Spatial Autoregression (Sar) Model: Parameter Estimation Techniques

Kazar, Baris/ Celik, Mete

ISBN 10: 1461418410 / ISBN 13: 9781461418412

Editore: Springer-Verlag New York Inc, 2012

Riguardo questo articolo

73 pages. 9.00x6.00x0.25 inches. In Stock.

Codice articolo x-1461418410

Dati bibliografici

• Titolo: Spatial Autoregression (Sar) Model: Parameter Estimation Techniques
• Editore: Springer-Verlag New York Inc
• Data di pubblicazione: 2012
• Lingua: Inglese
• ISBN 10: 1461418410
• ISBN 13: 9781461418412
• Rilegatura: Paperback
• Condizione: Brand New
• Peso: 0,13 chilogrammi

Descrizione articolo

Riassunto

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

Contenuti

Introduction.- Theory behind the SAR Model.-  Parallel Exact SAR Model Solutions.- Comparing Exact and Approximate SAR Model Solutions.- Parallel Implementations of Approximate SAR Model Solutions.- A New Approximation: Gauss-Lanczos Approximated SAR Model Solution.- Conclusions and Future Work.- Supplementary Materials.