Long-term traffic pattern forecasting using dynamic classifier selection

Abstract

Dynamic Classifier Selection (DCS) techniques aim to select the most competent classifiers from an ensemble per test sample. For each test sample, only a subset of the most competent classifiers is used to estimate its target value. The performance of the DCS highly depends on how we define the local region of competence, which is a local region in the feature space around the test sample. In this paper, we propose a new definition of region of competence based on a new proximity measure. We exploit the observed similarities between traffic profiles at different links, days and hours to obtain similarities between different values. Furthermore, long-term traffic pattern prediction is a complex problem and most of the traffic prediction literature are based on time-series and regression approaches and their prediction time is limited to next few hours or days. We tackle the long-term traffic pattern prediction as a classification of discretized traffic indicators to improve the accuracy of urban traffic pattern forecasting of next weeks by using DCS. We also employ two different link clustering methods, for grouping traffic links. For each cluster, we train a dynamic classifier system for predicting the traffic variables (flow, speed and journey time). Our results on strategic road network data shows that the proposed method outperforms the existing ensemble and baseline models in long-term traffic prediction.

Keywords

Long-term traffic prediction traffic link clustering dynamic classifier selection region of competence

1 Introduction

Long-term traffic prediction plays an important role in improving the quality of traffic management, alleviating road traffic congestion and making reasonable arrangements for police or other management resources [1]. Although there is a large number of works on traffic pattern prediction, the problem of long-term forecasting for the next weeks is still not well addressed. Existing traffic forecasting researches mainly focus on short-term traffic forecasting problem and their prediction time of high precision is limited to 5-15 minutes [2, 3]. Besides, these solutions have a poor stability and their accuracy for long-term prediction is low [2, 3]. Long-term forecasting researches [1 , 4–11] mostly focus on prediction of next few hours and days.

Traffic forecasting can be tackled using different modelling perspectives [12]: the statistical time-series perspective, the supervised regression perspective, clustering pattern recognition perspectives, and supervised classification perspective [13, 14]. While most of traffic forecasting literature are based on the time-series and regression approaches, in this paper, we tackle the long-term traffic pattern prediction as a multi-class classification problem. We discretize the traffic variables namely, average journey time, average speed and traffic flow into three levels (low, medium, high). An obvious advantage of this approach is that discrete values are closer to knowledge level representation than continuous ones and are easier to handle and interpret.

The problem addressed in this paper is the prediction of three discretized traffic parameters (average journey time, average speed and traffic flow) for next weeks. Long-term traffic prediction is a challenging problem as traffic state is easily interfered by random factors such as accidents or emergency situations. Numerous existing models focus on traffic forecasting of a particular traffic link, but there is no model that predicts all the traffic links of a country simultaneously. In this paper, we propose an ensemble prediction model to handle the challenging task of long-term traffic pattern forecasting for all highways in England. Given a traffic link (a road section), a day in week (1 to 7) and a time in day (1 to 24), we propose a model for predicting the traffic state for the specified link and time. Ensemble methods are popular research directions in machine learning and pattern recognition and aim to combine decisions from a set of weak learning algorithms (base learners) so that the generalization ability of the built classification model can achieve better performance compared to the base learners [15]. Although, ensemble learning method is widely applied to different problem, few models of traffic forecasting are proposed. A key problem in ensemble learning is choosing the best classifier for each instance. We propose a Dynamic Classifier Selection (DCS) [16] approach toward predicting the traffic variables for the next several weeks. Our main contributions are as follows:

1.1 Motivation and contribution

An ensemble learning model is proposed for predicting traffic parameters. The method splits the traffic links into different groups. While many works, train a separate prediction model for each traffic link we cluster traffic links based on their traffic profile similarities and train a dynamic selection classifier system for each group of similar links.

Most of traffic forecasting literature is based on the time-series and regression approaches. In this paper, we tackle the long-term traffic pattern prediction as a multi-class classification problem in which traffic variables (average journey time, average speed and traffic flow) are discretized into three levels (low, medium, high). An obvious advantage of this approach is that discrete values are closer to knowledge level representation than continuous ones and are easier to handle and interpret [17]. Besides, while most of the traffic prediction models predict the next few hours or days, the proposed classification approach help in predicting the next weeks.

We propose a new definition of region of competence [16] based on a new custom-defined similarity measure. We exploit the observed similarities between traffic profiles at different links, days and hours to obtain similarities between different values. In the proposed proximity measure, the distance between two values v_i and v_j of a feature (link, day or hour) is determined with respect to how much having these different values results in difference in response values.

We also introduce a new variant of the Oracle method [21], which we refer to as “OracleTr”, for computing the most competent classifier(s).

The rest of this paper is structured as follows. We review the related work in Section 2. In Section 3 DCS is described. In Section 4 DCS method. In Section 5, we give the evaluation and comparison results. Finally, Section 6 provides concluding remarks.

2 Related work

This section provides a brief overview of the earlier research contributions on traffic pattern forecasting.

2.1 Machine learning methods

Machine learning models identify traffic state with the construction of prediction models [23]. Different machine learning works try to predict different traffic variables including flow, volume, speed, density, or occupancy [24 –26]. The traffic flow prediction problem aims at estimating the number of vehicles for a specific region and time interval. In [24], based on multivariate linear regression model, the authors proposed a traffic flow prediction method. In [25], a dynamic travel time prediction model is given based on Support Vector Machines (SVM). A vast amount of works use Neural Networks (NN) for traffic prediction. In [26] the authors give a survey of different types of NN structures applied for traffic prediction.

Some research convert the time series problem into a classification problem. The work [28] focuses on congestion level prediction based on classification of discretized time series. The work [29] discretizes the traffic load which represents the quality of travel. In [30], a regression to classification procedure is incorporated to construct a more accurate classification-type loss function out of the regression problem of traffic volume forecasting. The work [31] also uses regression to classification (R2C) for prediction of level of service.

2.2 Long term traffic pattern prediction

Some researches has been done on long-term traffic prediction [1 , 4–9]. A novel traffic flow prediction framework has been proposed in [32]. The work [10] proposed a hybrid deep learning model based on wavelet decomposition, convolutional neural network-long and short-term memory neural network, for prediction of next-day traffic flow. [4] proposed a daily long-term traffic flow prediction based on deep neural networks. In [6], a long-term traffic situation forecasting model is proposed based on functional nonparametric regression. In [1], a method for long term travel time prediction using historical data is given. In [7], the authors proposed a framework for an online traffic prediction, which discovers the contextual specialization of predictors to create a strong hybrid predictor from several weak predictors. The work [8] proposed a long-term estimation method based on the automated discovery of patterns. The method proposed in [9] analyzes how to properly characterize traffic flow in urban road scenarios. They use a clustering phase to discover typical ties or patterns within the traffic flow data. In [2, 3], the authors propose a traffic flow prediction algorithm with higher accuracy and longer prediction time. They propose an unequal interval combining model based on improved LSTM and ARIMA, which can guarantee a higher rate of accuracy.

2.3 Ensemble learning methods in traffic prediction

Ensemble learning is a promising research direction in machine learning [15]. Ensemble learning methods are widely applied to different problems. There are some ensemble learning works in the area of traffic prediction [7 , 34]. Ensemble and dynamic classifier ensemble methods are alternative ways for improving the performance. In [34], the authors proposed a hybrid approach which combines NN and a simple statistical approach. The authors of [7] proposed a novel online framework that could learn from the current traffic state in real-time and predict the future traffic. In [22], the authors proposed a heterogeneous ensemble method with dynamic selection. Few works on classification over discretized traffic data. The work [33] proposed a stacked ensemble learning method using empirical mode decomposition. In [35, 36], the authors use gradient boosting regression tree method (GBM) to analyze and model travel time.

2.4 Computing the competence level

Several methods are commonly used for computing the competence level of base classifiers [16, 18]:

Modified classifier ranking. In this method [19], the competence level (ranking) of a classifier C_i for classifying x_j is estimated by the number of consecutive correctly classified samples in θ_j, the region of competence of x_j.

KNORA-Union. In this technique [20], the competence level (number of votes) of C_i is equal to the number of samples in θ_j, for which C_i predicted the correct label.

Oracle. In this scheme [21], classifiers which correctly predict all the samples in θ_j are selected. Oracle abstract model always selects the classifier that predicted the correct label, for the given query sample, if such a classifier exists.

Fig. 1

The three phases of a dynamic classifier selection system.

3 Dynamic classifier selection (DCS)

An alternative to using a single highly optimized classifier for a classification problem is to use Dynamic Classifier Selection (DCS) through an appropriate selection method. If the base classifiers make complementary decisions, appropriate selection of them will improve the classification accuracy with respect to that of individual classifiers [16]. A DCS system is composed of three stages [16]: (1) Generation, (2) Selection, and (3) Aggregation (Fig. 1). In the generation stage, a pool of classifiers {C₁, …, C_M} is trained to create a set of diverse “base” classifiers. In the selection stage, once a query sample x_j is given, the competence of each C_i for classifying x_j is estimated based on, θ_j, the local region in the validation data where x_j is located. The idea is that each base classifier in the pool has a different domain of expertise. This local region can be defined by different region of competence definitions [16], such as applying the k-NN method, to find the neighborhood of x_j. The definition of region of competence is of fundamental importance in achieving an acceptable performance. The standard definition is based on the k-NN method with the Euclidean distance measure which is not effective in many situations. In selection stage, the most competent classifier or a subset of the most competent classifiers is selected for classifying x_j. Employing an appropriate method for estimating the competence level, δ_i,j, of classifier C_i for classifying x_j is of key importance. Finally, in integration phase, the decisions of the selected classifiers are aggregated to obtain the decision. For more information about DCS models, the reader can refer to [16], where the authors categorize the main dynamic selection techniques and also conduct an extensive experimental analysis, considering a total of 18 state-of-the-art dynamic selection techniques.

4 Proposed model

4.1 Preprocessing

We propose a DCS system for predicting the traffic state variables of the Strategic Road Network (SRN) dataset [37], which provides average journey time, average speed and average traffic flow information for about 2500 links around the Highways England that maintain and improve the motorways and major “A roads” in England. The description of the SRN is given in Table 1A. detailed description of the features of this data can be found in Highways England website1.

Traffic variables have a periodic pattern. Figure 2(a) shows the average speed of 10 random links in 12 consecutive month of 2014. Also, at the top of Fig. 2(b) the daily average speed of a random link, and at the bottom, the daily average speed of all links is shown in March 2014.

Fig. 2

(a) average speed of 10 randomly selected links in 12 consecutive month of 2014, (b-top) daily average speed of a random link in march 2014, (b-bottom) daily average speed in all links in march 2014, (c) changes in the average speed in a random day in different time scales from one quarter (top) to two hours (bottom).

Outlier replacement. One necessary step is replacing outliers. We perform the outlier replacement step for each of AverageJT, AverageSpeed and Flow fields separately. For AverageJT and AverageSpeed fields, we compute the mean μ and standard deviation σ for each traffic link and we consider values less than μ - 3σ as left and values greater than μ + 3σ as right outliers and replace them respectively with μ - 3σ and μ + 3σ. For the Flow field, on the other hand, we replace the largest ρ percentile of the data (for each traffic link) with (100 - ρ) percentile value.

Data aggregation and smoothing. Aggregating the 15-minute time slots into n-hour time slots decreases the noise produced by outliers, and depending on the size of the slots, maintains the characteristics of the data [9]. Thus, we change the time scale from one quarter to two, four and eight quarter time scale. Figure 2(c) shows the changes in average speed in a typical link and day in these four scales. In these time scales, 96 time periods in a day are reduced to respectively 48, 24 and 12 time periods. In the experiments of this work, we consider 24 time periods. Beside the data aggregation step which increases data stability, we also use the moving average smoothing method to reduce the adverse impact of random factors such as accidents or emergency situations.

Discretization. We discretize the traffic response variables into three levels (low, medium, high). We examine three different discretization schemes: equal-width discretization, equal-frequency discretization [38] and deviation $Z$ -based discretization which uses the following formula:

$x_{d} = {\begin{matrix} 1 & x < μ - σ, \\ 2 & μ - σ < x < μ + σ, \\ 3 & x > μ + σ . \end{matrix}$ (1)

Where μ and σ are respectively mean and standard deviation of the field for the corresponding traffic link. After discretizing the “AverageJT”, “AverageSpeed” and “Flow” fields, discretized fields are named das, dajt, and dflow respectively. We discretize different traffic variables and tackle the traffic prediction problem as a multi-class classification problem.

Feature creation. In order to capture the weekly cycle of the data, we add a new feature, “diw” (day in week) which specifies the index of day in week. We also add “dim” (day in month) which specifies the index of day in month. Table 1 shows the features of the preprocessed SRN dataset.

Table 1

Description of the Strategic Road Network (SRN) dataset and the preprocessed features

No	Original feature	Preprocessed feature	Description
1	LinkRef	link id (1-2500)	A unique alphanumeric link id representing a junction to junction link (e.g., AL1495, AL1502)
2	LinkDescription	Removed	Description of the link
3	Date	dim (day in month (1-31))	Date of travel
		diw (day in week (1-7))
4	TimePeriod	tid (1-24)	One of 96 15-min intervals in the day (e.g., 0 indicates 00:00 to 00:15).
5	AverageJT	dajt (discretized average journey time (s))	Average journey time (in seconds), calculated every 15 min
6	AverageSpeed	das (discretized average speed (km/h))	Average speed(km/h)
7	DataQuality	Removed	Indicator showing the quality of the journey time data (1 indicates the highest quality data and 5 the lowest)
8	LinkLength	Removed	The length of the link(km).
9	Flow	dflow (discretized average flow)	An average of the observed flow for the link, time period and day

4.2 Proposed dynamic selection system

Given a query sample x_j = (l, w, h), where l is a traffic link, w is a day in week (1 to 7), and h is a time in day (1 to 24), we propose a dynamic classifier system model to predict the discrete traffic indicators for the specified link and time. Figure 3 shows the architecture of the proposed model. In the proposed dynamic classifier selection system, we cluster the traffic links into p partitions P₁, P₂, …, P_p based on their traffic profile similarities. We examine two different methods for computing the similarity of links. We denote by T_r and D_r the parts of training and dynamic selection (validation) datasets, respectively, corresponding to partition P_r, r = 1, …, p. For each cluster P_r, we build a separate dynamic classifier selection system. For this, we train a pool of classifiers according to the training dataset T_r. Once a query sample x_j from a link in P_r is given, the region of competence for x_j is computed in the dynamic selection dataset D_r, according to the proposed definition described in subsection4.2.2. In order to estimate the competence level of base classifiers for classifying x_j, we use the method described in section4.2.3. Finally, we choose the most competent classifier(s) for classifying x_j.

Fig. 3

The architecture of the proposed model.

4.2.1 Generating the pool of classifiers

We partition traffic links into 40 clusters (based on the evaluation results of subsection5.1(Fig 5)) and for each cluster we train a DCS system with an inhomogeneous pool of classifiers. Our pool of classifiers consists of SVM with One-vs-One strategy, k-NN with k = 4, Scaled Conjugate Gradient (SCG) NN, Levenberg-Marquardt (LM) NN and Bayesian Regularization (BR) NN models. NN models are initialized with random weight values, and their hidden layer has different number of nodes for different classifiers. We train 20 classifiers (according to evaluation results performed for different number of the classifiers) for each of theNN models.

4.2.2 Definition of region of competence

The definition of region of competence is of fundamental importance in achieving an acceptable performance. Beside the standard k-NN method with the Euclidean distance [19 –21], the CART method [22], is another method for computing the region of competence that uses the well-known CART algorithm. After obtaining a tree with the CART algorithm on the training data, they apply the tree on the test query. The selected data are all the examples from the leaf node where the test example falls. An important limitation of this method is that there is no upper bound on the number of similar examples. In this work, we propose two region of competence computation methods:

1) Clustering-based techniques [39, 40], in which the region of competence of a query sample is the set of points in its cluster. In this technique, training samples are clustered and the competence of each base classi?er is estimated for each cluster. During the generalization stage, given a query, x_j, the distance between x_j and the centroid of each cluster is obtained and the competence of each base classifier C_i for x_j will be the competence of C_i for classifying the samples in the nearest cluster. In order to apply this method for traffic prediction we cluster traffic links.

Fig. 4

Schematic diagram of the proposed method for computing the similarity of two triples x_i = (l′, w′, h′) and x_j = (l, w, h).

2) k most similar neighbors technique in which the region of competence of a query sample is defined as the set of k most similar points in the dynamic selection dataset. However, since the Euclidean distance measure is not efficient for this situation, we propose a new custom-defined similarity measure (subsection 4.2.4).

4.2.3 Computing the competence level

In order to estimate the competence level of base classifiers we modify the oracle model. In our modified variant, which we refer to as OracleTr, we use a threshold value, θ_c = ⌊ k/3 ⌋ +1 and select classifiers that correctly classify at least θ_c samples in the region of competence, where k is the size of region of competence. If no classifier can satisfy this condition, we chose the classifier(s) with the best performance.

4.2.4 Traffic pattern similarity measure

The distance measure adopted for calculating the distance among samples, is another issue, which has been shown to be crucial for improving the performance of k-NN methods. In order to compute the proximity of samples, some researches propose to use a custom-defined similarity measure which is based on statistical test theory. In this work, we exploit the observed similarities between traffic profiles at different links, days and hours to obtain similarities between different values. In order to estimate the region of competence of a query sample x_j = (l, w, h), where l is a traffic link, w is a day in week, and h is a time in day, we need to give an appropriate definition for similarity. There are several notions of proximity which are commonly used for finding the nearest neighbors including Euclidean and cityblock and etc.

We propose a custom-defined similarity measure for estimating the similarity between two tuples x_j = (l, w, h) and x_i = (l′, w′, h′). In the proposed similarity measure, the distance between two values v and v′ of a feature is determined with respect to how having these different values results in difference in response values. Figure 0ref figSMC shows the schematic diagram of the proposed similarity measure. First, the similarity between links, days in week and hours in day is computed with respect to the similarity of traffic pattern in those links, weekdays and hours. Then, the similarity of x_i and x_j, is obtained by combining the similarity of links l and l′, the similarity of weekdays w and w′, and the similarity of hours h and h′, with equal weights.

Links Similarity Matrix. The similarity of two links l and l′ is computed according to the similarity of traffic variable (average journey time, average speed and traffic flow) through time for those links. As shown in Fig. 4(a), for each link l, we obtain, $R_{L} (l)$ , a vector of the consecutive values of the traffic variable in the whole training data in l. The similarity of links l and l′, δ_L (l, l′), is defined as the correlation of the rows (vectors) for l and l′. We have: $δ_{L} (l, l^{'}) = corr (R_{L} (l), R_{L} (l^{'}))$ (2)

Weekdays Similarity Matrix. For a weekday w, w = 1, …, 7, we denote by $R_{W} (w)$ , the vector of traffic variable in all links and weeks in weekday w (Fig. 4(b)). The similarity of two weekdays w and w′ is defined as the correlation between $R_{W}$ (w) and $R_{W}$ (w′): $δ_{W} (w, w^{'}) = corr (R_{W} (w), R_{W} (w^{'}))$ (3)

Day Hours Similarity Matrix. For a day hour h, h = 1, …, 24, we denote by $R_{H} (h)$ , the vector of traffic variable in all links and days in hour h (Fig. 4(c)). The similarity of two hours h and h′ is defined as the correlation between $R_{H} (h)$ and $R_{H} (h^{'})$ : $δ_{H} (h, h^{'}) = corr (R_{H} (h), R_{H} (h^{'}))$ (4) Finally, as shown in Fig. 4(d), the similarity of two tuples x_j = (l, w, h), and x_i = (l′, w′, h′), is computed by combining the similarities between these three features. We have: $δ (x_{i}, x_{j}) = \frac{δ_{H} (h, h^{'}) + δ_{W} (w, w^{'}) + δ_{L} (l, l^{'})}{3}$ (5) Based on this similarity measure, given a test sample, x_j = (l, w, h), the similarity between x_j and the samples in dynamic selection (validation) dataset is computed by combining the similarities between these three features with equal weights (equation (5)), and k most similar samples are chosen as the region of competence. Note that for different traffic variables different similarity matrices are obtained.

4.3 Link clustering

We examine two different clustering methods for partitioning traffic links into groups according to their characteristics:

Clustering based on statistics vector (c_sv). In this method, links are clustered based on minimum, maximum, average and standard deviation of the traffic variable (for example “flow”) in the training data. We use the Euclidean distance metric on the normalized data to obtain the clusters.

Clustering based on average response vector (c_atv). In this method, links are clustered based the links similarity matrix obtained in subsection 4.2.4 (Fig. 4).

Also, for each of the above methods we examine two variants: one considering location and length of links and one omitting these fields. Our results demonstrated that considering these fields has no positive effect on classification results. The optimal number of clusters is determined manually with respect to the classification accuracy. Subsequently, for each cluster we obtain a separate DCS.

Fig. 5

The impact of the number of clusters on the prediction accuracy for different discretization and clustering methods.

5 Performance evaluation

In this section, we evaluate the performance of the proposed DCS model. We use the monthly SRN data for evaluation of the proposed method. We use the data of February to April of 2014 for training and data of May 2014 for evaluating the proposed method. We compare five alternatives:

Clust+KNN. In this case, traffic links are clustered into 40 clusters and for each cluster we train a single k-NN model.

NoClust+Ranking/Union/OracleTr. In these three cases, a dynamic classifier selection model is trained for all traffic links. The competence level of base classifiers is computed using the Ranking/Union/OracleTr method.

ClassicDistance(Clust+Ranking/Union/OracleTr). In these cases, the set of traffic links is clustered into 40 clusters and for each cluster a DCS model is trained. The competence level of base classifiers is computed using the Ranking/Union/OracleTr method.

ProposedDistance(Clust+Ranking/Union/OracleTr). As in previous case, with the only difference that the region of competence is computed using the similarity measure proposed in Section4.2.4.

We assess the impact of different parameters, namely the number of weeks of validation data, the forecasting horizon, and the size of the region of competence. We also find the optimal number of clusters. We use the accuracy and F-measure for evaluating the performance. The accuracy is defined as the number of items classified correctly divided by the number of all items classified and F-measure is the harmonic mean of precision and recall.

5.1 Finding the optimal number of clusters

An important problem is determining the optimal number of clusters. Figure 5 shows the impact of the number of clusters (1-100) on the performance for different discretization and clustering methods for average journey time (a), average speed (b) and flow (c). The result on 500 randomly selected links shows that increasing the number of clusters beyond 40 increases the processing time with almost no gain. Therefore, the number of clusters, in the rest of this paper is assumed to be 40. We also assessed the impact of the number of clusters on the prediction accuracy for different distance measures. The results, omitted due to lack of space, showed that the correlation distance measure outperforms the other measures.

5.2 Number of weeks of validation data

Validation data is the data that is used to validate a machine learning model. In order to assess the impact of the size of validation (dynamic selection) dataset, we changed the number of weeks of this data from one to ten weeks (7 to 70 days). Parts (a), (b) and (c) of Fig. 6 respectively show the impact of the number of weeks of validation data on prediction accuracy for average journey time, average speed and flow. The result shows that as the number of validation weeks increases, so does the prediction accuracy of all methods. The result also shows that clustering the traffic links based on the proposed similarity measure has a significant impact on achieving higher levels of prediction accuracy. Also, using the proposed similarity measure and the proposed definition of region of competence leads to a significant improvement in the prediction accuracy of all traffic variables.

Fig. 6

The impact of the number of weeks of validation (dynamic selection) data on the prediction accuracy.

5.3 Forecasting horizon

Multistep-ahead prediction is to use the predicted value of the current time to determine its value in the next time steps. In order to study the multi-step ahead prediction in the proposed model, we assess the impact of forecasting horizon on prediction performance. The performance of the proposed model is compared against some non-ensemble models including SVM, kNN, Scaled Conjugate Gradient (SCG) NN, Levenberg-Marquardt (LM) NN and Bayesian Regularization (BR) NN model. The result of the comparison, in Fig. 7, shows that as the forecasting horizon increases the prediction accuracy decreases. The result also shows that the proposed model achieves a significant improvement over the non-ensemble methods.

Fig. 7

The impact of the forecasting horizon on the prediction accuracy of the proposed DCS and base classifiers.

Fig. 8

Performance comparison of the proposed and previous methods for predicting.

5.4 Size of region of competence

Considering an appropriate size for the region of competence, which is the local region surrounding the test query, strongly impacts our estimation of the competence level of base classifiers [16]. In this section, we compare the performance of the previous and proposed models for predicting the average journey time (a), average speed (b) and flow (c) for different sizes of the region of competence. The result in Fig. 8 shows that using the proposed link clustering methods has a positive impact on achieving better performance. Using the proposed similarity measure improves the F-measure significantly. Both the link clustering method and the custom-defined similarity measure help in achieving a more accurate region of competence and a higher F-measure. The result in Fig. 8 also helps in determining the optimal size for the region of competence. Increasing the size of the region of competence improves the performance for all traffic variables. However, increasing the size beyond eight seems to have almost no positive effect on improving theperformance.

5.5 The impact of the proposed similarity measure

In this section, we evaluate and compare the performance of the proposed region of competence computation method, which is based on a newly proposed similarity measure, against the k-NN-based and CART [22] methods. We consider different days in week and different traffic variables. The results of the prediction experiments based on the modified classifier ranking algorithm for 7 days is shown in Table 2. The result shows that the proposed region of competence computation method generally achieves better prediction performance in terms of accuracy.

Table 2
Performance comparision of k-NN, CART and the proposed region of competence computation method

Target Average Speed Flow Average Journey Time

Day k-NN CART Proposed k-NN CART Proposed k-NN CART Proposed

March 25 66.80 66.13 65.74 92.29 87.42 92.91 70.22 69.55 71.97

March 26 67.30 66.80 69.70 92.67 86.67 92.95 70.72 70.97 74.70

March 27 64.22 64.55 66.25 91.42 78.38 91.57 69.18 67.51 71.73

March 28 64.97 62.43 67.15 90.34 70.93 89.92 64.06 61.27 64.99

March 29 62.84 60.76 67.60 89.79 70.05 90.22 61.47 59.93 61.30

March 30 68.76 65.43 69.01 90.88 81.76 90.96 71.93 71.51 76.71

March 31 66.97 65.43 69.88 92.17 87.21 93.20 69.68 69.14 73.02

Mean 65.98 64.50 67.90 91.36 80.35 91.67 68.18 67.13 70.63

Target	Average Speed	Flow	Average Journey Time
Day	k-NN	CART	Proposed	k-NN	CART	Proposed	k-NN	CART	Proposed
March 25	66.80	66.13	65.74	92.29	87.42	92.91	70.22	69.55	71.97
March 26	67.30	66.80	69.70	92.67	86.67	92.95	70.72	70.97	74.70
March 27	64.22	64.55	66.25	91.42	78.38	91.57	69.18	67.51	71.73
March 28	64.97	62.43	67.15	90.34	70.93	89.92	64.06	61.27	64.99
March 29	62.84	60.76	67.60	89.79	70.05	90.22	61.47	59.93	61.30
March 30	68.76	65.43	69.01	90.88	81.76	90.96	71.93	71.51	76.71
March 31	66.97	65.43	69.88	92.17	87.21	93.20	69.68	69.14	73.02
Mean	65.98	64.50	67.90	91.36	80.35	91.67	68.18	67.13	70.63

The performance of the dynamic selection highly depends on how we define the local region of competence [16]. The standard method for this is using the k-NN with the Euclidean distance [19 –21]. One limitation of these methods is that they weight all input variables (link, day, weekday, time period) equally, even if there are input variables with different levels of relevance in the explanation of the target variable. Another problem is that the Euclidean measure is not compatible with modular nature of time features like weekdays, day hours and etc. The CART method [22], as another method for computing the region of competence has the limitation that we have has no upper bound on the number of samples in the region of competence. Our results show that the proposed custom-defined similarity measure is effective in computation of the region of competence and helps in achieving higher accuracies.

5.6 Comparison and robustness analysis of the proposed DCS

In order to analyse the robustness of the proposed model, we verify its robustness by performing “what if analysis" experiments on the SRN dataset; we assess the impact of different links for 21 days of test data. Experiments are repeated several times to reach more accurate results. We compare the performance of the proposed and previous methods for next-weeks prediction. The proposed method is compared against the baseline models including KNN and Levenberg-Marquardt Neural Network (LM), the modified classifier ranking method (Rank) [19], the ensemble learning model (CART) and the long term traffic prediction method based on deep learning [4] (DL) which considers the contextual factors. Table 3 gives this comparison results in terms of accuracy (A) and F-measure (F) for five randomly selected traffic links. Please note that, the best performer in each row is underlined. The result show that the proposed method outperforms the previous methods significantly.

Table 3
Comparision of the proposed and previous methods for next week prediction in terms of accuracy (A) and F-measure (F)

Model KNN LM Rank DL CART Proposed

Link A (F) A (F) A (F) A (F) A (F) A (F)

AL1495 78.81 (82.3) 75.88 (79.4) 80.9 (87.25) 78.23 (85.02) 79.49 (82.55) 85.75 (88.71)

AL1502 94.24 (91.72) 91.23 (88.71) 96.25 (92.56) 93.33 (90.15) 90.15 (88.43) 96.44 (95.04)

AL1572 89.76 (93.71) 86.77 (90.75) 91.8 (98.82) 89.4 (95.83) 89.67 (92.68) 96.45 (99.1)

AL1712 94.66 (92.71) 91.67 (89.68) 96.75 (91.21) 94.32 (89.18) 89.44 (85.89) 95.85 (92.63)

AL1731 91.14 (93.19) 88.15 (90.12) 93.2 (97.07) 91.14 (95.01) 88.04 (90.77) 94.08 (97.15)

Model	KNN	LM	Rank	DL	CART	Proposed
Link	A (F)	A (F)	A (F)	A (F)	A (F)	A (F)
AL1495	78.81 (82.3)	75.88 (79.4)	80.9 (87.25)	78.23 (85.02)	79.49 (82.55)	85.75 (88.71)
AL1502	94.24 (91.72)	91.23 (88.71)	96.25 (92.56)	93.33 (90.15)	90.15 (88.43)	96.44 (95.04)
AL1572	89.76 (93.71)	86.77 (90.75)	91.8 (98.82)	89.4 (95.83)	89.67 (92.68)	96.45 (99.1)
AL1712	94.66 (92.71)	91.67 (89.68)	96.75 (91.21)	94.32 (89.18)	89.44 (85.89)	95.85 (92.63)
AL1731	91.14 (93.19)	88.15 (90.12)	93.2 (97.07)	91.14 (95.01)	88.04 (90.77)	94.08 (97.15)

We used ensemble learning method that integrate weak learner to increase accuracy, the performance of the ensemble learning highly depends on definition of the local region of competence and we define the similarity measure. Beside, we used clustering method to grouping traffic links that increased the accuracy. The result shows that clustering the traffic links based on the proposed similarity measure has a significant impact on achieving higher levels of prediction accuracy. Also, results show that using the proposed similarity measure and the proposed definition of region of competence leads to a significant improvement in the prediction accuracy of all traffic variables.

6 Conclusions and future work

In this paper, we proposed an ensemble learning method for long-term traffic pattern forecasting. First, we propose a DCS approach. As the performance of DCS highly depends on how we define the local region of competence, we propose a new custom-defined similarity measure for computing the similarity of traffic links, weekdays and day hours, based on which a new definition of region of competence is proposed. Second, we employ two different link clustering methods. For each cluster, we train a DCS for predicting average journey time, average speed and traffic flow. Third, we propose a new variant of the oracle method for competence level computation. Since discrete values are closer to knowledge level representation than continuous ones and are easier to handle, we tackles the long-term traffic pattern forecasting as a classification problem for discretized traffic variables rather than a time-series problem.

The main reason for the performance improvement of the proposed prediction model is that we employ ensemble learning using the proposed DCS method, which considers the observed similarities between traffic profiles at different links, days and hours to obtain similarities between different values.

The robustness of our model was verified by experiments on SRN dataset from multiple angles, different links and different days. Since the traffic parameters are affected by some contextual factors and spatio-temporal data, in the future we plan to create and add meta-features to our model to achieve more accurate results.

Footnotes

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