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Fast algorithms for a space-time concordance measure

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  • Sergio Rey

Abstract

This paper presents a number of algorithms for a recently developed measure of space-time concordance. Based on a spatially explicit version of Kendall’s $$\tau $$ τ the original implementation of the concordance measure relied on a brute force $$O(n^2)$$ O ( n 2 ) algorithm which has limited its use to modest sized problems. Several new algorithms have been devised which move this run time to $$O(n log(n) +np)$$ O ( n l o g ( n ) + n p ) where $$p$$ p is the expected number of spatial neighbors for each unit. Comparative timing of these alternative implementations reveals dramatic efficiency gains in moving away from the brute force algorithms. A tree-based implementation of the spatial concordance is also found to dominate a merge sort implementation. Copyright Springer-Verlag Berlin Heidelberg 2014

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  • Sergio Rey, 2014. "Fast algorithms for a space-time concordance measure," Computational Statistics, Springer, vol. 29(3), pages 799-811, June.
    • Handle: RePEc:spr:compst:v:29:y:2014:i:3:p:799-811
    DOI: 10.1007/s00180-013-0461-2
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    Cited by:

    1. Yaxin Fan & Xinyan Zhu & Bing She & Wei Guo & Tao Guo, 2018. "Network-constrained spatio-temporal clustering analysis of traffic collisions in Jianghan District of Wuhan, China," PLOS ONE, Public Library of Science, vol. 13(4), pages 1-23, April.
    2. Rey, Sergio, 2016. "Space-time patterns of rank concordance: Local indicators of mobility association with application to spatial income inequality dynamics," MPRA Paper 69480, University Library of Munich, Germany.

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