A cost-efficient approach for measuring Moran's index of spatial autocorrelation in geostationary satellite data

Spatial autocorrelation (SA), describing correlation of a particular feature/phenomenon with itself across space, is one of the major properties of any spatial data. Among the various measures of SA proposed till date, the Moran's index (I) is the most common as well as significant one. However, measuring Moran's I, which needs to deal with spatial weight between each pair of spatial data objects, becomes almost unfeasible in case of large-scale raster data, like geostationary satellite data, containing several millions of pixels. This paper proposes a method based on the Hadoop MapReduce framework for computing Moran's I in large-scale raster data. The main contribution of the work lies in the implementation of the Mapper and Reducer processes for a cost effective estimation of Moran's I, considering both rook case and queen case of spatial contiguity. The key feature of these algorithms is an efficient manipulation of the spatial weight matrix, and thereby reducing the overall memory and time requirement. The experimentation shows a promising result in this regard.