Solved – Clustering a dataset with both discrete and continuous variables

Question

I have a dataset X which has 10 dimensions, 4 of which are discrete values.
In fact, those 4 discrete variables are ordinal, i.e. a higher value implies a higher/better semantic.

2 of these discrete variables are categorical in the sense that for each of these variables, the distance e.g. from 11 to 12 is not the same as the distance from 5 to 6. While a higher variable value implies a higher in reality, the scale is not necessarily linear (in fact, it is not really defined).

My question is:

• Is it a good idea to apply a common clustering algorithm (e.g. K-Means and then Gaussian Mixture (GMM)) to this dataset which contains both discrete and continuous variables?

If not:

• Should I remove the discrete variables and focus only on the continuous ones?
• Should I better discretize the continuous ones and use a clustering algorithm for discrete data?

Answer 1

So you've been told you need an appropriate distance measure. Here are some leads:

• Clustering mixed data
• A generalized Mahalanobis distance for mixed data
• Estimating the Mahalanobis distance from mixed continuous and discrete data
• Generalization of the Mahalanobis distance in the mixed case
• Distance functions for categorical and mixed variables
• Informational distances and related statistics in mixed continuous and categorical variables

and, of course: Mahalanobis distance.