This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Empirical Data Modeling in Software Engineering Using Radial Basis Functions
June 2000 (vol. 26 no. 6)
pp. 567-576

Abstract—Many empirical studies in software engineering involve relationships between various process and product characteristics derived via linear regression analysis. In this paper, we propose an alternative modeling approach using Radial Basis Functions (RBFs) which provide a flexible way to generalize linear regression function. Further, RBF models possess strong mathematical properties of universal and best approximation. We present an objective modeling methodology for determining model parameters using our recent SG algorithm, followed by a model selection procedure based on generalization ability. Finally, we describe a detailed RBF modeling study for software effort estimation using a well-known NASA dataset.

[1] J.W. Bailey and V.R. Basili, ”A Meta Model for Software Development Resource Expenditure,” Proc. Int'l Conf. Software Eng., pp. 107–115, Mar. 1981.
[2] C.M. Bishop, Neural Networks for Pattern Recognition. Clarendon Press, 1995.
[3] B. Boehm, Software Engineering Economics, Prentice Hall, Upper Saddle River, N.J., 1981, pp. 533-535.
[4] G.E.P. Box, W.G. Hunter, and J.S. Hunter, Statistics for Experimenters. John Wiley&Sons, 1978.
[5] J.H. Friedman, ”On Bias, Variance, 0/1-Loss, and the Curse-of-Dimensionality,” Data Mining and Knowledge Discovery, vol. 1, pp. 55–77, 1997.
[6] S. Geman, E. Bienenstock, and R. Doursat, ”Neural Networks and the Bias/Variance Dilemma,” Neural Computation, vol. 4, pp. 1–58, 1992.
[7] F. Girosi and T. Poggio, ”Networks and the Best Approximation Property,” Biological Cybernetics, vol. 63, pp. 169–176, 1990.
[8] A.L. Goel and M. Shin, ”Software Engineering Data Analysis Techniques,” Proc. Int'l Conf. Software Eng., May 1997.
[9] M. Kearns and D. Ron, ”Algorithmic Stability and Sanity-Check Bounds for Leave-One-Out Cross-Validation,” Proc. 10th Ann. Conf. Computational Learning Theory, pp. 152–162, 1997.
[10] C. Kemerer, "An Empirical Validation of Software Cost Estimation Models," Comm. ACM, vol. 30, pp. 416-429, May 1987.
[11] L.P.W. Land, C. Saucer, and R. Jeffery, ”Validating the Defect Detection Performance Advantage of Group Designs for Software Reviews: Report of a Laboratory Experiment Using Program Code,” Proc. European Software Eng. Conf. Foundations of Software Eng., pp. 294–309, Sep. 1997.
[12] A. Porter and L. Votta, ”Understanding the Sources of Variation in Software Inspections,” ACM Trans. Software Eng. and Methodology, vol. 7, no. 1, pp. 41–79, Jan. 1998.
[13] M.J.D. Powell, ”The Theory of Radial Basis Function Approximation in 1990,” Advances in Numerical Analysis, vol. 2: Wavelets, Subdivision—Algorithms and Radial Basis Functions, pp. 105–210, W.A. Light, ed., Oxford Univ. Press, 1992.
[14] B.D. Ripley, ”Neural Networks and Related Methods for Classification,” J. Royal Statistical Soc.—Series B, pp. 409–456, 1994.
[15] M.J. Shepperd and C. Schofield, “Estimating Software Project Effort Using Analogies,” IEEE Trans. Software Eng., vol. 23, pp. 736-743, 1997.
[16] M. Shin, “Design and Evaluation of Radial Basis Function Model For Function Approximation,” PhD thesis, Syracuse Univ., May 1998.
[17] M. Shin and A.L. Goel, ”Radial Basis Function Model Development and Analysis Using the SG Algorithm,” technical report, Dept. of Electrical Eng. and Computer Science, Syracuse Univ., June 1998.
[18] L. Xu, A. Kizyzak, and A.L. Yuille, ”On Radial Basis Function Nets and Kernel Regression: Statistical Consistency, Convergence Rates, and Receptive Field Size,” Neural Networks, vol. 7, no. 4, pp. 609–628, 1994.

Index Terms:
Empirical modeling, radial basis functions, data analysis, software effort estimation.
Citation:
Miyoung Shin, Amrit L. Goel, "Empirical Data Modeling in Software Engineering Using Radial Basis Functions," IEEE Transactions on Software Engineering, vol. 26, no. 6, pp. 567-576, June 2000, doi:10.1109/32.852743
Usage of this product signifies your acceptance of the Terms of Use.