  This paper introduces a novel approach to statistics and data analysis,
departing from the conventional assumption of data residing in Euclidean space
to consider a Riemannian Manifold. The challenge lies in the absence of vector
space operations on such manifolds. Pennec X. et al. in their book Riemannian
Geometric Statistics in Medical Image Analysis proposed analyzing data on
Riemannian manifolds through geometry, this approach is effective with
structured data like medical images, where the intrinsic manifold structure is
apparent. Yet, its applicability to general data lacking implicit local
distance notions is limited. We propose a solution to generalize Riemannian
statistics for any type of data.
