Euclidean distance comparison weighted by correlation

#1
Hello,

I want to calculate the Euclidean distance between two objects across a set of n variables. For those n variables I have generated a correlation matrix. From that correlation matrix I would like to produce a weight vector that I can apply before calculating the distance, so that the more correlated variables in the data set are weighted lower.

What is the most appropriate method for calculating the weight vector based off of the correlation matrix?

Thanks,
Fraser