Pairwise dissimilarity representations are frequently used as an alternative to feature vectors in pattern recognition. One of the problems encountered in the analysis of such data, is that the dissimilarities are rarely Euclidean, while statistical learning algorithms often rely on Euclidean dissimilarities. Such non-Euclidean dissimilarities are often corrected or a consistent Euclidean geome...

According to Felix Klein's Erlanger program (1872), a (classical) geometry is the study of properties of a space X invariant under a group G of transformations of X. In practice G will be a Lie group which acts transitively on X, so that X is represented as a homogeneous space G=H, where H G is a closed subgroup. For example Euclidean geometry is the geometry of n-dimensional Euclidean space R ...