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A fast multi-resolution method for detection of significant spatial overdensities

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Title: A fast multi-resolution method for detection of significant spatial overdensities
Authors: Daniel B. Neill, Andrew W. Moore
Publication Year: 2018
Collection: KiltHub Research from Carnegie Mellon University
Subject Terms: Other information and computing sciences not elsewhere classified, Cluster analysis Computer programs, Numerical grid generation (Numerical analysis), Monte Carlo method, Information and Computing Sciences not elsewhere classified
Description: "Given an N x N grid of squares, where each square s[subscript ij] has a count c[subscript ij] and an underlying population p[subscript ij], our goal is to find the square region S with the highest density, and to calculate the significance of this region by Monte Carlo testing. Any density measure D, which depends on the total count and total population of the region, can be used. For example, if each count c[subscript ij] represents the number of disease cases occurring in that square, we can use Kulldorff's spatial scan statistic D[subscript K] to find the most significant spatial disease cluster. A naive approach to finding the region of maximum density would be to calculate the density measure for every square region: this requires O(RN┬│) calculations, where R is the number of Monte Carlo replications, and hence is generally computationally infeasible. We present a novel multi-resolution algorithm which partitions the grid into overlapping regions, bounds the maximum score of subregions contained in each region, and prunes regions which cannot contain the maximum density region. For sufficiently dense regions, this method finds the maximum density region in optimal O(RN┬▓) time, and in practice it results in significant (10-200x) speedups as compared to the naive approach."
Document Type: article in journal/newspaper
Language: unknown
DOI: 10.1184/R1/6587384.v1
Availability: https://doi.org/10.1184/R1/6587384.v1
https://figshare.com/articles/journal_contribution/A_fast_multi-resolution_method_for_detection_of_significant_spatial_overdensities/6587384
Rights: In Copyright
Accession Number: edsbas.2F4DEDF4
Database: BASE
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  – Url: https://doi.org/10.1184/R1/6587384.v1#
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  Data: A fast multi-resolution method for detection of significant spatial overdensities
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  Data: <searchLink fieldCode="AR" term="%22Daniel+B%2E+Neill%22">Daniel B. Neill</searchLink><br /><searchLink fieldCode="AR" term="%22Andrew+W%2E+Moore%22">Andrew W. Moore</searchLink>
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  Data: 2018
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  Data: KiltHub Research from Carnegie Mellon University
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  Data: <searchLink fieldCode="DE" term="%22Other+information+and+computing+sciences+not+elsewhere+classified%22">Other information and computing sciences not elsewhere classified</searchLink><br /><searchLink fieldCode="DE" term="%22Cluster+analysis+Computer+programs%22">Cluster analysis Computer programs</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+grid+generation+%28Numerical+analysis%29%22">Numerical grid generation (Numerical analysis)</searchLink><br /><searchLink fieldCode="DE" term="%22Monte+Carlo+method%22">Monte Carlo method</searchLink><br /><searchLink fieldCode="DE" term="%22Information+and+Computing+Sciences+not+elsewhere+classified%22">Information and Computing Sciences not elsewhere classified</searchLink>
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  Data: "Given an N x N grid of squares, where each square s[subscript ij] has a count c[subscript ij] and an underlying population p[subscript ij], our goal is to find the square region S with the highest density, and to calculate the significance of this region by Monte Carlo testing. Any density measure D, which depends on the total count and total population of the region, can be used. For example, if each count c[subscript ij] represents the number of disease cases occurring in that square, we can use Kulldorff's spatial scan statistic D[subscript K] to find the most significant spatial disease cluster. A naive approach to finding the region of maximum density would be to calculate the density measure for every square region: this requires O(RN┬│) calculations, where R is the number of Monte Carlo replications, and hence is generally computationally infeasible. We present a novel multi-resolution algorithm which partitions the grid into overlapping regions, bounds the maximum score of subregions contained in each region, and prunes regions which cannot contain the maximum density region. For sufficiently dense regions, this method finds the maximum density region in optimal O(RN┬▓) time, and in practice it results in significant (10-200x) speedups as compared to the naive approach."
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  Data: 10.1184/R1/6587384.v1
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  Data: https://doi.org/10.1184/R1/6587384.v1<br />https://figshare.com/articles/journal_contribution/A_fast_multi-resolution_method_for_detection_of_significant_spatial_overdensities/6587384
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        Value: 10.1184/R1/6587384.v1
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      – SubjectFull: Cluster analysis Computer programs
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      – TitleFull: A fast multi-resolution method for detection of significant spatial overdensities
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