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I am aware that there are algorithms to cluster categorical data, such as k-modes. However what happens when you miss-classify an observation? In contrast to numerical data, placing a categorical observation in a "wrong" cluster can be detrimental - if someone who has cancer turns out not to have cancer, for example, due to misclassification, it is much worse than someone with a height of 1.80 cm turning out to be 1.82 cm.

Is there a way to overcome this issue in clustering?

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    $\begingroup$ In common usage, clustering is different from classifying. You might say that in clustering there is "no right or wrong", whereas in classifying there definitely is. So I encourage you to think about which of the two you are really using. $\endgroup$
    – rolando2
    Commented Oct 4, 2017 at 18:24

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Clustering is what the algorithm happens to find. So there is no "wrong" unless you compare some approximative algorithm to an exact algorithm it is supposed to approximate.

You can't "learn" it to recognize cancer; so don't expect clusters to relate to something as simple as "cancer". So I'd rather not automate anything based on clustering, but solely use it to explore your data.

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