Some clustering algorithms require independence of variables but (especially working with real data) variables are often highly correlated.
I have been suggested to apply a Principal Component Analysis to solve the problem (using the resulting linear combination as input for the clustering). But such a solution may affect the resulting clusters since correlated varibles "repeat" the same information in the linear combination.
I.T.Jolliffe (1972; 2002) suggest a method of Variables Reductions (called 'method B4') that select one variable for each Component (the one with highest loading). Even if other method have been considered more effective (specially if the goal is to mantaine as much variance of the original variables as possible), Joliffe's method B4 is the only one -- that I have found -- that ensures the independent of the selected variables.
Question: Are there other more effective methods for selecting independent variables?