AADT prediction using support vector regression with
data-dependent parameters
Manoel Castro-Neto
a, Youngseon Jeong
b, Myong K. Jeong
b,*, Lee D. Han
aaDepartment of Civil and Environmental Engineering, University of Tennessee, Knoxville, TN 37996, USA bDepartment of Industrial and Information Engineering, University of Tennessee, Knoxville, TN 37996, USA
Abstract
Traffic volume is a fundamental variable in several transportation engineering applications. For instance, in transportation planning, the annual average daily traffic (AADT) is a primary element that has to be estimated for the year of horizon of the analysis. The huge amounts of money to be invested in designed transportation systems are strongly associated with the traffic volumes expected in the system, which means that it is important that the AADT should be accurately predicted. In this paper, a modified version of a pattern recognition technique known as support vector machine for regression (SVR) to forecast AADT is presented. The proposed method-ology computes the SVR prediction parameters based on the distribution of the training data. Therefore, the proposed method is called SVR with data-dependent parameters (SVR-DP). Using 20 years of AADT for both rural and urban roads in 25 counties in the state of Tennessee, the performance of the SVR-DP was compared with those of Holt exponential smoothing (Holt-ES) and of ordinary least-square linear regression (OLS-regression). SVR-DP performed better than both methods; although the Holt-ES also presented good results.
Ó2008 Elsevier Ltd. All rights reserved.
Keywords: Support vector regression; Support vector machine; Time series analysis; Traffic volume prediction
1. Introduction
Traffic volume is the basic element in transportation engineering. Basically, all transportation engineering pro-jects involve traffic volume as a key input, including signal timing, geometric design, pavement design, transportation planning, highway improvement, congestion management, roadway maintenance, air pollution modeling, emergency evacuation plans, among others. Many transportation resources, such as the ASSHTO guidelines for traffic data programs (AASHTO, 1992), outline a large number of transportation engineering activities that require estimates of traffic volume demand parameters such as the annual average daily traffic (AADT).
The concept of AADT is simple: Roess, Prassas, and
McShane (2004)define AADT as ‘‘the average 24-h volume
at a given location over a full 365-year (366 in a leap year)”. In other words, AADT is the average number of vehicles that pass a roadway section each day in a particu-lar year.
State departments of transportation (DOT’s) and local transportation agencies commonly have collected and pre-dicted AADT for a variety of design, planning, and administrative purposes (Seaver, Chatterjee, & Seaver, 2000). These governmental agencies commit a large amount of time and funding to maintain their traffic vol-ume data collection programs (Sharma, Lingras, Xu, &
Liu, 1999), commonly known as traffic counting
pro-grams. In these programs, the AADT data for various locations can be measured by using permanent traffic counters. However, for most cases, comprehensive 365-day data collection is not economically feasible, such as in local roads in rural areas, nor even possible in cases where AADT for future-years is needed. In these cases AADT has to be predicted.
0957-4174/$ - see front matterÓ2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2008.01.073
* Corresponding author. Tel.: +1 865 974 0234; fax: +1 865 974 0588. E-mail address:mjeong@utk.edu(M.K. Jeong).
www.elsevier.com/locate/eswa
Expert Systems with Applications 36 (2009) 2979–2986
2. Objective of study
The main objective of this research was to evaluate the performance of a modified version of the support vector machine for regression (SVR) technique in forecasting AADT one year into the future without using any external (predictor) variable. The proposed methodology computes the SVR prediction parameters based on the distribution of the training data. Therefore, the proposed method is called SVR with data-dependent parameters (SVR-DP).
In order to evaluate its performance, SVR-DP was compared to Holt exponential smoothing (Holt-ES) and ordinary least-square linear regression (OLS-regression) techniques.
3. Literature review – research background
3.1. AADT Prediction – previous studies
Due to the importance of knowing traffic demand, many AADT prediction studies have been published. In the liter-ature, two main types of AADT prediction studies can be clearly identified:current-yearandfuture-yearAADT esti-mation studies. In the former type, the AADT for a partic-ular year (usually current-year) is estimated using predictor variables associated with that year. In these studies, new estimation methods are compared to the traditional factor method of AADT estimation. In the latter type of study, the AADT values for future years are estimated based on the AADT from previous years, and external variables are also sometimes used. Following, a literature review on both types of AADT prediction studies is presented.
3.2. Current-year AADT estimation studies
In this type of study, several papers evaluating different AADT estimation techniques have been published. A com-monly used technique has been the OLS-regression, where one or more independent variables that are believed to be associated with AADT are included in the model. For instance, Neveu (1983) included population, automobile ownership, number of households, and employment as pre-dictors to estimate AADT for roads with different func-tional classes, including interstate highway, principal arterial, minor arterial, and collector. In another study,
Mohamad, Sinha, Kuczec, and Scholer (1998) developed
a multiple regression model to estimate AADT for county roads, having the following as predictor variables: county population, road type (rural or urban), access to other roads, and total arterial mileage in the county. Zhao and
Chung (2001)developed multiple regression models
includ-ing road functional class, number of lanes, land use and socio-economic characteristics.
As an alternative to the traditional OLS-regression
(Eom, Park, Heo, & Hunstiger (2006), Zhao & Park
(2004)) applied geographically weighted regression
(GWR) to estimate AADT for non-expressways roads.
As opposed to the OLS-regression methodology, where the model parameters are estimated for the whole area of study (global parameters), GWR estimates different param-eters for different locations (local paramparam-eters) by weighting the observations inversely to their distance to the location where the AADT is estimated. In their study, five indepen-dent variables were included: number of lanes, accessibility to employment, population and employment in the buffer area, and direct access to expressways. They also developed OLS-regression models for comparison and concluded that GWR had better performance. GWR is expected to per-form better than OLS-regression in applications, including transportation, where location is an important factor to be considered.
In another study involving 80 counties in the state of Georgia,Seaver et al. (2000)developed a statistical strategy to estimate AADT for rural local roads. They applied prin-cipal component analysis (PCA) to identify which variables (out of 42 initial candidates) should be used in the model. The next step was the use of regression clustering to identify groups with similar characteristics. Finally, within each clus-ter, multiple regression variable selection techniques were used to find models that had good AADT predictability.
More sophisticated methods have also been used in cur-rent-year AADT estimation studies.Sharma et al. (1999)
applied neural networks (multilayered, feed-forward, and back-propagation) to estimate AADT for 63 sites in Min-nesota highway network. They concluded that neural net-work did not perform better than the traditional factor approach under a scenario in which the count stations were classified and grouped appropriately. Yi, Sheng, and Yu
(2004) applied wavelet transform to estimate seasonal
adjustment factors used in the traditional factor approach to estimate AADT in the state of Ohio. The results showed an improvement ranging from 10% to 20% over the con-ventional estimation of the seasonal factors. More recently,
Jiang, McCord, and Goel (2006)combined imagery
(satel-lites and air photos) and ground-based data to improve AADT estimates for coverage segments.
3.3. Future-year AADT estimation studies
This is the type of study presented in this paper. A liter-ature review has indicated that less attention has been given to prediction of AADT for future-years. However,
Al-Masaeid, Al-Suleiman, and Obaidat (1998)developed
mul-tiple regression models to forecast AADT for future-years for rural and desert towns, having as predictor variables the AADT of present year, change in population, change in employment level, number of health centers, and number of shops.
3.4. Support vector regression with data-dependent parameters (SVR-DP)
theoreti-cal foundation, good generalization performance, the absence of local minima, and sparse representation of solu-tion (Vapnik, 1995). Nonetheless, the implementation of many SVR algorithms requires the computation of ade-quate SVR parameters, which are crucial to the quality of SVR models developed. Several approaches have been presented in the literature for computing SVR parameters. The most accurate technique is the use of resampling meth-ods such as cross-validation. However, these methmeth-ods are very expensive in terms of data requirements and computa-tion time. In order to alleviate this problem, Cherkassky
and Ma (2004) presented a data-dependent technique in
which SVR parameters are computed based on the distri-bution of the incoming training data.
Therefore, an SVR methodology that uses data-depen-dent parameters is proposed in this paper. This methodol-ogy uses SVR to predict AADT data in order to enhance prediction accuracy and provides an efficient way of com-puting SVR parameters. This is achieved by incorporating the equations for computing SVR parameters into the con-ventional SVR algorithm in order to obtain data-depen-dent parameters and reduce computational time. The use of data-dependent parameters guarantees that the value of the parameters will give smaller support vectors and a less complex model (Cherkassky & Ma, 2004).
In transportation engineering, SVR was recently used to predict short-term (hourly) traffic flow (Ding, Zhao, &
Jiao, 2002) and travel times (Wu, Ho, & Lee, 2004). SVR
was found to perform significantly better than other con-ventional predictors considered in those papers. Following, a review of the SVR algorithm and methods of computing SVR parameters is presented.
3.5. A review of support vector machine for regression (SVR) technique
A detailed description of the SVR algorithm is given in
Vapnik (1995). Given a set of data points (x1,y1),
(x2,y2),. . ., (xm,ym) for regression, where xi2X#Rn;
yi2Y#R; mis the total number of training samples, a lin-ear regression function can be stated as
fðxÞ ¼wTUðx
iÞ þb ð1Þ
in a feature space F, where w is a vector in F and U(xi) maps the inputxto a vector inF. Assuming ane-insensitive loss function (Vapnik, 1995), thewandbin Eq.(1)are ob-tained by solving the following optimization problem:
minimize 1 2w
TwþCPm
i¼1
nþi þni
subject to :
yiwTUðxiÞ b6eþnþi wTUðx
iÞ þbyi6eþn
i
nþi;ni P0;
8 > <
> :
ð2Þ
wheree(P0) is the maximum deviation allowed during the
training andC(>0) represents the associated penalty for ex-cess deviation during the training. The slack variables
nþi andni, correspond to the size of this excess deviation for positive and negative deviations, respectively. The first term of Eq. (2), wTw, is the regularized term; thus, it controls the function capacity; the second term
Pm i¼1 n
þ
i þn
i
, is the empirical error measured by the
e-insensitive loss function. Using the appropriate Karush– Kuhn–Tucker conditions to Eq. (2) yields the following dual form of the optimization problem:
maximize
1 2
P
i;j a
i aþi
a
j aþj
hxixji
eP i
a
i þaþi
þP i
yi ai aþi
8 > < > :
subject to :
P
i a
i aþi
¼0
a
i;aþi
2 ½0;C
8 <
:
ð3Þ
For non-linear applications, applying the appropriate ker-nel function (khxixji), to the dot product of input vectors lead to the following formulation:
maximize
1 2
P
i;j
ai aþi
aj aþj
khxixji
eP i
a
i þaþi
þP i
yi ai aþi
8 > < > :
subject to : P
i a
i aþi
¼0
a
i;aþi
2 ½0;C
8 > > < > > :
ð4Þ
Therefore, the SVR equation for non-linear predictions becomes
fðxÞ ¼X i
a
i aþi
khxixi þb: ð5Þ
3.6. A review of techniques for selecting SVR parameters
The quality and performance of SVR models depends on the setting of three parameters: the type of kernel, the value ofC, and the value ofefor thee-insensitive loss func-tion. For any particular type of kernel, the values ofCand
e affect the quality and performance of the SVR models. According to the definition of these terms, the value of e
affects the number of support vectors used for prediction; therefore, a larger value ofewill lead to a smaller number of support vectors and a less complex model. The value of C, on the other hand, determines the tradeoff between model complexity and the degree of deviations allowed in the optimization formulation. Hence, a larger value of C undermines the complexity of the model.
The most common approach is based on users’ prior knowledge or expertise in implementing SVR algorithms
(Mattera & Haykin, 1999; Scho¨lkopf, Burges, & Smola,
1999). In this sense, this approach could be subjective and it is not appropriate for new users of SVR. Mattera
and Haykin (1999) proposed that the value ofCbe equal
approach is the use of resampling techniques for parameter selection (Cherkassky & Mulier, 1998; Scho¨lkopf et al., 1999). Even though this is a good approach, it is data-intensive, which means it is very expensive to implement in terms of computational time, especially for larger data-sets and online applications. One more approach is that e
values should be selected in proportion to the variance of the input noise (Kwok, 2001; Smola, Murata, Scho¨lkopf,
& Muller, 1998); however, this approach is independent
of the sample size.
As a result of the drawbacks of these various approaches,Cherkassky and Ma (2004)presented another approach based on the training data. They proposed that the value ofCshould be based on the training data without resorting to resampling, using the following estimation:
C¼maxðjyþ3ryj;jy3ryjÞ; ð6Þ
whereyandryare the mean and standard deviation of the y values of the training data. One advantage of this proach is that it is robust to possible outliers. This ap-proach is equivalent to the apap-proach in Mattera and
Haykin (1999)when the data have no outliers, but it
pro-vides better C values when outliers are present. Since e
determines the number of support vectors used for predic-tion, the value of e should be proportional to the input noise level. It was in line with this observation that
Cher-kassky and Ma (2004)proposed that the value ofeshould
be proportional to the standard deviation of the input noise. Using the idea of the Central Limit Theorem, they proposed thatebe given by
e¼3r
ffiffiffiffiffiffiffiffi lnn n
r
; ð7Þ
whereris the standard deviation of the input noise andnis the number of training samples. Since the value ofris not knowna priori, the following equation can be use to esti-mater using the idea ofk-nearest-neighbor’s method:
r¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
n1=5k
n1=5k1 1
n
Xn
i¼1
ðyi^yiÞ
2 s
; 26k66 ð8Þ
wherenis the number of training samples,krepresents the low-bias/high variance estimators, and ^y is the predicted value ofyby fitting a linear regression to the training data to estimate the noise variance.
3.7. Holt-ES Method
Exponential smoothing (ES) techniques can be very effective methods for short-term forecasts. Holt-ES has been widely used to both smooth and forecast time series data where trend, but not seasonality, is present. Since its forecast pattern is linear, Holt-ES tends not to perform well for multiple-step ahead forecasts. Holt-ES technique is implemented by using the formulation:
St¼aYtþ ð1aÞðSt1þbt1Þ
bt¼bðStSt1Þ þ ð1bÞbt1
Ftþm¼Stþbtm
ð9Þ
where a and b are the smoothing constants, St is the smoothed value at the end of periodt,btis the smoothed trend in period t, and m is the forecast horizon. The two smoothing constants (a and b) can be either subjectively chosen by the user or objectively optimized based on a cri-terion such as RMSE or MAPE. Smooth constants close to 1 put more weights on the most recent observations, while smooth constants close to 0 allow distant past observations to have a larger influence. Also, to initialize the smoothing process, initial values ofS1andb1are needed, which can be accomplished by backcasting. For those familiar with AR-IMA models, Holt’s ES is equivalent to ARAR-IMA (0, 2, 2).
3.8. OLS linear regression model
OLS-regression is probably the most popular statistical technique. The AADT (Yt) for a year (Xt) is given by the following simple model:
Yt¼b0þb1Xtþet ð10Þ
whereb0and b1 are the parameters that minimizes P
e2
t,
the sum of square errors. The least-square parametersb1 andb0are estimated byb1andb0by the following so called normal equations
b1¼ P
ðXtXÞðYtYÞ
P
ðXtXÞ2
b0¼Yb1X 8
<
: ð11Þ
ThenYtis simply estimated by b
Yt¼b0þb1Xt ð12Þ
4. Data description
This section describes the data used in this research, which were obtained from the Tennessee DOT traffic counting program.
4.1. The Tennessee DOT (TDOT) statewide traffic counting program
As a case study for this research, the TDOT traffic count-ing program data were used. This database contains AADT data collected annually since 1985 for more then 11,000 traffic count stations strategically located throughout all counties (95) of the Tennessee state. Every year, the AADT of most of the stations are estimated by using the traditional factor approach, in which 24–48 h worth of data (ADT) is collected and seasonal volume factors are applied to it. The count stations are characterized according to road functional classification shown inTable 1.
pre-dictor variable. The problem with this approach is that usually the AADT pattern is not linear. AADT data aggre-gated at type of road or at county level usually do not fit a straight regression line well. This problem becomes more dramatic when longer forecasting horizons are needed for planning purposes.
The AADT data used in this study were collected between 1985 and 2004 in 25 counties in the state of Ten-nessee. The AADT data were then aggregated by county and by type of facility (rural and urban). Therefore, a total of 50 (252) time series were used, one of which is illus-trated inFig. 1.
4.2. Methodology of study
The first step was to aggregate the AADT data by county and by two types of road: urban and rural. Twenty-five out of 95 counties were selected for this study, resulting in a total of 50 (252) time series. The counties were selected based on the total AADT amount over the 20-year period of study; counties with higher AADT were selected. For each AADT time series, the three forecast methods, SVR-DP, Holt-ES, and OLS-regression were applied. The implementation of each method, explained in detail, follows.
4.3. Implementing SVR with dependent parameters (SVR-DP)
First of all, the data were scaled in order to avoid prob-lems with influential data in the prediction model. The
Zscore scaling method was used in this paper; this scales
the training sets by mean-centering the data and scaling to a unit variance. The mean and the standard deviation of the training set were then used to scale the correspond-ing test set. This step avoided the computational difficulty associated with using larger numeric values and also guar-anteed that all data points in the training set were given equal opportunity in the prediction model. This also reduces computation time, especially when using SVR.
For the implementations, a typical time series prediction scenario was used as presented by Tashman (2000)with a prediction horizon of one time step. The time series proce-dure is described in this way: consider given a time series {x(t), t= 1,2,. . .} and prediction origin O. A time from which the prediction is generated, and a set of training sam-ples, AO,B is constructed from the segment of time series {x(t), t= 1,. . .,O} as AO,B= {X(t), y(t), t=B,. . ., 01}, where X(t) = [x(t),. . .,x(tB+ 1)]T, y(t) = x(t+ 1). Bis the embedding dimension of the training set
AO,B, which in this study is taken to be five. The predictor P(AO,B;X) is trained from the training setAO,B. Then, pre-dict x(O+ 1) using ^xðOþ1Þ ¼PðAO;B; XðOÞÞ. When
x(O+ 1) becomes available, the prediction origin is updated; that is,O=O+ 1 and the procedure is repeated. As the origin increases, the training set keeps growing and this can become very expensive. However, this procedure takes advantage of the fact that the training set is aug-mented one sample at a time and therefore, the model continues to be updated and improved as more data arrive. The computation of the SVR parameters was based on the data-dependent process presented earlier. Therefore, in order to enhance model prediction using SVR and to guar-antee a less complex model, the SVR algorithm was mod-ified by incorporating Eqs. (6)–(8) into the conventional
Table 1
Road functional classes used by the TDOT traffic counting program
Rural area 01 – principal arterial interstate 02 – Other principal arterial 06 – Minor arterial 07 – Major collector 08 – Minor collector 09 – Local
Urban area 11 – Principal arterial interstate
12 – Principal arterial, other freeways and expressways 14 – Other principal arterial
16 – Minor arterial 17 – Collector 19 – Local
1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 1.8
2 2.2 2.4 2.6 2.8
3x 10
4 Knox County - Rural Roads
AADT
Year
SVR algorithm in order to obtain a data-dependent algo-rithm, which will reduce computation time. For SVR-DP implementations, we used RBF kernel defined as exp(pjxixjj2) withp= 0.5.
After the SVR-DP parameters were found, the model was tested using the same 5-year window methodology to predict AADT for yearsY16toY20. Thus, five 1-year hori-zon forecasts were made for each series. The five predicted values were finally unscaled by using the mean and the standard deviation of the training set. The forecast accu-racy was measured by both the mean absolute percentage error (MAPE) and root mean squared error (RMSE). The process was repeated for each of the 50 AADT time series considered in this study.
4.4. Implementing Holt’s exponential smoothing (ES)
The SVR-DP technique presented in this paper was compared with Holt’s ES method, in which the AADT for a particular year Yt was predicted considering the AADT values of all previous years Y1to Yt1. As in the implementation of the SVR-PD model, five one-step ahead forecasts (years 2000–2004) were made for each series. MAPE and RMSE for each series were then computed.
4.5. Implementing OLS-regression
The prediction of the ADDT (Yt) for a particular year (Xt) is simply the one year ahead extrapolation of the regression line fitted with the data points (Xi, Yi), for i= 1,. . .,t1. For instance, Y20 was predicted by the regression model fitted on the 19 previous data points. As in the implementation of the other two models, five one-step ahead predictions were made, each of them being the AADT prediction for year 2000 through 2004. MAPE and RMSE for each one of the 50 time series were calcu-lated to access forecasting accuracy.
5. Experimental results
For each county, the performances of the models are represented by the MAPE and RMSE calculated over the 5 predictions (AADT from year 2000 to 2004). The picto-rial representation of the results for the 25 urban roads is shown in Fig. 2, and the one for rural roads is shown in
Fig. 3. FromFigs. 2 and 3, it can be seen that SVR-DP
out-performed OLS-regression for both rural and urban data. The SVR-DP also performed better than the Holt-ES,
although the performances of both techniques were not discrepant.
Table 2 shows the numerical overall results with
MAPE and RMSE values averaged across the 25 coun-ties. Note that the average MAPE for the SVR-DP tech-nique was only 2.26% for urban and 2.14% for rural, which are very low values for AADT forecasting pur-poses. As shown in Table 2, Holt’s ES also presented a
5 10 15 20 25
0 2 4 6 8 10 12 14 16
Urban Roads
MAPE (%)
County
SVR OLS Holt ES
5 10 15 20 25
0 500 1000 1500 2000
County
RMSE (veh/day)
SVR OLS Holt ES
Fig. 2. A pictorial representation of MAPE and RMSE – urban roads.
5 10 15 20 25
0 2 4 6 8 10
Rural Roads
MAPE (%)
County
SVR OLS Holt ES
5 10 15 20 25
0 200 400 600 800
County
RMSE (veh/day)
SVR OLS Holt ES
Fig. 3. A pictorial representation of MAPE and RMSE – rural roads.
Table 2
Overall results performance
Urban roads Rural roads
SVR-DP Holt’s ES OLS SVR-DP Holt’s ES OLS
Overall average MAPE (%) 2.26 2.69 3.85 2.14 2.55 3.70
good performance with an overall MAPE of 2.69% for urban and 2.55% for rural.
6. Conclusions and final comments
A modified support vector regression (SVR) approach has been proposed for future-year AADT estimation. The modified SVR uses data-dependent parameters in order to reduce computational time and to achieve better predictors. This can also widen the application of SVR in intelligent transportation systems especially for dynamic decision support systems. The comparison results showed that SVR-DP outperformed the OLS-regression tech-nique, which is commonly used for future-year AADT forecasting purposes. The SVR-DP also performed better than the Holt’s ES, but one can argue that both tech-niques performed similarly. The outstanding performance of SVR-DP can be attributed to the remarkable charac-teristics of SVR and the incorporation of a data-depen-dent procedure for computing SVR parameters. This reduces uncertainty relating to parameter selection and computation time.
Holt’s ES also presented a good forecasting capability. For some transportation agencies, such as DOT and MPO, Holt-ES might be the preferred option due to its simplicity in terms of both implementation and interpreta-tion. However, transportation analysts should be aware that Holt-ES has two significant limitations: it does not perform well for long forecast horizons nor for data with seasonality. Therefore, Holt-ES should be avoided for longer AADT forecast horizon terms. These two con-straints are not part of the SVR-DP technique.
Furthermore, the theoretical foundation SVR-DP is ideal for traffic volume forecasting. By computing the SVR parameters based on the distribution of past data, the SVR model can exploit information contained in a large set of data. As a result of large variations in traffic volume, the modified SVR approach is likely to incorpo-rate unexpected changes in the model and attempt to create one single mapping function. Future work is ongoing to extend the theoretical foundation of SVR to short-time traffic volume predictions by accounting for some of the uncertainties associated with such models.
In conclusion, the SVR-DP technique provides an accu-rate forecasting technique where no external explanatory variable is used. This can be seen as very advantageous because the inclusion of external variables might not be feasible. Besides, for future-year AADT estimation studies such as the one presented here, external variables would have to be predicted into the future and this might add a significant error to the model.
6.1. Recommendations for future research
The forecasting performance of the SVR-DP should be further investigated. The authors recommend that future research be directed in the following ways. The proposed
methodology could be applied for longer forecast horizons. For many transportation planning applications, AADT needs to be predicted many years into the future. The meth-odology also could be applied for short-term traffic predic-tion for ITS operapredic-tions. For that purpose, the online version of SVR has been implemented by the authors in another study. Finally, for large geodatabases such as the ones generated by traffic counting programs, a new meth-odology combining spatial data analysis and SVR could be investigated.
Acknowledgement
The authors are grateful to the Tennessee DOT and the National Transportation Research Center for providing the necessary data. This work was supported by NSF Ca-reer Award CMMI-0644830.
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