Spatial Dependency Modeling Using Spatial Auto-Regression

Parameter estimation of the spatial auto-regression model (SAR) is important because we can model the spatial dependency, i.e., spatial autocorrelation present in the geo-spatial data. SAR is a popular data mining technique used in many geo-spatial application domains such as regional economics, ecology, environmental management, public safety, public health, transportation, and business. However, it is computationally expensive because of the need to compute the logarithm of the determinant of a large matrix due to Maximum Likelihood Theory (ML). Current approaches are computationally expensive, memory-intensive and not scalable. In this paper, we propose a new ML-based approximate SAR model solution based on the Gauss-Lanczos algorithm and compare the proposed solution with two other ML-based approximate SAR model solutions, namely Taylor's series, and Chebyshev polynomials. We also algebraically ranked these methods. Experiments showed that the proposed algorithm gives better results than the related approaches when the data is strongly correlated and problem size is large.