The lack of some traffic flow data seriously affects the quality of data collection and analysis in the traffic system. Completing the missing data is one of the most important steps in achieving the functions of intelligent transportation systems. In this paper an approach based on fuzzy C-means (FCM) imputes missing traffic volume data in loop detectors. With spatial–temporal correlation between detectors, the conventional vector-based data structure is first transformed into a matrix-based data pattern. Then, the genetic algorithm is applied to optimize the parameters of cluster size and weighting factor in the FCM model. Finally, the actual traffic flow volume collected at different locations is designed as a testing data set, and two indicators including root mean square error and relative accuracy are used to evaluate the imputation performance of the proposed method by comparison with some conventional methods (multiple linear regression, autoregressive integrated moving average model, and average historical method) by missing ratio. The applications in four scenarios demonstrate that the FCM-based imputation method outperforms conventional methods.
Get full access to this article
View all access options for this article.
References
1.
BoylesS.Comparison of Interpolation Methods for Missing Traffic Volume Data. Presented at 90th Annual Meeting of the Transportation Research Board, Washington, D.C., 2011.
2.
NiD., LeonardJ. D.II, GuinA., and FengC.Multiple Imputation Scheme for Overcoming the Missing Values and Variability Issues in ITS Data. Journal of Transportation Engineering, Vol. 131, 2005, pp. 931–938.
3.
PatelR.Intelligent Transportation: Serving the User Through Deployment. Annual Meeting of ITS, Washington, D.C., 1995, pp. 15–17.
4.
QuL., LiL., ZhangY., and HuJ.PPCA-Based Missing Data Imputation for Traffic Flow Volume: A Systematical Approach. IEEE Transactions on Intelligent Transportation Systems, Vol. 10, No. 3, 2009, pp. 512–522.
5.
ChenJ., and ShaoJ.Nearest Neighbor Imputation for Survey Data. Journal of Official Statistics, Vol. 16, No. 2, 2000, pp. 113–131.
6.
NguyenL.H., and SchererW.T.Imputation Techniques to Account for Missing Data in Support of Intelligent Transportation Systems Applications. Technical Report UVACTS-13-0-78. Center for Transportation Studies, University of Virginia, Charlottesville, 2003.
7.
GoldD.L., TurnerS. M., GajewskiB.J., and SpiegelmanC.Imputing Missing Values in ITS Data Archives for Intervals Under 5 Minutes. Presented at 80th Annual Meeting of the Transportation Research Board, Washington, D.C., 2000.
8.
ZhongM., LingrasP., and SharmaS.Estimation of Missing Traffic Counts Using Factor, Genetic, Neural, and Regression Techniques. Transportation Research Part C, Vol. 12, 2004, pp. 139–166.
9.
BaharaeenS., and MasudA.S.A Computer Program for Time Series Forecasting Using Single and Double Exponential Smoothing Techniques. Computers and Industrial Engineering, Vol. 11, 1986, pp. 151–155.
10.
HoltC. C.Forecasting Seasonals and Trends by Exponentially Weighted Moving Averages. International Journal of Forecasting, Vol. 20, 2004, pp. 5–10.
11.
de BoorC.A Practical Guide to Splines.Springer Verlag, New York, 1978.
12.
ChenC., KwonJ., RiceJ., SkabardonisA., and VaraiyaP.Detecting Errors and Imputing Missing Data for Single-Loop Surveillance Systems. In Transportation Research Record: Journal of the Transportation Research Board, No. 1855, Transportation Research Board of the National Academy of Sciences, Washington, D.C., 2003, pp. 160–167.
13.
Al-DeekH. M., and ChandraC. V. S. R.New Algorithms for Filtering and Imputation of Real-Time and Archived Dual-Loop Detector Data in I-4 Data Warehouse. In Transportation Research Record: Journal of the Transportation Research Board, No. 1867, Transportation Research Board of the National Academy of Sciences, Washington, D.C., 2004, pp. 116–126.
14.
GhoshB., BasuB., and O'MahonyM. M.Time-Series Modeling for Forecasting Vehicular Traffic Flow in Dublin. Presented at 84th Annual Meeting of the Transportation Research Board, Washington, D.C., 2005.
15.
RedfernE.J., WatsonS. M., TightM.R., and ClarkS.D.A Comparative Assessment of Current and New Techniques for Detecting Outliers and Estimating Missing Values in Transport Related Time Series Data. Presented at Highways and Planning Summer Annual Meeting, Institute of Science and Technology, University of Manchester, England, 1993.
16.
RamseyB., and HaydenG.AutoCounts: A Way to Analyze Automatic Traffic Count Data. Traffic Engineering and Control, Vol. 35, No. 4, 1994, pp. 245.
17.
WilliamsB.M., and HoelL.A.Modeling and Forecasting Vehicular Traffic Flow as a Seasonal ARIMA Process: Theoretical Basis and Empirical Results. Journal of Transportation Engineering, Vol. 129, No. 6, 2003, pp. 664–672.
18.
BoxG., and JenkinsJ.Time Series Analysis: Forecasting and Control.Holden-Day, San Francisco, Calif., 1970.
19.
LiL., LiY., and LiZ.Efficient Missing Data Imputing for Traffic Flow by Considering Temporal and Spatial Dependence. Transportation Research Part C, Vol. 34, 2013, pp. 108–120.
20.
TanH., YuankaiW., FengJ., WangW., and RanB.Traffic Missing Data Completion with Spatial–Temporal Correlations. Presented at 93rd Annual Meeting of the Transportation Research Board, Washington, D.C., 2014.
21.
Di NuovoA. G.Missing Data Analysis with Fuzzy C-Means: A Study of Its Application in a Psychological Scenario. Expert Systems with Applications, Vol. 38, No. 6, 2011, pp. 6793–6797.
22.
HathawayR.J., and BezdekJ.C.Clustering Incomplete Relational Data Using the Non-Euclidean Relational Fuzzy C-Means Algorithm. Pattern Recognition Letters, Vol. 23, 2002, pp. 151–160.
23.
LiaoZ., LuX., YangT., and WangH.Missing Data Imputation: A Fuzzy K-Means Clustering Algorithm over Sliding Window. 6th International Conference on Fuzzy Systems Knowledge Discovery, Tianjin, China, Aug. 2009, pp. 133–137.
24.
LiD., GuH., and ZhangL.Y.A Fuzzy C-Means Clustering Algorithm Based on Nearest-Neighbor Intervals for Incomplete Data. Expert Systems with Applications, Vol. 37, No. 10, 2010, pp. 6942–6947.
25.
TimmH., DoringC., and KruseR.Different Approaches to Fuzzy Clustering of Incomplete Datasets. International Journal of Approximate Reasoning, Vol. 35, No. 3, 2004, pp. 239–249.
26.
LiD., DeogunJ., SpauldingW., and ShuartB.Towards Missing Data Imputation: A Study of Fuzzy K-Means Clustering Method. Rough Sets and Current Trends in Computing, Vol. 3066, 2004, pp. 573–579.
27.
HollandJ. H.Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor, 1975.
28.
AbdellaM., and MarwalaT.The Use of Genetic Algorithms and Neural Networks to Approximate Missing Data in Database. 3rd International Conference on Computational Cybernetics, April 2005, pp. 207–212.
29.
MarwalaT.Computational Intelligence for Missing Data Imputation, Estimation and Management: Knowledge Optimization Techniques.IGI Publishing, Hershey, Pa., 2009.
