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