Hyperbolic Dimensionality Reduction via Horospherical Projections
HoroPCA
This code is the official PyTorch implementation of the ICML 2021 paper:
HoroPCA: Hyperbolic Dimensionality Reduction via Horospherical Projections
Ines Chami*, Albert Gu*, Dat Nguyen*, Christopher Ré
Stanford University
Paper: https://arxiv.org/abs/2106.03306
Abstract. This paper studies Principal Component Analysis (PCA) for data lying in hyperbolic spaces. Given directions, PCA relies on: (1) a parameterization of subspaces spanned by these directions, (2) a method of projection onto subspaces that preserves information in these directions, and (3) an objective to optimize, namely the variance explained by projections. We generalize each of these concepts to the hyperbolic space and propose HoroPCA, a method for hyperbolic dimensionality reduction. By focusing on the core problem of extracting principal directions, HoroPCA theoretically better preserves information in the original data such as distances, compared to previous