  Point clouds of 3D objects exhibit an inherent compositional nature where
simple parts can be assembled into progressively more complex shapes to form
whole objects. Explicitly capturing such part-whole hierarchy is a long-sought
objective in order to build effective models, but its tree-like nature has made
the task elusive. In this paper, we propose to embed the features of a point
cloud classifier into the hyperbolic space and explicitly regularize the space
to account for the part-whole hierarchy. The hyperbolic space is the only space
that can successfully embed the tree-like nature of the hierarchy. This leads
to substantial improvements in the performance of state-of-art supervised
models for point cloud classification.
