Jenks natural breaks optimization

The Jenks natural breaks optimization, also called the Jenks natural breaks classification method, is a data clustering method for deciding how to split an ordered set of values into classes. It looks for the grouping that makes each class as uniform as possible, by minimizing the average squared deviation of the values from their own class mean, while keeping the class means as far apart from one another as it can. In practice it is an iterative search: start from some division of the ordered data, compute the sum of squared deviations from the class means, move values between classes and repeat until that sum stops falling. All possible break combinations can instead be examined to guarantee the best one, and a goodness of variance fit between 0 and 1 reports how well the classes explain the data. The method is closely related to Otsu method and Fisher discriminant analysis. It was developed by the American cartographer George F. Jenks to make choropleth maps represent data more accurately.