An efficient realization of deep learning for traffic data imputation

Traffic data provide the basis for both research and applications in transportation control, management, and evaluation, but real-world traffic data collected from loop detectors or other sensors often contain corrupted or missing data points which need to be imputed for traffic analysis. For this end, here we propose a deep learning model named denoising stacked autoencoders for traffic data imputation. We tested and evaluated the model performance with consideration of both temporal and spatial factors. Through these experiments and evaluation results, we developed an algorithm for efficient realization of deep learning for traffic data imputation by training the model hierarchically using the full set of data from all vehicle detector stations. Using data provided by Caltrans PeMS, we have shown that the mean absolute error of the proposed realization is under 10 veh/5-min, a better performance compared with other popular models: the history model, ARIMA model and BP neural network model. We further investigated why the deep leaning model works well for traffic data imputation by visualizing the features extracted by the first hidden layer. Clearly, this work has demonstrated the effectiveness as well as efficiency of deep learning in the field of traffic data imputation and analysis.     

Rationalizing Reliable Imputation Durations of Genetically Designed Time Delay Neural Network and Locally Weighted Regression Models

Abstract

Estimating missing values is known as data imputation. Previous research has shown that genetic algorithms (GAs) designed locally weighted regression (LWR) and time delay neural network (TDNN) models can generate more accurate hourly volume imputations for a period of 12 successive hours than traditional methods used by highway agencies. It would be interesting and important to further refine the models for imputing larger missing intervals. Therefore, a large number of genetically designed LWR and TDNN models are developed in this study and used to impute up to a week-long missing interval (168 hours) for sample traffic counts obtained from various groups of roads in Alberta, Canada. It is found that road type and functional class have considerable influences on reliable imputations. The reliable imputation durations range from 4–5 days for traffic counts with most unstable patterns to over 10 days for those with most stable patterns. The study results clearly show that calibrated GA-designed models can provide reliable imputations for missing data with ‘block patterns’, and demonstrate their further potentials in traffic data programs.     

Short-term traffic flow rate forecasting based on identifying similar traffic patterns

The ability to timely and accurately forecast the evolution of traffic is very important in traffic management and control applications. This paper proposes a non-parametric and data-driven methodology for short-term traffic forecasting based on identifying similar traffic patterns using an enhanced K-nearest neighbor (K-NN) algorithm. Weighted Euclidean distance, which gives more weight to recent measurements, is used as a similarity measure for K-NN. Moreover, winsorization of the neighbors is implemented to dampen the effects of dominant candidates, and rank exponent is used to aggregate the candidate values. Robustness of the proposed method is demonstrated by implementing it on large datasets collected from different regions and by comparing it with advanced time series models, such as SARIMA and adaptive Kalman Filter models proposed by others. It is demonstrated that the proposed method reduces the mean absolute percent error by more than 25%. In addition, the effectiveness of the proposed enhanced K-NN algorithm is evaluated for multiple forecast steps and also its performance is tested under data with missing values. This research provides strong evidence suggesting that the proposed non-parametric and data-driven approach for short-term traffic forecasting provides promising results. Given the simplicity, accuracy, and robustness of the proposed approach, it can be easily incorporated with real-time traffic control for proactive freeway traffic management.     

Overview of missing physical commodity trade data and its imputation using data augmentation

The physical aspects of commodity trade are becoming increasingly important on a global scale for transportation planning, demand management for transportation facilities and services, energy use, and environmental concerns. Such aspects (for example, weight and volume) of commodities are vital for logistics industry to allow for medium-to-long term planning at the strategic level and identify commodity flow trends. However, incomplete physical commodity trade databases impede proper analysis of trade flow between various countries. The missing physical values could be due to many reasons such as, (1) non-compliance of reporter countries with the prescribed regulations by World Customs Organization (WCO) (2) confidentiality issues, (3) delays in processing of data, or (4) erroneous reporting. The traditional missing data imputation methods, such as the substitution by mean, substitution by linear interpolation/extrapolation using adjacent points, the substitution by regression, and the substitution by stochastic regression, have been proposed in the context of estimating physical aspects of commodity trade data. However, a major demerit of these single imputation methods is their failure to incorporate uncertainty associated with missing data. The use of computationally complex stochastic methods to improve the accuracy of imputed data has recently become possible with the advancement of computer technology. Therefore, this study proposes a sophisticated data augmentation algorithm in order to impute missing physical commodity trade data. The key advantage of the proposed approach lies in the fact that instead of using a point estimate as the imputed value, it simulates a distribution of missing data through multiple imputations to reflect uncertainty and to maintain variability in the data. This approach also provides the flexibility to include fundamental distributional property of the variables, such as physical quantity, monetary value, price elasticity of demand, price variation, and product differentiation, and their correlations to generate reasonable average estimates of statistical inferences. An overview and limitations of most commonly used data imputation approaches is presented, followed by the theoretical basis and imputation procedure of the proposed approach. Lastly, a case study is presented to demonstrate the merits of the proposed approach in comparison to traditional imputation methods.     

Heteroscedastic Gaussian processes for uncertainty modeling in large-scale crowdsourced traffic data

Accurately modeling traffic speeds is a fundamental part of efficient intelligent transportation systems. Nowadays, with the widespread deployment of GPS-enabled devices, it has become possible to crowdsource the collection of speed information to road users (e.g. through mobile applications or dedicated in-vehicle devices). Despite its rather wide spatial coverage, crowdsourced speed data also brings very important challenges, such as the highly variable measurement noise in the data due to a variety of driving behaviors and sample sizes. When not properly accounted for, this noise can severely compromise any application that relies on accurate traffic data. In this article, we propose the use of heteroscedastic Gaussian processes (HGP) to model the time-varying uncertainty in large-scale crowdsourced traffic data. Furthermore, we develop a HGP conditioned on sample size and traffic regime (SSRC-HGP), which makes use of sample size information (probe vehicles per minute) as well as previous observed speeds, in order to more accurately model the uncertainty in observed speeds. Using 6 months of crowdsourced traffic data from Copenhagen, we empirically show that the proposed heteroscedastic models produce significantly better predictive distributions when compared to current state-of-the-art methods for both speed imputation and short-term forecasting tasks.     

A hybrid approach to integrate fuzzy C-means based imputation method with genetic algorithm for missing traffic volume data estimation

Although various innovative traffic sensing technologies have been widely employed, incomplete sensor data is one of the most major problems to significantly degrade traffic data quality and integrity. In this study, a hybrid approach integrating the Fuzzy C-Means (FCM)-based imputation method with the Genetic Algorithm (GA) is develop for missing traffic volume data estimation based on inductance loop detector outputs. By utilizing the weekly similarity among data, the conventional vector-based data structure is firstly transformed into the matrix-based data pattern. Then, the GA is applied to optimize the membership functions and centroids in the FCM model. The experimental tests are conducted to verify the effectiveness of the proposed approach. The traffic volume data collected at different temporal scales were used as the testing dataset, and three different indicators, including root mean square error, correlation coefficient, and relative accuracy, are utilized to quantify the imputation performance compared with some conventional methods (Historical method, Double Exponential Smoothing, and Autoregressive Integrated Moving Average model). The results show the proposed approach outperforms the conventional methods under prevailing traffic conditions.     

Integrated model for traffic flow forecasting under rainy conditions

Inclement weather, such as heavy rain, significantly affects road traffic flow operation, which may cause severe congestion in road networks in cities. This study investigates the effect of inclement weather, such as rain events, on traffic flow and proposes an integrated model for traffic flow parameter forecasting during such events. First, an analysis of historical observation data indicates that the forecasting error of traffic flow volume has a significant linear correlation with mean precipitation, and thus, forecasting accuracy can be considerably improved by applying this linear correlation to correct forecasting values. An integrated online precipitation‐correction model was proposed for traffic flow volume forecasting based on these findings. We preprocessed precipitation data transformation and used outlier detection techniques to improve the efficiency of the model. Finally, an integrated forecasting model was designed through data fusion methods based on the four basic forecasting models and the proposed online precipitation‐correction model. Results of the model validation with the field data set show that the designed model is better than the other models in terms of overall accuracy throughout the day and under precipitation. However, the designed model is not always ideal under heavy rain conditions. Copyright © 2016 John Wiley & Sons, Ltd.     

Statistical methods for detecting nonlinearity and non-stationarity in univariate short-term time-series of traffic volume

Short-term traffic volume data are characterized by rapid and intense fluctuations with frequent shifts to congestion. Currently, research in short-term traffic forecasting deals with these phenomena either by smoothing them or by accounting for them by nonlinear models. But, these approaches lead to inefficient predictions particularly when the data exhibit intense oscillations or frequent shifts to boundary conditions (congestion). This paper offers a set of tools and methods to assess on underlying statistical properties of short-term traffic volume data, a topic that has largely been overlooked in traffic forecasting literature. Results indicate that the statistical characteristics of traffic volume can be identified from prevailing traffic conditions; for example, volume data exhibit frequent shifts from deterministic to stochastic structures as well as transitions between cyclic and strongly nonlinear behaviors. These findings could be valuable in the implementation of a variable prediction strategy according to the statistical characteristics of the prevailing traffic volume states.     

A spatiotemporal correlative k-nearest neighbor model for short-term traffic multistep forecasting

The k-nearest neighbor (KNN) model is an effective statistical model applied in short-term traffic forecasting that can provide reliable data to guide travelers. This study proposes an improved KNN model to enhance forecasting accuracy based on spatiotemporal correlation and to achieve multistep forecasting. The physical distances among road segments are replaced with equivalent distances, which are defined by the static and dynamic data collected from real road networks. The traffic state of a road segment is described by a spatiotemporal state matrix instead of only a time series as in the original KNN model. The nearest neighbors are selected according to the Gaussian weighted Euclidean distance, which adjusts the influences of time and space factors on spatiotemporal state matrices. The forecasting accuracies of the improved KNN and of four other models are compared, and experimental results indicate that the improved KNN model is more appropriate for short-term traffic multistep forecasting than the other models are. This study also discusses the application of the improved KNN model in a time-varying traffic state.     

Modelling user satisfaction in public transport systems considering missing information

Collecting data to obtain insights into customer satisfaction with public transport services is very time-consuming and costly. Many factors such as service frequency, reliability and comfort during the trip have been found important drivers of customer satisfaction. Consequently, customer satisfaction surveys are quite lengthy, resulting in many interviews not being completed within the aboard time of the passengers/respondents. This paper questions as to whether it is possible to reduce the amount of information collected without a compromise on insights. To address this research question, we conduct a comparative analysis of different Ordered Probit models: one with a full list of attributes versus one with partial set of attributes. For the latter, missing information was imputed using three different methods that are based on modes, single imputations using predictive models and multiple imputation. Estimation results show that the partial model using the multiple imputation method behaves in a similar way to the model that is based on the full survey. This finding opens an opportunity to reduce interview time which is critical for most customer satisfaction surveys.

     

Use of sequential learning for short-term traffic flow forecasting

Accurate short-term traffic flow forecasting has become a crucial step in the overall goal of better road network management. Previous research [H. Kirby, M. Dougherty, S. Watson, Should we use neural networks or statistical models for short term motorway traffic forecasting, International Journal of Forecasting 13 (1997) 43–50.] has demonstrated that a straightforward application of neural networks can be used to forecast traffic flows along a motorway link. The objective of this paper is to report on the application and performance of an alternative neural computing algorithm which involves ‘sequential or dynamic learning’ of the traffic flow process. Our initial work [H. Chen, S. Clark, M.S. Dougherty, S.M. Grant-Muller, Investigation of network performance prediction, Report on Dynamic Neural Network and Performance Indicator development, Institute for Transport Studies, University of Leeds Technical Note 418, 1998 (unpublished)] was based on simulated data (generated using a Hermite polynomial with random noise) that had a profile similar to that of traffic flows in real data. This indicated the potential suitability of dynamic neural networks with traffic flow data. Using the Kalman filter type network an initial application with M25 motorway flow data suggested that a percentage absolute error (PAE) of approximately 9.5% could be achieved for a network with five hidden units (compared with 11% for the static neural network model). Three different neural networks were trained with all the data (containing an unknown number of incidents) and secondly using data wholly obtained around incidents. Results showed that from the three different models, the ‘simple dynamic model’ with the first five units fixed (and subsequent hidden units distributed amongst these) had the best forecasting performance. Comparisons were also made of the networks’ performance on data obtained around incidents. More detailed analysis of how the performance of the three networks changed through a single day (including an incident) showed that the simple dynamic model again outperformed the other two networks in all time periods. The use of ‘piecewise’ models (i.e. where a different model is selected according to traffic flow conditions) for data obtained around incidents highlighted good performance again by the simple dynamic network. This outperformed the standard Kalman filter neural network for a medium-sized network and is our overall recommendation for any future application.     

Local online kernel ridge regression for forecasting of urban travel times

Accurate and reliable forecasting of traffic variables is one of the primary functions of Intelligent Transportation Systems. Reliable systems that are able to forecast traffic conditions accurately, multiple time steps into the future, are required for advanced traveller information systems. However, traffic forecasting is a difficult task because of the nonlinear and nonstationary properties of traffic series. Traditional linear models are incapable of modelling such properties, and typically perform poorly, particularly when conditions differ from the norm. Machine learning approaches such as artificial neural networks, nonparametric regression and kernel methods (KMs) have often been shown to outperform linear models in the literature. A bottleneck of the latter approach is that the information pertaining to all previous traffic states must be contained within the kernel, but the computational complexity of KMs usually scales cubically with the number of data points in the kernel. In this paper, a novel kernel-based machine learning (ML) algorithm is developed, namely the local online kernel ridge regression (LOKRR) model. Exploiting the observation that traffic data exhibits strong cyclic patterns characterised by rush hour traffic, LOKRR makes use of local kernels with varying parameters that are defined around each time point. This approach has 3 advantages over the standard single kernel approach: (1) It allows parameters to vary by time of day, capturing the time varying distribution of traffic data; (2) It allows smaller kernels to be defined that contain only the relevant traffic patterns, and; (3) It is online, allowing new traffic data to be incorporated as it arrives. The model is applied to the forecasting of travel times on London’s road network, and is found to outperform three benchmark models in forecasting up to 1 h ahead.     

A technique for the investigation of scheme benefits in large-scale transport networks

Existing methods of evaluating large-scale transport networks involve the use of mathematical models of traffic flow which are generally both large and complex. However, the time and cost involved in the use of these models normally restricts their use for the detailed forecasting of traffic flows and costs to the assessment of a relatively small number of alternative patterns of overall investment. In order to evaluate the individual projects and groups of projects which go to make up an overall investment plan, it is, therefore, usually necessary to make simplifying assumptions about the influence of any one project on the overall traffic pattern, so as to isolate it from the influence of neighbouring projects. These assumptions generally result in the loss of a certain amount of the detail normally available from a standard model, and the task of assessing the relative value of different projects and the amount of interaction between them is made more difficult.This paper describes a new technique, designed to permit the evaluation of individual projects whilst still retaining the level of detail available from a full-scale mathematical model. The aim has been to produce a cheap and easy-to-use technique, capable of producing substantially the same results as a standard model. The technique uses newly developed computer algorithms which short-cut the full-scale model by forecasting the changes in an existing travel pattern resulting from the influence of a particular project. Initial tests suggest that approaching the problem in this way can save up to 70% of the computing time and costs involved in the use of a standard model for the evaluation of individual projects.The technique as described here is envisaged as a tool for aiding strategic investment decisions. It can, however, provide data for more detailed investigations, and could, with modifications, carry out these investigations on smaller problems than those for which it was originally designed.Crown copyright reserved, 1973     

Analysis of peak and non‐peak traffic forecasts using combined models

Accurate and timely traffic forecasting is crucial to effective management of intelligent transportation systems (ITS). To predict travel time index (TTI) data, we select six baseline individual predictors as basic combination components. Applying the one‐step‐ahead out‐of‐sample forecasts, the paper proposes several linear combined forecasting techniques. States of traffic situations are classified into peak and non‐peak periods. Based on detailed data analyses, some practical guidance and comments are given in what situation a combined model is better than an individual model or other types of combined models. Indicating which model is more appropriate in each state, persuasive comparisons demonstrate that the combined procedures can significantly reduce forecast error rates. It reveals that the approaches are practically promising in the field. To the best of our knowledge, it is the first time to systematically investigate these approaches in peak and non‐peak traffic forecasts. The studies can provide a reference for optimal forecasting model selection in each period. Copyright © 2010 John Wiley & Sons, Ltd.     

Real-time traffic state estimation in urban corridors from heterogeneous data

In recent years, rapid advances in information technology have led to various data collection systems which are enriching the sources of empirical data for use in transport systems. Currently, traffic data are collected through various sensors including loop detectors, probe vehicles, cell-phones, Bluetooth, video cameras, remote sensing and public transport smart cards. It has been argued that combining the complementary information from multiple sources will generally result in better accuracy, increased robustness and reduced ambiguity. Despite the fact that there have been substantial advances in data assimilation techniques to reconstruct and predict the traffic state from multiple data sources, such methods are generally data-driven and do not fully utilize the power of traffic models. Furthermore, the existing methods are still limited to freeway networks and are not yet applicable in the urban context due to the enhanced complexity of the flow behavior. The main traffic phenomena on urban links are generally caused by the boundary conditions at intersections, un-signalized or signalized, at which the switching of the traffic lights and the turning maneuvers of the road users lead to shock-wave phenomena that propagate upstream of the intersections. This paper develops a new model-based methodology to build up a real-time traffic prediction model for arterial corridors using data from multiple sources, particularly from loop detectors and partial observations from Bluetooth and GPS devices.     

Short-term prediction of border crossing time and traffic volume for commercial trucks: A case study for the Ambassador Bridge

Short-term forecasting of traffic characteristics, such as traffic flow, speed, travel time, and queue length, has gained considerable attention from transportation researchers and practitioners over past three decades. While past studies primarily focused on traffic characteristics on freeways or urban arterials this study places particular emphasis on modeling the crossing time over one of the busiest US–Canada bridges, the Ambassador Bridge. Using a month-long volume data from Remote Traffic Microwave Sensors and a yearlong Global Positioning System data for crossing time two sets of ANN models are designed, trained, and validated to perform short-term predictions of (1) the volume of trucks crossing the Ambassador Bridge and (2) the time it takes for the trucks to cross the bridge from one side to the other. The prediction of crossing time is contingent on truck volume on the bridge and therefore separate ANN models were trained to predict the volume. A multilayer feedforward neural network with backpropagation approach was used to train the ANN models. Predicted crossing times from the ANNs have a high correlation with the observed values. Evaluation indicators further confirmed the high forecasting capability of the trained ANN models. The ANN models from this study could be used for short-term forecasting of crossing time that would support operations of ITS technologies.     

Short‐term traffic forecasting: Overview of objectives and methods

In the last two decades, the growing need for short‐term prediction of traffic parameters embedded in a real‐time intelligent transportation systems environment has led to the development of a vast number of forecasting algorithms. Despite this, there is still not a clear view about the various requirements involved in modelling. This field of research was examined by disaggregating the process of developing short‐term traffic forecasting algorithms into three essential clusters: the determination of the scope, the conceptual process of specifying the output and the process of modelling, which includes several decisions concerning the selection of the proper methodological approach, the type of input and output data used, and the quality of the data. A critical discussion clarifies several interactions between the above and results in a logical flow that can be used as a framework for developing short‐term traffic forecasting models.     

Phase transition model of non-stationary traffic flow: Definition,properties and solution method

We consider the problem of modeling traffic phenomena at a macroscopic level. Increasing availability of streaming probe data allowing the observation of non-stationary traffic motivates the development of models capable of leveraging this information. We propose a phase transition model of non-stationary traffic in conservation form, capable of propagating joint measurements from fixed and mobile sensors, to model complex traffic phenomena such as hysteresis and phantom jams, and to account for forward propagation of information in congested traffic. The model is shown to reduce to the Lighthill–Whitham–Richards model within each traffic phase for the case of stationary states, and to have a physical mesoscopic interpretation in terms of drivers’ behavior. A corresponding discrete formulation appropriate for practical implementation is shown to provide accurate numerical solution to the proposed model. The performance of the model introduced is assessed on benchmark cases and on experimental vehicle trajectories from the NGSIM datasets.     

Identification of vehicle sensor locations for link-based network traffic applications

Information on link flows in a vehicular traffic network is critical for developing long-term planning and/or short-term operational management strategies. In the literature, most studies to develop such strategies typically assume the availability of measured link traffic information on all network links, either through manual survey or advanced traffic sensor technologies. In practical applications, the assumption of installed sensors on all links is generally unrealistic due to budgetary constraints. It motivates the need to estimate flows on all links of a traffic network based on the measurement of link flows on a subset of links with suitably equipped sensors. This study, addressed from a budgetary planning perspective, seeks to identify the smallest subset of links in a network on which to locate sensors that enables the accurate estimation of traffic flows on all links of the network under steady-state conditions. Here, steady-state implies that the path flows are static. A “basis link” method is proposed to determine the locations of vehicle sensors, by using the link-path incidence matrix to express the network structure and then identifying its “basis” in a matrix algebra context. The theoretical background and mathematical properties of the proposed method are elaborated. The approach is useful for deploying long-term planning and link-based applications in traffic networks.     

Adaptive traffic parameter prediction: Effect of number of states and transferability of models

Traffic parameters can show shifts due to factors such as weather, accidents, and driving characteristics. This study develops a model for predicting traffic speeds under these abrupt changes within regime switching framework. The proposed approach utilizes Hidden Markov, Expectation Maximization, Recursive Least Squares Filtering, and ARIMA methods for an adaptive forecasting method. The method is compared with naive and mean updating linear and nonlinear time series models. The model is fitted and tested extensively using 1993 I-880 loop data from California and January 2014 INRIX data from Virginia. Analysis for number of states, impact of number of states on forecasting, prediction scope, and transferability of the model to different locations are investigated. A 5-state model is found to be providing best results. Developed model is tested for 1-step to 45-step forecasts. The accuracy of predictions are improved until 15-step over nonadaptive and mean adaptive models. Except 1-step predictions, the model is found to be transferable to different locations. Even if the developed model is not retrained on different datasets, it is able to provide better or close results with nonadaptive and adaptive models that are retrained on the corresponding dataset.