Comparing Exact and Approximate Spatial Auto-regression Model Solutions for Spatial Data Analysis

The spatial auto-regression (SAR) model is a popular spatial data analysis technique, which has been used in many applications with geo-spatial datasets. However, exact solutions for estimating SAR parameters are computationally expensive due to the need to compute all the eigenvalues of a very large matrix. Recently we developed a dense-exact parallel formulation of the SAR parameter estimation procedure using data parallelism and a hybrid programming technique. Though this parallel implementation showed scalability up to eight processors, the exact solution still suffers from high computational complexity and memory requirements. These limitations have led us to investigate approximate solutions for SAR model parameter estimation with the main objective of scaling the SAR model for large spatial data analysis problems. In this paper we present two candidate approximate-semi-sparse solutions of the SAR model based on Taylor series expansion and Chebyshev polynomials. Our initial experiments showed that these new techniques scale well for very large data sets, such as remote sensing images having millions of pixels. The results also show that the differences between exact and approximate SAR parameter estimates are within 0.7% and 8.2% for Chebyshev polynomials and Taylor series expansion, respectively, and have no significant effect on the prediction accuracy.