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Introduction to Point Pattern Analysis

# Introduction to Point Pattern Analysis - Introduction to...

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Introduction to Point Pattern Analysis Erum Tariq (2004) School of Mines & Technology, South Dakota Abstract Point Pattern Analysis is a class of techniques that endeavor to identify patterns in spatial data. We utilize the Quadrant Count Method as an introductory algorithm of point pattern analysis. While this algorithm is very simplistic we do uncover a few mathematical and statistical subtleties. We will apply this method to the tree data that is taken from a survey carried out by D.J. Gerrard on a 19.6 acre square plot in Lansing Woods, Michigan. We attempt to classify clustering, or lack of clustering, of hickory tress in the survey area.

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Introduction The solutions to many mathematical questions, both pure and applied, rely on the ability of the investigator to uncover a pattern. In basic terms, Point Pattern Analysis is an investigation focused on finding patterns in data comprised of points in a spatial region. One common application of Point Pattern Analysis is epidemiology. The medical community is often interested in the spread of infectious disease such as: SARS, chicken pox, and West Nile virus among others. It is possible to identify pattern to the spread of infection then this might lead to an understanding of how the spread of an illness is related to social behavior, environmental factors, genetic susceptibility, or many other health care factors. In general, a spatial data set takes the form: X= } | { , N m R x x m k k ε . However, it is possible for the data to contain spatial location plus additional information. For example, earthquake data typically gives the location of earthquakes along a fault line and will often have the size and the time of each earthquake. Data that contains spatial data plus additional information is often referred to as marked spatial data . In our analysis, we will be concerned with only the spatial information and we will disregard any additional information associated with the data. Moreover, the examples we will work with are limited to two-dimensional data. Our interest will lie in quantifying the dispersion of objects within a confined geographical area. We try to understand the interaction of pattern and process and use point pattern analysis as a mechanism for detecting patterns associated as compared to random processes. The random process that will serve for our comparison will be the homogenous Poisson process, which will be described in more detail in section 2. D.J Gerrard describes an investigation of a 19 .6 acre square plot in Lansing Woods, Michigan [3]. This data includes hickories, maples and oaks grown on a square plot. The data for hickories is given in Cartesian coordinates, that is, i i y x , ( ) form, where R y and x i i . Also, the points are plotted on a unit square region.Our main goal of Point Pattern Analysis is to find out whether the distribution of the hickory trees is random, clustered or regularly dispersed. The kind of pattern involved would further our understanding of the behavior of the hickory trees and thus can be of great use to ecologists and biologists. For example, if the pattern is clustered, the biologists may
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