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I know there is same question in cross validated. But it is somewhat different.

Clustering of mixed type data with R

At there Q&A, as using daisy funtion(), we can use categorical data type in clustering.

But, I'm wondering that as sequence the nominal variable (for example, 1 is small apartment, 2 is middle-size apartment, 3 is building and the higher number, the better), can I use kmeans clustering with this nominal variable?

Of course, in this case, this nominal variable is converted as int type(=continuous type).

Please let me know, why it can't or can. I want to know theory explanation.

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  • $\begingroup$ so, you just want to convert a nominal variable to continous? or something more? $\endgroup$
    – carlo
    Mar 21, 2017 at 14:26
  • $\begingroup$ @carlo Yes. right. But the nominal variable has rank. For example, 1 is small apartment, 2 is middle-size apartment, 3 is building and the higher number, the better. I know that converting nominal variable to continuous is wrong. So i rank the nominal variable's data. Then.. Is it right ?? $\endgroup$
    – 서영재
    Mar 24, 2017 at 0:41
  • $\begingroup$ Your example seems to be ordinal rather then nominal. In any case, daisy works fine for what you want to do, I have used the Matlab port of it for my master thesis. Just be careful to accurately tell it which variable is what type. $\endgroup$
    – David Ernst
    Sep 3, 2017 at 21:17

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It depends on the desired effect.

For example with k-means, if you encode these values as 1,2,3 the distance of 1 to 3 is 2²=4, i.e., 4 times as much as the differences of 1 to 2, and 2 to 3 (1²=1).

This can be desired, or problematic. It depends on your data's meaning, there is not a single mathematical 'more correct' way.

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