  Ordinal embedding aims at finding a low dimensional representation of objects
from a set of constraints of the form "item $j$ is closer to item $i$ than item
$k$". Typically, each object is mapped onto a point vector in a low dimensional
metric space. We argue that mapping to a density instead of a point vector
provides some interesting advantages, including an inherent reflection of the
uncertainty about the representation itself and its relative location in the
space. Indeed, in this paper, we propose to embed each object as a Gaussian
distribution. We investigate the ability of these embeddings to capture the
underlying structure of the data while satisfying the constraints, and explore
properties of the representation. Experiments on synthetic and real-world
datasets showcase the advantages of our approach. In addition, we illustrate
the merit of modelling uncertainty, which enriches the visual perception of the
mapped objects in the space.
