Fast spatial autocorrelation

Physical or geographic location proves to be an important feature in many data science models, because diverse natural and social phenomenon have a spatial component. Spatial autocorrelation measures the extent which locally adjacent observations of same are correlated. Although statistics like Moran’s I Geary’s C widely used measure autocorrelation, they slow: All popular methods run $$\Omega (n^2)$$ time, rendering them unusable for large datasets, long time-courses with moderate numbers points. We propose new $$S_A$$ statistic based on notion that variance observed when merging pairs nearby clusters should increase slowly spatially autocorrelated variables. give linear-time algorithm calculate variable input agglomeration order (available at https://github.com/aamgalan/spatial_autocorrelation ). For typical dataset $$n \approx 63,000$$ points, our can computed 1 second, versus 2 hours more C. Through simulation studies, we demonstrate identifies correlations variables generated spatially-dependent model half magnitude earlier than either Finally, prove several theoretical properties : namely it behaves as true correlation is invariant under addition multiplication by constant.