et al. (011) explored to combne multvarate adaptve regresson splnes (MARS) wth another machne learnng technque (random forest). Xu et al. (013) amed to buld the genetc programmng (GP) model for real-tme crash predcton on freeways. The applcaton of the model was evaluated. Raman and Selvaraj (014) optmzed the Aggregated Feature Selecton (VAAFS) wth Votng Algorthm. An optmal number of sgnfcant features wth majorty votes were selected. Other smlar traffc accdent predcton can be found n these lteratures (Tesema et al., 005; Lee and We, 010; Zhang et al., 014; Nassr et al., 014; Zong et al., 013a; Yao et al., 014). Some research has proposed nnovatve models to predct traffc accdent. Yasd (1991) and Quek et al. (006) employed artfcal neural networks for traffc forecastng whch was appled on a road secton. Xe et al. (007) evaluated the applcaton of Bayesan neural network models for predctng motor vehcle crashes. Kunt et al. (011) employed twelve accdent-related parameters n a genetc algorthm (GA), pattern search and artfcal neural network (ANN) modellng methods. Stelmach (01) dealed wth mathematcal modelng of the arcraft landng phase usng artfcal neural networks. The severty of freeway traffc accdents was predcted by these models. Smlar researches had been studed by these lteratures (Zong et al., 013b, Abdelwahab & Abdel-Aty, 001; Deublen et al., 013).Though artfcal neural network has characterstc of dentfyng complex non-lnear system, there are problems, such as slow convergence speed, over-learnng and local extreme. All these problems affect the predcton precson of t. In recent years, support vector machne s used n traffc accdent predcton. SVM can study and optmze tself and adjust accordng to the varaton of data (Yao et al., 014). Problems of small sample, non-lnear and local extreme can be solved by t. L et al. (008) predcted motor vehcle crashes applyng Support Vector Machne (SVM) models. The study showed that SVM models predct crash data more effectvely and the accuracy s hgher than tradtonal Negatve Bnomal (NB) models. L et al. (01) developed a SVM model for predctng the njury severty assocated wth ndvdual crashes. The performance of the SVM model and the ordered probt (OP) model were compared. Yang and Zhao (013) ntroduced accdent rate per cars and accdent rate per capta n the paper. Based on the theory of support vector machne (SVM), the mproved SVM models were proposed. SVM also has some dsadvantages. For example, the performance of support vector machne depends on the parameters. Before the tranng phase, there are three parameters Cv,, need to be determned. Many lteratures suggested that heurstc algorthms have been successfully used n many complex problems (Yu et al., 010, 011, 013), ther algorthms are tested to be effectve by the results. Furthermore, n majorty of cases, the best results found are obtaned by these algorthms, partcularly on real-lfe optmzaton problems. To select the parameter values of SVM automatcally, heurstc algorthms are also used n ths paper Contrbutons There are two man contrbutons n ths paper: frstly, a predcton model of traffc accdent based on PSO-SVM s proposed. Partcle swarm optmzaton (PSO) algorthm s ntroduced to fnd the optmal parameter combnaton of SVM. Hghway mleage, vehcle number and populaton sze are put nto the model to get the number of traffc fataltes, whch s the most comparable ndcator n traffc accdent; secondly, the performance of the PSO-SVM, SVM and neural network predcton model are compared. Both fttng and predctng abltes of the models are evaluated through computng error values. The rest of the paper s organzed as follows: secton ntroduces the prncple of support vector machne. The model and process of traffc accdent predcton based on PSO-SVM are descrbed respectvely n secton 3 and 4; Test results and error value comparson of dfferent model are presented n secton 5; fnally, the conclusons and drecton for future research are presented n secton 6.. The prncple of support vector machne (SVM) The theory study of Support Vector Machne (SVM) has been farly mature. Ths method s a learnng

3 AoT Vol. 39/Issue method n small sample stuaton proposed by Vapnk (1999), based on the theory of statstcal learnng law. Support Vector Machne (SVM) algorthm maps the sample space to a hghdmensonal feature space by nonlnear mappng, transferrng the search for the optmal lnear regresson hyperplane algorthm nto solvng convex programmng problem under convex constrant, so as to get the global optmal soluton (Gan et al., 010; Guan et al., 008).At the same tme, the Support Vector Machne (SVM) method changes the product calculaton n the hgh-dmensonal space nto the kernel functon calculaton n the orgnal space by defnng a kernel functon (Dong et al., 005), whch greatly smplfes the calculaton. In case that the tranng sample s nonlnear, the fttng functon can be obtaned through the method as follows. Through a nonlnear functon, each sample pont s mapped to a hgh-dmensonal feature space, the lnear regresson n the hghdmensonal feature space s performed, and then the nonlnear regresson of the orgnal space s got. The fttng functon can be expressed as the followng equaton (Cao and Francs, 003). y() x (1) Where, s for the weght vector, x s nput vector, and represents the offset value To mnmze the followng two values through tranng, 1 1 P( f ) c L ( y f ( x )) l l () y f ( x ) y f ( x ) L ( y f ( x)) 0 y f ( x) (3) Where, l s the total number of tranng samples, l 1 c L ( y f ( x)) s for the experenced error l 1 term, s a regular tem. L ( y f ( x)) represents the loss functon, balancng the weghtng functon of tranng error term and the complex term. c s the penalty factor, stands for loss functon parameter, whose value affects the number of support vector. Here ntroduces the slack varables and, and then the optmzaton problem can be * converted nto: 1 mn ( ) (4) * c y ( x) st.. * ( x) y Where, the Lagrange multpler a and * a (5) are ntroduced, and the problem s transferred further nto a smple optmzaton problem of the dual problem, * * max y ( a a ) ( a a ) 1 * * ( a a )( a j a j ) k( x, x j ) j * ( a a) 0 * (6) s. t. 0 a C,0 a C (7) The fnal predcton functon fnshed s as follows, * ( ) (, j) (8) y a a k x x Where, k( x, x ) represents the kernel functon, j whch can complete the product operaton of the nput samples n low dmenson of aunknown nonlnear mappng functon n a hgh dmensonal feature space. The kernel functon.s the core of SVM, and dfferent kernel functons have dfferent structure. The detaled deduced process can refer to lterature (Chang, 005; Cao and Xu, 007) 3. The predcton model of traffc fataltes based on PSO-SVM To acheve comprehensve measure of traffc accdent, choosng the ndex of traffc accdent should follow three prncples: measurablty, representatveness and comparablty. Traffc system s conssted of three basc factors, whch are people, vehcle and road. Traffc accdents have 3

4 Tng L, Yunong Yang, Yonghu Wang, Chao Chen, Jnbao Yao Traffc fataltes predcton based on support vector machne great randomness, affected by many factors whch are quanttatve factors and qualtatve factors. In related lterature of traffc accdent predcton, hghway mleage, vehcle number, Lane wdth, average daly traffc and populaton sze are selected as mpact factors (Cao and Xu, 007). In ths paper, from the pont of person, vehcle and road factors, hghway mleage, vehcle number, populaton sze are selected to be the set of mpact factors. Traffc accdent predcton ndex currently wdely used are number of traffc fataltes, number of njury, number of road accdents and economc loss. Because there are major dfferences on the defnton of njures and statstcs about road accdents s ncomplete. The number of traffc fataltes s the predctor ndex whch s the most comparable one. Therefore, the structure of traffc fataltes predcton model can be seen n Fg. 1. Hghway mleage Vehcle number Populaton sze The process of SVM tranng Number of traffc deaths Fg. 1. The structure dagram of traffc fataltes predcton model 4. The process of traffc fataltes predcton based on PSO-SVM Support Vector Machne (SVM) s a theory of machne learnng law n small sample stuaton, and t has the very advantage n predcton, but there s no specfc theory for parameter selecton to depend on n the learnng process for support vector machne, whch serously restran the predcton accuracy and effect of the Support Vector Machne (SVM) method. The value of penalty factor c and kernel parameter affects the predcton accuracy of SVM, and fndng the optmal c and s the prorty. At present parameter s usually defned artfcally based on the specfc ssues, and the optmal parameter combnaton s determned by choosng the parameters for many tmes and comparng wth each other. Parameters that are manually set, are blnd and of low effcency, so t s needed to adopt swarm ntellgence optmzaton algorthm to mprove the parameter choosng of the Support Vector Machne (SVM).At the same tme, the desgn and mplementaton of Partcle Swarm Optmzaton algorthm (PSO) s relatvely smple. Not only the convergence speed s fast, but the parameters requred to be set are less (Cao and Xu, 007). Partcle Swarm Optmzaton (PSO) algorthm s nspred by brds foragng behavor proposed by Eberhart and Kennedy (1995), whch s a random search optmzaton algorthm generated by swarm ntellgence based on group cooperaton and competton. Compared wth evolutonary computaton, partcle swarm optmzaton algorthm adopts a global search strategy, uses v-s model wth smple operaton, and abandons the complex genetc manpulaton. Its specal memory mechansm can adjust the search strategy by keepng track of the current search based on real-tme, whch makes PSO a knd of effcent parallel search algorthm. As a result of the fast convergence speed of partcle swarm optmzaton algorthm and few requrements on parameter settng, PSO has drawn extensve concern n the academc feld. In the process of partcle swarm optmzaton algorthm solvng the problem, each partcle are representatve for a soluton to the asked problem. Through the preset ftness functon, each partcle has ts correspondng ftness value. Partcle velocty determnes the drecton and dstance moved, at the same tme, by takng examples from moton nerta of the partcle tself and the surroundng partcle, the velocty can be dynamcally updated tmely, so as to acheve the search process of the soluton. In every optmzaton search process, the partcle s updated by two values. One value s the optmal soluton obtaned by the partcle tself, known as the ndvdual extremum, and the other s global optmal soluton, called the global extremum. The specfc steps are as follows: Step1: Intalzaton. Intalze the number of the populaton and teratons, and speed. Step: Choose ftness functon. The mean square error s to be set as ftness functon Step3: Update the partcle poston. Compare the current partcle ftness value and the best locaton to the orgnal. If the orgnal ftness value s better, then the best ftness value remans unchanged. But f the current partcle ftness value s better, the current ftness value s set to the best locaton. 4

5 AoT Vol. 39/Issue Smlarly s the comparson of the current ftness value and the global optmal value. Step4: Adjust the partcle velocty and poston dynamcally. V V c P X c P X, g X X V. 1 1 Where,, s the nerta weght to control the nfluence degree of the current speed by 1,,..., n the former, and c 1 and c are accelerated factors, and are random numbers wthn the range of 1 0,1. Step5: Judgment result. If the result has been the optmal, then output current optmal parameter values. If the optmal value s not acheved, then transfer to Step. Thus, the predcton model combned PSO algorthm wth SVM (referred to as PSO-SVM method) s proposed to predct the traffc fataltes. The concrete steps of PSO-SVM method are as shown n Fg. Start and set parameter Intalze the populaton sze, weght and so on Calculate ftness values accordng to the ftness functon Estmate the optmal locaton and update partcle velocty and dsplacement No Whether the accuacy of the teraton number or predcton accuracy s acheved Yes SVM tranng and predcton No Whether predcton accuracy s acheved Yes end Fg.. The concrete steps of PSO - SVM method 5

6 Tng L, Yunong Yang, Yonghu Wang, Chao Chen, Jnbao Yao Traffc fataltes predcton based on support vector machne 5. Numercal test 5.1. Data The occurrence of traffc accdents s a result of the combned acton of many nfluence factors, for example, road traffc envronment, vehcle number, etc. In ths paper, hghway mleage, vehcle number and populaton sze are nput varables for predctng accdent. Traffc fatalty s one of the results whch are most harmful n traffc accdent. And traffc accdents nvolvng the fataltes have been hghly valued and statstcs have few omssons. Therefore, traffc fatalty s used as the output varables. We collect the data from the webste of Natonal Bureau of Statstcs of Chna, and the related data s shown n Table 1. Sample data from 1981 to 01 are chosen as expermental data. Samples of are tranng data, whle are test data. In the 6 process of tranng samples, parameters of PSO are set as follows: The populaton scale s of 0, the teraton number s 00, the cross rate s 0.7. The ntal values of acceleratng factor c 1 and c are 1.5 and 1.7 respectvely. Data normalzaton As the unts of data are dfferent and orders of magntude dfference are bg, the data for each varable have to be normalzed. If the model calculate wth raw data drectly, data submerged s lkely to happen. After normalzng, the data wll ft well whch mproves the precson of predcton. The normalzaton s accomplshed usng the followng equaton: A A A l A A1 A... A Table 1. Traffc accdent statstcs of Chna Year Traffc fataltes Hghway mleage Vehcle number Populaton sze people ten thousand km ten thousand ten thousand (9)

7 AoT Vol. 39/Issue Where, A s the th orgnal value of varables that needs to be normalzed. In ths paper, t refers to the th orgnal value of hghway mleage, vehcle number and populaton sze. And s the th value l A of hghway mleage, vehcle number and populaton sze after normalzaton. Performance ndex Two evaluaton crtera are adopted for ths study to compare the performance of models. The specfc formula s as follows: Mean absolute percentage error n 1 y ˆ y MAPE (10) n y The tranng of the model The tranng curve of traffc fataltes based on SVM predcton model s shown n Fg. 3. The black ones are actual output, whle yellow ones are fttng output. It can be seen that they ft well. The mean absolute percentage error5.0133% and coeffcent of determnaton (R ) s The traffc accdent predcton model based on PSO-SVM has strong dentfcaton ablty, and the fttng s stable The predcton of the model The traffc fataltes of can be predcted by the model that has been traned. Fg. 4 shows the absolute percentage error of the traffc accdent predcton. Mean absolute percentage error s 4.311% and coeffcent of determnaton (R ) s Coeffcent of determnaton ( R ) 1 n 1 n 1 ( y yˆ ) ( y y) (11) Where, n s the sze of fttng or predctng sample; s the estmated traffc fataltes at year ; and s y ˆ the observed number of traffc fataltes, s the average value of traffc fataltes. The model performance s better f the value of MAPE s smaller and R s larger. y y Fg. 4. Absolute percentage error of the traffc fataltes predcton Fg. 3.Tranng dagram of SVM predcton model 7

8 Tng L, Yunong Yang, Yonghu Wang, Chao Chen, Jnbao Yao Traffc fataltes predcton based on support vector machne In ths paper, predcton results of PSO-SVM, SVM and BPNN are compared as the Table.Mean absolute percentage errors are 4.311%, 6.49% and 7.388% respectvely. R are 0.947, and Fg. 5 shows the predct results of the several method. It s obvous that the predcton model of SVM based on PSO s better than SVM and BPNN model. And the SVM model s slghtly better than neural network model. Ths s because the SVM method wth global optmalty wll not get nto local mnmum pont. Ths avods the defects of the neural network method and mproves the predcton precson. SVM based on PSO searches the value of mportant parameters, consecutvely. The C artfcal selecton for parameters can be avoded, so as to mprove the predcton accuracy. 6. Conclusons The SVM model has the advantages of strong learnng ablty n small sample stuaton, fast learnng speed and good generalzaton ablty and so on. The PSO model s smple n program mplementaton, less n settng parameters and fast n calculatng convergence speed. The predcton model of traffc fataltes based on PSO-SVM, whch uses PSO to optmze the parameters of SVM, s the optmal SVM predcton model. Table. Predct results comparson of PSO-SVM, SVM and BPNN Actual value Year (people) PSO-SVM SVM BPNN Predcted value APE Predcted value APE Predcted value % % % % % % % % % % % % % % % % % % APE Fg. 5.Comparson of predct results 8

9 AoT Vol. 39/Issue The example analyss results show that the forecastng method based on PSO-SVM model s superor to the forecastng method of neural network and the ANN method n terms of the same data, and t overcomes the problem of "over learnng" phenomenon n neural network tranng progress, avods the local optmal soluton, and has extremely good generalzaton ablty. Therefore, the predcton model based on PSO-SVM s better than that of general predcton model of traffc fataltes and wth better predcton accuracy. Acknowledgments Ths research was supported n Natonal Natural Scence Foundaton of Chna and , Laonng Excellent Talents n Unversty LR015008, and the central unverstes DUT16YQ104. References [1] ABDEL-ATY, M., HALEEM, K., 011. Analyzng angle crashes at unsgnalzed ntersectons usng machne learnng technques. Accdent Analyss & Preventon, 43(1), pp [] ABDELWAHAB, H. T., ABDEL-ATY, M. A., 001. Development of artfcal neural network models to predct drver njury severty n traffc accdents at sgnalzed ntersectons. Transportaton Research Record: Journal of the Transportaton Research Board, 1746(1), pp [3] CAO, C., XU, J., 007. Short-term traffc flow predcaton based on PSO-SVM. Proceedngs of the frst nternatonal conference on transportaton engneerng, 46, p. 8. [4] CAO, L. J., FRANCIS, E. H., 003. Support vector machne wth adaptve parameters n fnancal tme seres forecastng. IEEE Transactons on Neural Networks, 14(6). [5] CHANG, L. Y., 005. Analyss of freeway accdent frequences: negatve bnomal regresson versus artfcal neural network. Safety scence, 43(8), pp [6] CLARKE, D. D., FORSYTH, R., WRIGHT, R., Machne learnng n road accdent research: decson trees descrbng road accdents durng cross-flow turns. Ergonomcs, 41(7), pp [7] DEUBLEIN, M., SCHUBERT, M., ADEY, B. T., KÖHLER, J., FABER M. H., 013. Predcton of road accdents: A Bayesan herarchcal approach. Accdent Analyss & Preventon, 51, pp [8] DONG, B., CAO, C., LEE, S. E., 005. Applyng support vector machnes to predct buldng energy consumpton n tropcal regon. Energy and Buldngs, 37, pp [9] GAN, X. S.,DUANMU, J., CONG, W Fatalness assessment of flght safety hdden danger based on support vector machne. Journal of Safety Scence and Technology, 6(3), pp [10] GHASEMLOU, K., AYDI, M. M., YILDIRIM, M. S., 015. Predcton of pedal cyclsts and pedestran fataltes from total monthly accdents and regstered prvate car numbers. Archves of Transport, 015, 34(), pp [11] GUAN, Z., SONG, T, QI, L., 008. An Applcaton of Support Vector Machne n Foundaton Settlement Predcton [J]. Transactons of Shenyang Lgong Unversty,, p. 04. [1] KENNEDY, J., EBERHART, R. C., 1995 Partcle swarm optmzaton, Proc. of IEEE Internatonal Conference on Neural Networks, Pscataway, NJ, pp [13] KUNT, M. M., AGHAYAN, I., NOII, N., 011. Predcton for traffc accdent severty: comparng the artfcal neural network, genetc algorthm, combned genetc algorthm and pattern search methods. Transport, 6(4), pp [14] LEE, Y., WEI, C. H., 010. A computerzed feature selecton method usng genetc algorthms to forecast freeway accdent duraton tmes. Computer-Aded Cvl and Infrastructure Engneerng, 5(), pp [15] LI, X., LORD, D., ZHANG, Y.,XIE, Y Predctng motor vehcle crashes usng support vector machne models. Accdent Analyss & Preventon, 40(4), pp [16] LI, Z., LIU, P., WANG, W., XIE, Y., 01. Usng support vector machne models for crash njury severty analyss. Accdent Analyss & Preventon, 45, pp [17] MITAS, A. W., KONIOR, W., KONIOR A., 013. VMS parameters mpact on safety and 9

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