Exploring different geometries has shown to be useful for
exploiting inherent properties of data at hand, becoming attractive to
compute embeddings therein. For example, hyperbolic geometry shows
superior performance when embedding hierarchical data. This suggests
that the ability to explore different geometries for embedding data might
be an important consideration, just as the models and algorithms used
to perform the embedding. However, utilising non-Euclidean geometries
to embed data can sometimes be a laborious task, as the whole pro-
cess needs to be first analytically derived for each geometry chosen (e.g.,
spherical, hyperbolic) and then adapted to it. This discourages the ex-
ploration of richer spaces to embed data in. Using the framework of
Riemannian manifolds, we explore a new choice of geometry. We con-
sider a modified version of the Poincaré disc to accept individual (per-
dimension) curvatures instead of a single global one, resulting in what
we refer to as the Poincaré ellipsis. We experiment with link prediction
on graph nodes embedded onto these new spaces, showing the perfor-
mance implications and highlighting the ease to explore new variants of
hyperbolic geometry.