What is a cluster?

GAM is a cluster hunter but what is a cluster? The simplest way of defining a cluster is as a localised excess incidence rate that is unusual in that there is more of some variable than might be expected. Examples would include: a local excess disease rate, a crime hot spot, a unemployment black spot, unusually high positive residuals from a model, the distribution of a plant or surging glaciers or earthquake epicentres, pattern of fraud etc. Virtually any variable that has a geographical distribution can be input into GAM. The assumption is that identifying these extreme areas (or outliers or unusual areas) may be useful in that there could be implicit geographical associations with other variables that can be identified and would be of interest. Pattern detection via the identification of clusters is a very simple and generic form of geographical analysis that has many applications in many different contexts. The emphasis is on localised clustering or patterning because this may well contain the most useful information.
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