Hyperbolic Procrustes Analysis Using Riemannian Geometry

Ya Wei Eileen Lin, Yuval Kluger, Ronen Talmon

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Label-free alignment between datasets collected at different times, locations, or by different instruments is a fundamental scientific task. Hyperbolic spaces have recently provided a fruitful foundation for the development of informative representations of hierarchical data. Here, we take a purely geometric approach for label-free alignment of hierarchical datasets and introduce hyperbolic Procrustes analysis (HPA). HPA consists of new implementations of the three prototypical Procrustes analysis components: translation, scaling, and rotation, based on the Riemannian geometry of the Lorentz model of hyperbolic space. We analyze the proposed components, highlighting their useful properties for alignment. The efficacy of HPA, its theoretical properties, stability and computational efficiency are demonstrated in simulations. In addition, we showcase its performance on three batch correction tasks involving gene expression and mass cytometry data. Specifically, we demonstrate high-quality unsupervised batch effect removal from data acquired at different sites and with different technologies that outperforms recent methods for label-free alignment in hyperbolic spaces.

Original languageEnglish
Title of host publicationAdvances in Neural Information Processing Systems 34 - 35th Conference on Neural Information Processing Systems, NeurIPS 2021
EditorsMarc'Aurelio Ranzato, Alina Beygelzimer, Yann Dauphin, Percy S. Liang, Jenn Wortman Vaughan
Pages5959-5971
Number of pages13
ISBN (Electronic)9781713845393
StatePublished - 2021
Event35th Conference on Neural Information Processing Systems, NeurIPS 2021 - Virtual, Online
Duration: 6 Dec 202114 Dec 2021

Publication series

NameAdvances in Neural Information Processing Systems
Volume8

Conference

Conference35th Conference on Neural Information Processing Systems, NeurIPS 2021
CityVirtual, Online
Period6/12/2114/12/21

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Signal Processing
  • Computer Networks and Communications

Fingerprint

Dive into the research topics of 'Hyperbolic Procrustes Analysis Using Riemannian Geometry'. Together they form a unique fingerprint.

Cite this