Advertisement

Spatial AutoRegression (SAR) Model

Parameter Estimation Techniques

  • Baris M. Kazar
  • Mete Celik

Part of the SpringerBriefs in Computer Science book series (BRIEFSCOMPUTER)

Table of contents

  1. Front Matter
    Pages i-x
  2. Baris M. Kazar, Mete Celik
    Pages 1-5
  3. Baris M. Kazar, Mete Celik
    Pages 7-17
  4. Baris M. Kazar, Mete Celik
    Pages 19-33
  5. Baris M. Kazar, Mete Celik
    Pages 35-46
  6. Baris M. Kazar, Mete Celik
    Pages 47-50
  7. Baris M. Kazar, Mete Celik
    Pages 59-60
  8. Baris M. Kazar, Mete Celik
    Pages 61-73

About this book

Introduction

Explosive growth in the size of spatial databases has highlighted the need for spatial data mining techniques to mine the interesting but implicit spatial patterns within these large databases. This book explores computational structure of the exact and approximate spatial autoregression (SAR) model solutions. Estimation of the parameters of the SAR model using Maximum Likelihood (ML) theory is computationally very expensive because of the need to compute the logarithm of the determinant (log-det) of a large matrix in the log-likelihood function. The second part of the book introduces theory on SAR model solutions. The third part of the book applies parallel processing techniques to the exact SAR model solutions. Parallel formulations of the SAR model parameter estimation procedure based on ML theory are probed using data parallelism with load-balancing techniques. Although this parallel implementation showed scalability up to eight processors, the exact SAR model solution still suffers from high computational complexity and memory requirements. These limitations have led the book to investigate serial and parallel approximate solutions for SAR model parameter estimation. In the fourth and fifth parts of the book, two candidate approximate-semi-sparse solutions of the SAR model based on Taylor's Series expansion and Chebyshev Polynomials are presented. Experiments show that the differences between exact and approximate SAR parameter estimates have no significant effect on the prediction accuracy. In the last part of the book, we developed a new ML based approximate SAR model solution and its variants in the next part of the thesis. The new approximate SAR model solution is called the Gauss-Lanczos approximated SAR model solution. We algebraically rank the error of the Chebyshev Polynomial approximation, Taylor's Series approximation and the Gauss-Lanczos approximation to the solution of the SAR model and its variants. In other words, we established a novel relationship between the error in the log-det term, which is the approximated term in the concentrated log-likelihood function and the error in estimating the SAR parameter for all of the approximate SAR model solutions.

Keywords

Maximum Likelihood Theory Spatial Autocorrelation Spatial Autoregression Model Spatial Data Mining Spatial Databases

Authors and affiliations

  • Baris M. Kazar
    • 1
  • Mete Celik
    • 2
  1. 1.Oracle America Inc.NashuaUSA
  2. 2., Department of Computer EngineeringErciyes UniversityKayseriTurkey

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-1842-9
  • Copyright Information The Author(s) 2012
  • Publisher Name Springer, Boston, MA
  • eBook Packages Computer Science
  • Print ISBN 978-1-4614-1841-2
  • Online ISBN 978-1-4614-1842-9
  • Series Print ISSN 2191-5768
  • Series Online ISSN 2191-5776
  • Buy this book on publisher's site
Industry Sectors
Pharma
Automotive
Chemical Manufacturing
Biotechnology
Finance, Business & Banking
Electronics
IT & Software
Telecommunications
Energy, Utilities & Environment
Aerospace
Engineering