**Principal component analysis,**which is a method for finding a linear combination of variables such that the possible correlation between them disappears i.e. elimination of the diagonal elements of the covariance matrix. Statistical independence implies the elimination of correlation but the opposite is not necessarily true because there is possible association between the variables on higher orders. The Independent Component Analysis seems to be the generalization needed to go beyond the simple correlation.

- Bartlett, M.S. and Movellan, J.R. and Sejnowski, T.J., Face recognition by independent component analysis, IEEE Transactions on neural networks,13, pp 1450--1464, 2002

- Hyvarinen, A. and Oja, E. Independent component analysis: a tutorial, Neural Networks, 13, pp 411--430 2000

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