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How do you know which clustering is correct unless you are clustering on a data set where you already have a "correct" somehow verifiable clustering solution? k-means is definitely not an optimization technique and the n clustering solutions you get have to be evaluated for something like "viability" or some kind of at least face validity. At least this was my experience in using clustering for market segmentation. Are you suggesting that the Gaussian approach provides some type of optimized solution?

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I also think so

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