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A population given inhabiting an area. I can trace every individual and I've got the hypothesis there is a break in distribution like individuals born in the upper half of the area will rarely move to the lower half and vice versa.

Tracking each individual how can I determine the line/border which divides the population in a upper and lower half. What's the math or algorithm behind to draw this imaginary line?

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    $\begingroup$ Make sure to not let your hypothesis cloud your analysis. What if there are three, or five populations with distinct moving patterns? $\endgroup$ – Luigi Dec 1 '14 at 14:12
  • $\begingroup$ Even if there are more than two populations the general question is still to determine if there is a break in distribution and how "geographically" locate this. $\endgroup$ – osx Dec 1 '14 at 16:19
  • $\begingroup$ You should look into ordination techiques, to which you can apply different clustering techniques. Take a look at the R package vegan, which can do but ordination and calculate clustering. $\endgroup$ – fileunderwater Dec 12 '14 at 14:08
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There are a lot of approaches to this kind of problem. Starting with the simplest approach I think you'd benefit from using a K-means classification, with K=2 (or higher numbers to address @Luigi's concerns about model bias.) Once you've defined the geometric center of each population, you can treat them as foci, and use the equidistant points between each focus to define the boundary of interest. That does import another assumption (that the boundary is equidistant to the two points).

A more sophisticated way to divide two clusters is with a support vector machine but because this is a machine learning approach, you'd need to manually annotate a number of training data sets as "group 1" or "group 2." But after training, the SVM will define the optimal boundary (hypersurface) between these groups.

The two types of approaches (clustering versus machine learning) differ in where the manually-imported assumptions lie. One can combine them fruitfully -- using K-means to define the populations and SVM to define the dividing boundary.

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