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Spatial AutoRegression (SAR) Model: Parameter Estimation Techniques (SpringerBriefs in Computer Science)

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Explosive growth in the size of spatial databases has highlighted the need for spatial data analysis and spatial data mining techniques to mine the interesting but implicit spatial patterns within these large databases. Extracting useful and interesting patterns from massive geo-spatial datasets is important for many application domains, such as regional economics, ecology and environmental management, public safety, transportation, public health, business, and travel and tourism [14, 57, 59], because space is everywhere. Many classical data mining algorithms, such as linear regression, assume that the learning samples are independently and identically distributed (i.i.d.). This assumption is violated in the case of spatial data due to spatial autocorrelation [2, 57] and in such cases classical linear regression yields a weak model with not only low prediction accuracy [59] but also residual error exhibiting spatial dependence. Modeling spatial dependencies improves overall classification and prediction accuracies.

The spatial autoregression model (SAR) [18, 31, 57] is a generalization of the linear regression model to account for spatial autocorrelation. It has been successfully used to analyze spatial datasets in regional economics and ecology [14, 59]. The model yields better classification and prediction accuracy [14, 59] for many spatial datasets exhibiting strong spatial autocorrelation. However, it is computationally expensive to estimate the parameters of SAR. For example, it can take an hour of computation for a spatial dataset with 10,000 observation points on a single IBM Regatta processor using a 1.3GHz pSeries 690 Power4 architecture with 3.2 GB memory [32, 33]. This has limited the use of SAR to small problems, despite its promise to improve classification and prediction accuracy for larger spatial datasets. For example, SAR was applied to accurately estimate crop parameters [61] using airborne spectral imagery; however, the study was limited to 74 pixels. A second study, reported in [41], was limited to 3888 observation points.
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