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Generalization of the Procrustes coefficient to functional data

Abstract The relationship between two sets of variables can be defined in multiple ways. Although the problem in case of multivariate data has been already described in the literature in a comprehensive way, there is still a need to investigate relationships between multivariate functional data. At the moment we know how to compute functional ρV coefficient and functional distance correlation coefficient. However, it does not cover all aspects of linkages between variables. In this article, we introduce a new association measure for functional multivariate data – the functional Procrustes coefficient. The Procrustes coefficient (known also as RLS coefficient) for multivariate data is widely used in ecology, morphology and neuroscience. An illustration on a real example will be provided.