On Procrustes Analysis in Hyperbolic Space
| Autor: | Ivan Dokmanic, Puoya Tabaghi |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Signal Processing (eess.SP)
Applied Mathematics Hyperbolic geometry Hyperbolic space 020206 networking & telecommunications 02 engineering and technology Translation (geometry) Signal Processing FOS: Electrical engineering electronic engineering information engineering 0202 electrical engineering electronic engineering information engineering Isometry Point (geometry) Electrical Engineering and Systems Science - Signal Processing Electrical and Electronic Engineering Procrustes analysis Orthogonal Procrustes problem Rotation (mathematics) Algorithm Mathematics |
| Zdroj: | IEEE Signal Processing Letters. 28:1120-1124 |
| ISSN: | 1558-2361 1070-9908 |
| DOI: | 10.1109/lsp.2021.3081379 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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