The week's pick
Reseach Article
A Generalized Piecewise Regression for Transportation Models
| International Journal of Computer Applications |
| Foundation of Computer Science (FCS), NY, USA |
| Volume 129 - Number 17 |
| Year of Publication: 2015 |
| Authors: Al-Sayed Ahmed Al-Sobky, Ibrahim M.I. Ramadan |
10.5120/ijca2015907139
|
Al-Sayed Ahmed Al-Sobky, Ibrahim M.I. Ramadan . A Generalized Piecewise Regression for Transportation Models. International Journal of Computer Applications. 129, 17 ( November 2015), 16-22. DOI=10.5120/ijca2015907139
Abstract
This paper introduces a new piecewise regression methodology that can be used when linear regression fails to represent data. Effort can be saved to determine the best non-linear model shape using this methodology. Therefore, in this paper a nonlinear relationship is introduced using only one independent variable by a simple and direct way. The new approach depends on dividing the data set into several groups and then estimating the best line or segment for each group to perform a continuous broken line. The locations of breakpoints are determined by minimizing the sum of squared errors while the number of segments is determined by maximizing the adjusted coefficient of determination. The proposed approach can be used in many transportation applications such as trip generation models, zonal trip rates, nonlinear correlation coefficient, accident modeling, and traffic characteristics models. The proposed approach was tested against many practical examples and found that it can describe most of the transportation relationships properly and can decrease the number of variables used in the transportation modeling process. The proposed approach can be extended in the future to get the nonlinear relationship using more than one independent variable to cover the rest of transportation applications.
References
- Lyman ott, 1988: “An Introduction to statistical methods and data analysis” , PWS- Kent publishing company, Boston , USA.
- Greene, W, 2000,“Econometric Analysis, Upper Saddle River”: Prentice-Hall.
- Jang, J.S.R., 1993, “ ANFIS: Adaptive-network-based fuzzy inference system”, IEEE Trans. Syst., Man, Cybern. 23, 665-685.
- MathworksInc, 2014, MATLAB 2014a User’s Guide.
- R.J. Oosterbaan, D.P.Sharma, K.N.Singh and K.V.G.K.Rao, 1990, Crop production and soil salinity: evaluation of field data from India by segmented linear regression. In: Proceedings of the Symposium on Land Drainage for Salinity Control in Arid and Semi-Arid Regions, February 25th to March 2nd, 1990, Cairo, Egypt, Vol. 3, Session V, p. 373 - 383.
- Ryan, Sandra E.; Porth, Laurie S, 2007, “A tutorial on the piecewise regression approach applied to bed load transport data”. Gen. Tech. Rep. RMRS-GTR-189. Fort Collins, CO: U.S. Department of Agriculture, Forest Service, Rocky Mountain Research Station. 41 p.
- Tapas Kanungo, et al. An Efficient k-Means, 2002,“Clustering Algorithm: Analysis and Implementation”. IEEE Transactions On Pattern Analysis And Machine Intelligence, Vol. 24, No. 7.
- Subhagata Chattopadhyay, et al, 2011, “A COMPARATIVE STUDY OF FUZZY C-MEANS
- Gunnar Carlsson ,FacundoM´emoli , 2010, “Characterization, Stability and Convergence of Hierarchical Clustering Methods”, Journal of Machine Learning Research 11 (2010) 1425-1470
- Charles A. Bouman, et al, 2005, “CLUSTER: An Unsupervised Algorithm for Modeling Gaussian Mixtures”, http://www.ece.purdue.edu/~bouman
- Harald Hruschka, and Martin Natter, 1992, “ Using Neural network for clustering based market segmentation”, Forschungsbericht/ Research memorandum No 307.
- Hartigan, J., & Wang, M. A K-means clustering algorithm, 1979, Applied Statistics, 28, 100–108.
- Sandra E. Ryan, and Laurie S. Porth, 2007, “ A Tutorial on the Piecewise Regression Approach Applied to Bedload Transport Data”, General Technical Report RMRS-GTR-189
Index Terms
Keywords