Adaptive indefinite kernels in hyperbolic spaces

Learning embeddings in hyperbolic space has gained increasing interest in the community, due to its property of negative curvature, as a way of encoding data hierarchy. Recent works investigate the improvement of the representation power of hyperbolic embeddings through kernelization. However, existing developments focus on defining positive definite (pd) kernels, which may affect the intriguing property of hyperbolic spaces. This is due to the structures of hyperbolic spaces being modeled in indefinite spaces (e.g., Kreĭn space). This paper addresses this issue by developing adaptive indefinite kernels, which can better utilize the structures in the Kreĭn space. To this end, we first propose an adaptive embedding function in the Lorentz model and define indefinite Lorentz kernels (iLks) via the embedding function.…