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I need to perform cluster analysis on my data set which includes both continuous and categorical type of variables. Having read around, I think K-Means is not a suitable technique for mixed data. Can I use Two-Step Clustering for the analysis? If yes, how are the categorical and continuous variables treated, technically?

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Twostep cluster does handle both categorical and continuous variables, which should be obvious from the dialog box interface. See the algorithms information via the Help menu for exact details on the criterion function.

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