A Geometry-Aware Algorithm to Learn Hierarchical Embeddings in Hyperbolic Space
This work addresses a specific challenge in representation learning for hierarchical data, offering an incremental improvement over existing hyperbolic embedding methods.
The paper tackled the difficulty of learning hyperbolic embeddings for hierarchical data by identifying three performance-harming issues and developing a geometry-aware algorithm with dilation and regularization, achieving superior performance on synthetic and real-world datasets.
Hyperbolic embeddings are a class of representation learning methods that offer competitive performances when data can be abstracted as a tree-like graph. However, in practice, learning hyperbolic embeddings of hierarchical data is difficult due to the different geometry between hyperbolic space and the Euclidean space. To address such difficulties, we first categorize three kinds of illness that harm the performance of the embeddings. Then, we develop a geometry-aware algorithm using a dilation operation and a transitive closure regularization to tackle these illnesses. We empirically validate these techniques and present a theoretical analysis of the mechanism behind the dilation operation. Experiments on synthetic and real-world datasets reveal superior performances of our algorithm.