On Euclidean Corrections for Non-Euclidean Dissimilarities

Non-Euclidean dissimilarity measures can be well suited for building representation spaces that are more beneficial for pattern classification systems than the related Euclidean ones [1,2]. A non-Euclidean representation space is however cumbersome for training classifiers, as many statistical techniques rely on the Euclidean inner product that is missing there. In this paper we report our findings on the applicability of corrections that transform a non-Euclidean representation space into a Euclidean one in which similar or better classifiers can be trained. In a case-study based on four principally different classifiers we find out that standard correction procedures fail to construct an appropriate Euclidean space, equivalent to the original non-Euclidean one.