# Cluster analysis with skewed distibutions

For my master's thesis I would like to use different clustering algorithms to cluster municipalities (as objects) in regard to their land-use characteristics (as variables).

Analyzing my data descriptively I noted that I have a lot of extremely left skewed distributions (for example a lot of municipalities have zero values for some land use options and other have very high values). This is also true after standardizing my data by area or population...

Can anyone give me some advice on how does this will affect my cluster analysis? I think it may be important regarding the choice of my distance measurement (for example the absence of values to be interpreted as a non-similaritiy).

I didn't found a lot of information in this case in the common literature.

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Welcome to the site. I fixed up your grammar and spelling. I also removed the signature since the site adds one automatically. –  Peter Flom Jan 10 '13 at 10:56
@PeterFlom Hello Peter, thank you for the editing and the warm welcome :) –  Joschi Jan 10 '13 at 13:32

For example, one may argue that "area" inherently is a quadratic value (and "volume" is inherently cubic). And thus, in order to make attributes more comparable, a x_new = sqrt(x_old) transformation may be sensible for some attributes.
sqrt will only make values smaller than 1 larger: sqrt(4)=2. So you need to get the normalization steps into the appropriate order (and hope that your input data wasn't already normalized incompatibly) –  Anony-Mousse Jan 10 '13 at 14:20