Detecting general multi-dimensional nonlinear correlations: the module "dist_corr" of the Mastrave modelling library. Mastrave project technical report
Linear correlation analysis of complex nonlinear physical or computationally derived quantities - despite straightforward to be implemented with the help of basic numerical tools - may be far sub-optimal in assessing the actual strength of existing relationships between quantities. Moreover, in many applications not only the correlation between pairs of quantities is of interest, but also the more general correlation between a certain group of quantities and another one. Multi-dimensional nonlinear correlation analysis may offer elegant and concise ways of exploring unknown complex relationships either among set of mono-dimensional quantities or of logically connected groups of quantities. Brownian Distance Correlation (BDC) has been proven to be a powerful generalization of the classical linear correlation to detect “all kinds of possible relationships” between real-valued random variables. Within the Mastrave modelling library, a semantic array programming implementation of BDC – extended to also consider multi-dimensional analysis between groups of quantities – is here described. The implementation also offers the possibility of exploring user-defined metrics.
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