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Suppose we are looking at a scatter chart and from there, by visual inspection, I would like to pick up the coordinates (initial centers) based on the density of the points. Whats are options or tricks known.

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    $\begingroup$ If you want to use K-means, then consider k-means++ centroid initialization $\endgroup$
    – MotiNK
    Commented Jun 13, 2017 at 10:20

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At least a dozen of methods have been proposed.

Too many to list them all here.

The ELKI tool contains a number of them to try out and compare.

See Wikipedia for a few of them, and check relevant literature. There are several studies that compare different methods.

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