Predicting Spatial Data With Rbf Networks

Spatial prediction needs to account for spatial information, which makes conventional radial basis function (RBF) networks inappropriate, for they assume independent and identical distribution. In this paper, we fuse spatial information at different layers of RBF. Experiments show fusion at hidden layer gives the best result and suggest that the optimal value is around one for the coefficient, which is used in the linear combination at the output layer.

[1]  Donald Geman,et al.  Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images , 1984 .

[2]  Ali S. Hadi,et al.  Finding Groups in Data: An Introduction to Chster Analysis , 1991 .

[3]  Noel A Cressie,et al.  Statistics for Spatial Data, Revised Edition. , 1994 .

[4]  F. Girosi,et al.  Networks for approximation and learning , 1990, Proc. IEEE.

[5]  James D. Keeler,et al.  Layered Neural Networks with Gaussian Hidden Units as Universal Approximations , 1990, Neural Computation.

[6]  Shang-Liang Chen,et al.  Orthogonal least squares learning algorithm for radial basis function networks , 1991, IEEE Trans. Neural Networks.

[7]  Noel A. C. Cressie,et al.  Statistics for Spatial Data: Cressie/Statistics , 1993 .

[8]  Noel A Cressie,et al.  Statistics for Spatial Data. , 1992 .

[9]  Hans-Peter Kriegel,et al.  Spatial Data Mining: A Database Approach , 1997, SSD.

[10]  M. J. D. Powell,et al.  Radial basis functions for multivariable interpolation: a review , 1987 .

[11]  C. D. Kemp,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[12]  Anil K. Jain,et al.  Unsupervised texture segmentation using Gabor filters , 1990, 1990 IEEE International Conference on Systems, Man, and Cybernetics Conference Proceedings.

[13]  Weili Wu,et al.  Spatial contextual classification and prediction models for mining geospatial data , 2002, IEEE Trans. Multim..

[14]  Grahame B. Smith Stuart Geman and Donald Geman, “Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images”; , 1987 .

[15]  Anil K. Jain,et al.  A Markov random field model for classification of multisource satellite imagery , 1996, IEEE Trans. Geosci. Remote. Sens..

[16]  James P. LeSage Arc Mat , a Matlab toolbox for using ArcView Shape files for spatial econometrics and statistics , 2004 .

[17]  Heekuck Oh,et al.  Neural Networks for Pattern Recognition , 1993, Adv. Comput..

[18]  Joachim M. Buhmann,et al.  Contextual classification by entropy-based polygonization , 2001, Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001.

[19]  R. Webster,et al.  A geostatistical basis for spatial weighting in multivariate classification , 1989 .

[20]  David J. Hand,et al.  Discrimination and Classification , 1982 .

[21]  Henry Leung,et al.  Signal detection using the radial basis function coupled map lattice , 2000, IEEE Trans. Neural Networks Learn. Syst..

[22]  J. Mason,et al.  Algorithms for approximation , 1987 .

[23]  Samy Bengio,et al.  Local Machine Learning Models for Spatial Data Analysis , 2000 .

[24]  Gérard Govaert,et al.  Convergence of an EM-type algorithm for spatial clustering , 1998, Pattern Recognit. Lett..