I am looking for an embedding method that allows projecting images data onto spherical manifolds while preserving their positivity.
As it is well known, the pixels' values of images are positive quantities. However, projecting them on spherical manifolds yields positive and negative values.
For example, it seems that "Spherical Embeddings for non-Euclidean Dissimilarities" method doesn't guarantee the generation of positive directional quantities as the embedded positions are determined via the full eigendecomposition. In the figure below, we can see that the embedding of the points spreads around the whole sphere and not only on the positive quadrant.
My question is how to restrict the embeddings to generate only points located on the positive quadrant in order to obtain positive qualities (positions) after mapping?
As a trivial solution, one can simply set negative values to be zero, but this will concentrate all negative points on the sphere's center and will not help?