Say I have two clusters A and B with mean ma and mb respectively. Both have different covariance matrices Ca and Cb. I want to determine Mahalanobis distance between both clusters. However, how to determine the covariance matrix to calculate the Mahalanobis distance as there are two different covariance matrices.
I have the following suggestion:
Pool the data and compute the covariance matrix based on the pooled dataset, let it be S, if S is positive definite, define V=Ca - Cb, where Ca and Cb are points correponding to the centers of the two clusters, the following quadratic expression can be taken as a measure of the generalized distance between the two clusters:
D(Ca,Cb)= V'*(invS)*V
Hope this is useful.
Thank you Mr. Ghosh. Is Bhattacharya Distance also applicable in this case?
i suggest that you first test the null hypothesis of equality of the co-variance matrices associated with the two clusters, if the null hypothesis is found to be reject-able at given pre-determined level of significance, you go forward with Bhattacharya distance based analysis.
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