Dimension Reduction for the Hyperbolic Space
itai benjamini, Yury Makarychev
TL;DR
This paper introduces a new method for reducing dimensions in hyperbolic spaces, enabling embeddings with bounded distortion especially for distant points, which enhances geometric data analysis.
Contribution
It presents the first dimension reduction technique for hyperbolic space that maintains bounded distortion for far apart points.
Findings
Effective embedding of hyperbolic space with bounded distortion
Dimension reduction preserves geometric relationships for distant points
Advances in hyperbolic data embedding techniques
Abstract
A dimension reduction for the hyperbolic space is established. When points are far apart an embedding with bounded distortion into the hyperbolic plane is achieved.
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Taxonomy
TopicsAdvanced Numerical Analysis Techniques · Digital Image Processing Techniques · Computational Geometry and Mesh Generation