Fuzzy clustering for Optimally Weighted Cluster Kriging

Kriging or Gaussian Process Regression has been successfully applied in many fields. One of the major bottlenecks of Kriging is the complexity in both processing time (cubic) and memory (quadratic) in the number of data points. To overcome these limitations, a variety of approximation algorithms have been proposed. One of these approximation algorithms is Optimally Weighted Cluster Kriging (OWCK). In this paper, OWCK is extended and enhanced by the use of fuzzy clustering methods in order to increase the accuracy. Several options are proposed and evaluated against both the original OWCK and a variety of other Kriging approximation algorithms.

[1]  Susana Gomez,et al.  Advances in Optimization and Numerical Analysis , 1994 .

[2]  I-Cheng Yeh,et al.  Modeling of strength of high-performance concrete using artificial neural networks , 1998 .

[3]  B. Silverman,et al.  Some Aspects of the Spline Smoothing Approach to Non‐Parametric Regression Curve Fitting , 1985 .

[4]  Ola Hössjer,et al.  Fast kriging of large data sets with Gaussian Markov random fields , 2008, Comput. Stat. Data Anal..

[5]  J. C. Dunn,et al.  A Fuzzy Relative of the ISODATA Process and Its Use in Detecting Compact Well-Separated Clusters , 1973 .

[6]  Michael L. Stein,et al.  Interpolation of spatial data , 1999 .

[7]  Carl E. Rasmussen,et al.  A Unifying View of Sparse Approximate Gaussian Process Regression , 2005, J. Mach. Learn. Res..

[8]  Sean B. Holden,et al.  The Generalized FITC Approximation , 2007, NIPS.

[9]  Hao Wang,et al.  Optimally Weighted Cluster Kriging for Big Data Regression , 2015, IDA.

[10]  Douglas A. Reynolds Gaussian Mixture Models , 2009, Encyclopedia of Biometrics.

[11]  A. Asuncion,et al.  UCI Machine Learning Repository, University of California, Irvine, School of Information and Computer Sciences , 2007 .

[12]  D. Ginsbourger,et al.  Kriging is well-suited to parallelize optimization , 2010 .

[13]  Zoubin Ghahramani,et al.  Sparse Gaussian Processes using Pseudo-inputs , 2005, NIPS.

[14]  D. Krige A statistical approach to some basic mine valuation problems on the Witwatersrand, by D.G. Krige, published in the Journal, December 1951 : introduction by the author , 1951 .

[15]  Matthias W. Seeger,et al.  Gaussian Processes For Machine Learning , 2004, Int. J. Neural Syst..

[16]  Iain Murray,et al.  A framework for evaluating approximation methods for Gaussian process regression , 2012, J. Mach. Learn. Res..

[17]  Neil D. Lawrence,et al.  Gaussian Process Latent Variable Models for Visualisation of High Dimensional Data , 2003, NIPS.

[18]  Stefan Schaal,et al.  Incremental Online Learning in High Dimensions , 2005, Neural Computation.

[19]  Roger Woodard,et al.  Interpolation of Spatial Data: Some Theory for Kriging , 1999, Technometrics.

[20]  Volker Tresp,et al.  A Bayesian Committee Machine , 2000, Neural Computation.