Dissimilarity metrics evaluate differences in a set of variables between spatial locations. They are required in all boundary delineation methods except numerical wombling. That is, they are required in polygon wombling, categorical wombling, and spatially constrained clustering. For each pair of locations, the chosen dissimilarity metric is calculated, and that value forms the basis of multivariate analyses within BoundarySeer.
To understand dissimilarity metrics, first think about proximity metrics. Proximity metrics can be used to quantify how close different locations are in physical space, and are calculated from the x and y coordinates of each location. Examples of proximity metrics include Euclidean distance, which is the straight line distance between observations, and Manhattan distance, which is a "stair stepping" way to measure distance which can be calculated by taking the sum of the absolute value of the differences between values of the x and y variables.
Dissimilarity metrics address how close two sets of observations are in variable space - in other words, you can think of the variables for each location being plotted in a many-dimensional space, and then imagine estimating "distances" between these points. Both Euclidean distance and Manhattan distance can be used as metrics of dissimilarity as well as proximity, as can many other metrics. Dissimilarity metrics are closely related to similarity metrics; the range of values for both is often between 0 and 1. In many cases, you can convert between a measure of similarity and one of dissimilarity by subtracting the first metric from 1 to get the other (e.g., S = 1-D; D = 1-S).
There are many ways of quantifying distance or dissimilarity, and we include only the most common ones in this release of BoundarySeer. Subsequent versions of BoundarySeer will have more metrics available, including a highly flexible equation editor that will allow you to specify almost any metric and to design new ones as the need arises.
Often, different distance and dissimilarity metrics are used in different scientific fields; population genetics uses metrics of genetic distance, ecology employs metrics of ecological distance, and so on. Thus, when choosing an appropriate metric you should survey the literature to identify those commonly used in your field.
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