An Approach to Modeling Domain-Wide Information, based on Limited Points’ Data – Part II
American Journal of Software Engineering and Applications
Volume 2, Issue 2, April 2013, Pages: 40-48
Received: Mar. 28, 2013;
Published: Apr. 2, 2013
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John Charlery, Dept. of Computer Science, Mathematics & Physics, Faculty of Science and Technology, University of the West Indies, Cave Hill Campus, Bridgetown, Barbados BB11000
Chris D. Smith, Dept. of Computer Science, Mathematics & Physics, Faculty of Science and Technology, University of the West Indies, Cave Hill Campus, Bridgetown, Barbados BB11000
Predicting values at data points in a specified region when only a few values are known is a perennial problem and many approaches have been developed in response. Interpolation schemes provide some success and are the most widely used among the approaches. However, none of those schemes incorporates historical aspects in their formulae. This study presents an approach to interpolation, which utilizes the historical relationships existing between the data points in a region of interest. By combining the historical relationships with the interpolation equations, an algorithm for making predictions over an entire domain area, where data is known only for some random parts of that area, is presented. A performance analysis of the algorithm indicates that even when provided with less than ten percent of the domain’s data, the algorithm outperforms the other popular interpolation algorithms when more than fifty percent of the domain’s data is provided to them.
Chris D. Smith,
An Approach to Modeling Domain-Wide Information, based on Limited Points’ Data – Part II, American Journal of Software Engineering and Applications.
Vol. 2, No. 2,
2013, pp. 40-48.
N. I. Fisher, T. Lewis, B. J. J. Embleton, Statistical Analysis of Spherical Data, Cambridge University Press, 1987.
D. Dorsel, T. La Breche, Kriging. , January 2009.
R. V. Jesus, Kriging. An Accompanied Example in IDRISI, GIS Centrum, University of Lund for Oresund, Summer University, 2003.
M.L. Stein, Interpolation of Spatial Data. Some Theory for Kriging, Springer, New York, 1999.
W.C.M. Van Beers, J. P.C. Kleijnen, Kriging Interpolation in Simulation . A Survey, in. R .G. Ingalls, M. D. Rossetti, J. S. Smith, and B. A. Peters (Eds.), Proceedings of the 2004 Winter Simulation Conference,Washington, DC, 2004, pp. 113-121.
D. T. Lee, B.J. Schachter, Two Algorithms for Constructing a Delaunay Triangulation. International Journal of Computer and information Sciences, Vol. 9, 1980, pp. 219-242.
P-J. Laurent, Wavelets, Images, and Surface Fitting, in. A. Le Mehaute (Ed.), A.K Peters Ltd., 1994.
W. H. F. Smith, P. Wessel, Gridding with Continuous Curvature Splines in Tension, Geophysics, 55, 1990.
D. Shepard, A two-dimensional interpolation function for irregularly spaced data. Proceedings of the 23rd ACM National Conference (128), 1968, pp.517-524.
R. Sierra, Rigid Registration. , May 2009.
J. Parag, Class Presentation. , May 2009.
D. Kleinbaum, L. Kupper, K. Muller, Applied Regression Analysis and other Multivariable Method, Duxbury Press, 1987.
Wasson J. Statistics in Educational Research - An Internet Based Course. , April 2009.
J. Deacon, Correlation, and regression analysis for curve fitting. , January 2009.
R.J. Rummel, Understanding Correlation. , December 2009.
E. Yudkowsky, An Intuitive Explanation of Bayesian Reasoning, , May 2009.
P. E. Gill, W. Murray, Algorithms for the solution of the nonlinear least-squares problem. SIAM Journal of Numeral Analysis, 15 , 1978, pp. 977-992.
W. R. Greco, M. T. Hakala. Evaluation of methods for estimating the dissociation constant of tight binding enzyme inhibitors, Journal of Biological Chemistry, (254), 1979, pp.12104-12109.
D. F. Symancyk, Visualizing Gaussian Elimination, , May 2006.