I am using "Single linkage" hierarchical algorithm to cluster my data points with Gower Distance as my data have both qualitative and quantitative variables.
After applying this for the full model (all variables) I would like to start excluding those variables which are actually the not so important for my data. I was thinking of using principal component analysis (PCA) but I can't because my variables are a mixture of both categorical and continuous. Can someone suggest what is best method to select variables?
Finally I would like to use the Elbow Method to check exactly what is the optimal number of clusters?
Can someone help me with this logic?
I am using R-Studio for my analysis.