K-means clustering on large number of variables

Question

Suppose K-means clustering need to be performed on large number of variables. Then,

1. normalisation should be performed on all variables or only the variables having high variance?

2. How can we define "high variance"?

3. Also, once the clustering is done, to infer the meaning out of the clusters, we would again have to change the normalised variables to original values.

Is my understanding right?

Answer 1

Don't just normalize data because some variables have "high variance".

High variance can be perfectly fine, if that variable is important.

You are supposedly trying to solve a problem. Choose the normalization that is appropriate for your problem. Don't ignore the meaning of the variables.