On Procrustes Analysis in Hyperbolic Space

Puoya Tabaghi, Ivan Dokmanic

Research output: Contribution to journalArticlepeer-review

Abstract

Congruent Procrustes analysis aims to find the best matching between two point sets through rotation, reflection and translation. We formulate the Procrustes problem for hyperbolic spaces, review the canonical definition of the center mass for a point set, and give a closed-form solution for the optimal isometry between noise-free point sets. Our algorithm is analogous to the Euclidean Procrustes analysis, with centering and rotation replaced by their hyperbolic counterparts. When the data is corrupted with noise, our algorithm computes a sub-optimal alignment. We thus propose a gradient-based fine-tuning method to improve the matching accuracy.

Original languageEnglish (US)
Article number9435083
Pages (from-to)1120-1124
Number of pages5
JournalIEEE Signal Processing Letters
Volume28
DOIs
StatePublished - 2021
Externally publishedYes

Keywords

  • Hyperbolic geometry
  • procrustes analysis

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering
  • Applied Mathematics

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