Learning Multiple Maps from Conditional Ordinal Triplets

Ordinal embedding seeks a low-dimensional representation of objects based on relative comparisons of their similarities. This low-dimensional representation lends itself to visualization on a Euclidean map. Classical assumptions admit only one valid aspect of similarity. However, there are increasing scenarios involving ordinal comparisons that inherently reflect multiple aspects of similarity, which would be better represented by multiple maps. We formulate this problem as conditional ordinal embedding, which learns a distinct low-dimensional representation conditioned on each aspect, yet allows collaboration across aspects via a shared representation. Our geometric approach is novel in its use of a shared spherical representation and multiple aspect-specific projection maps on tangent hyperplanes. Experiments on public datasets showcase the utility of collaborative learning over baselines that learn multiple maps independently.