Of all of the problems that we might attack with numerical methods, one of my favourites is cluster analysis; the task of dividing a set of data into subsets of similar data. Now I'm fully aware that my having favourite applications of numerical methods might lead you to suspect that I live at the most cringingly awkward end of nerd street, but please bear with me; the reason that I find cluster analysis so appealing, and that I hope you will too, is that it is a rare example of a mathematical problem that we struggle to even properly define.
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