Should I standardize my variables for this particular case of cluster analysis?

Question

I'm trying to cluster a list of records based on a (percentage) frequency distribution of variables which add up to 100%. Like

1. Record1 - VarA(25%) VarB(25%) varC(50%) varD(0%)
2. Record2- VarA(50%) VarB(15%) varc(0%) VarD(35%)

and so on. I have standardized variables before while dealing with different dimensions(lengths and weights) etc. In this case I do not think standardization is appropriate. Also is k means clustering appropriate in this context, I wanted to use k means and use the distribution observed at the centroid of the cluster for the whole cluster. Thanks a ton.

Answer 1

As the dimensions are on the same scale and measure the same kind of quantity (relative share), you don't need to standardize / whiten your data.

I'm not convinced that k-means is appropriate here. It will likely work though.

The reason is that since your data is histograms (they sum up to 1), you will likely get much better results with distance functions designed for this type of distributions; i.e. histogram intersection distance, jensen-shannon divergence etc.

Unfortunately, k-means is really designed for squared Euclidean distance (= Variance minimization), and you shouldn't blindly combine it with other measures. Instead, use a k-means variant that will converge with arbitrary distances, such as k-medoids = PAM.