Measuring Moran's I in a Cost-Efficient Manner to Describe a Land-Cover Change Pattern in Large-Scale Remote Sensing Imagery

Abstract

Detection and analysis of a land-cover change pattern from remotely sensed imagery have gained increasing research interests in recent years. A number of spatial statistics and landscape pattern metrics have been explored for this purpose. Moran's index (Moran's I) of spatial autocorrelation is one such spatiostatistical measure, which has been proved to be useful in characterizing the land-cover change, especially in Landsat data. However, since the Moran's I estimation needs to deal with spatial weight between each pair of spatial data objects, it becomes almost unfeasible to apply Moran's I in the case of large-scale remote sensing data, containing several millions of pixels. This paper proposes a method for computing Moran's I in the Hadoop MapReduce framework and thereby helps in describing spatial patterns in large-scale remotely sensed data. The contributions of the work include: 1) the exhaustive description of the Mapper and Reducer implementation for cost-effective estimation of Moran's I, and 2) the computational complexity analysis of the respective algorithms. Furthermore, two case studies have been presented, considering both the rook case and the queen case of spatial contiguity. Case Study 1 demonstrates the computational efficiency of the proposed implementation, and Case Study 2 illustrates an application of Moran's I in describing the urban sprawling pattern in two large spatial zones in Kolkata, India.