Hyperbolic Diffusion Embedding and Distance for Hierarchical Representation Learning
This work addresses the challenge of hierarchical representation learning for fields like graph analysis, offering a novel approach with theoretical guarantees.
The paper tackles the problem of representing and measuring distances in hierarchical data by introducing a method that combines diffusion geometry with hyperbolic geometry to embed data into hyperbolic spaces, theoretically proving it recovers hierarchical structure and demonstrating its effectiveness on benchmarks.
Finding meaningful representations and distances of hierarchical data is important in many fields. This paper presents a new method for hierarchical data embedding and distance. Our method relies on combining diffusion geometry, a central approach to manifold learning, and hyperbolic geometry. Specifically, using diffusion geometry, we build multi-scale densities on the data, aimed to reveal their hierarchical structure, and then embed them into a product of hyperbolic spaces. We show theoretically that our embedding and distance recover the underlying hierarchical structure. In addition, we demonstrate the efficacy of the proposed method and its advantages compared to existing methods on graph embedding benchmarks and hierarchical datasets.