In my dataset we have both continuous and discrete variables. I want to know whether we can do hierarchical clustering using both type of variables.
One way is to use Gower similarity coefficient which is a composite measure; it takes quantitative (such as rating scale), binary (such as present/absent) and nominal (such as worker/teacher/clerk) variables.
When all variables are quantitative then the coefficient is a normalized Manhattan distance converted into similarity. When all variables are binary then the coefficient is a famous Jaccard matching coefficient. When all variables are nominal then the coefficient is dice matching coefficient that you obtain from your nominal vars if recode them into dummy vars. Usually a program calculating Gower will allow you to weight variables, that is, their contribution, to the composite formula.
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