Nonlinear data projection on a sphere with a controlled trade-off between trustworthiness and continuity

This paper presents a nonlinear method aimed to project data on a non-Euclidean manifold, when their structure is too complex to be embedded in an Euclidean space. The method optimizes a pairwise distance criterion that implements a control between trustworthiness and continuity that respectively represent the risks of attening and tearing the projection. The method is illustrated to project data on a sphere, but can be extended to other manifolds such as the torus and the cylinder.