Research Colloquium Presentation by Bo Xiong

3 years ago

Hyperbolic Embeddings

In the machine learning community, data is usually represented in Euclidean space, while real-world data like scale-free networks and knowledge graphs exhibit a highly non-Euclidean latent anatomy, and suffer from large distortion when embedded in Euclidean space. Non-Euclidean Riemannian manifolds like hyperbolic and spherical space have demonstrated outstanding performance in embedding tree-like or spherical structures individually but cannot embed the mixed structures.

In this talk, we show some basic concepts of differential geometry and non-Euclidean Riemannian embeddings, including hyperbolic embeddings, spherical embeddings and product space embeddings. We also discuss the motivations to go beyond the Riemannian space that generalizes hyperbolic and spherical embeddings. We derive some basic operations like matrix-vector multiplications, bias translations in semi-Riemannian manifolds, which are useful for knowledge graph embedding.

The slides of the presentation can be found here