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Finding Irregularly Shaped Clusters: AMOEBA
Finding Irregularly Shaped Clusters: AMOEBA
Spatial Clusters and AMOEBA• Knox (1989) calls a cluster "a geographically
bounded group of occurrences of sufficient size and concentration to be unlikely to have occurred by chance.“
• There are several outstanding issues in spatial cluster analysis– Assessing statistical significance– Accounting for global autocorrelation– Over and under identification– Shape
• AMOEBA - A Multidirectional Optimal Ecotope-Based Analysis
Source: New York State Department of Health
Source: New York State Department of Health
Circular Cluster Search
Figure from S. Openshaw, www.geovista.psu.edu/sites/geocomp99/Gc99/051/pres_051.ppt
Love Canal
Pollutant Plumes
AMOEBA Procedure
For each observation i, local statistic values are obtained for all combinations of contiguous neighbors j of i. The set of j observations that maximizes the local statistic become members of the ecotope together with the ith observation.
AMOEBA Procedure
The procedure is repeated, examining all combinations of the units contiguous to the ecotope together with the already existing ecotope. That new set of j observations that maximizes the local statistic become members of the ecotope.
AMOEBA Procedure
The ecotope is complete when no combinations of contiguous units increase the statistic value.
AMOEBA Example 1
AMOEBA Cluster
AMOEBA Example 2
AMOEBA Cluster
AMOEBA Example 3
AMOEBA Cluster
AMOEBA Example 4
AMOEBA Cluster
AMOEBA/SaTScan Comparison
AMOEBA/SaTScan Comparison
AMOEBA/SaTScan Comparison
AMOEBA/SaTScan Comparison
Other Approaches• Tango and Takahashi (2005) – An examination
of all combinations of connected sub-graphs up to a specified length
• Duzcmal and Asuncao (2004) – A simulated annealing approach using connected sub-graphs
• Patil and Taille (2004) – An upper level set approach to finding space-time clusters
• Jacquez et al. (2008) – Boundaries and links between contiguous units.
DHF July 1987
STARS Visualization of DHF Rates in Thailand
January 1983February 1983March 1983April 1983May 1983June 1983July 1983August 1983September 1983October 1983November 1983December 1983January 1984February 1984March 1984April 1984May 1984June 1984July 1984
1984-1997
AMOEBA Clustering• AMOEBA algorithm will not include areas of low
risk within a cluster of high values and vice-versa
• The AMOEBA may be used with any local clustering statistic
• The search algorithm and statistic should match your research questions
• Irregularly shaped clusters often improve the value of clusters as an exploratory analysis tool
