What index is used to compute the principal components? Is it Euclidean? Or maybe some correlation coefficients as Pearson? It seems that covariance between principal components is calculated in always Eucidean: https://en.wikipedia.org/wiki/Distance_correlation#Distance_covariance

If not always the Euclidean space is used, with what software I can compute principal components with Pearson covariance without using Euclidean distance? 

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