Hydra: A method for strain-minimizing hyperbolic embedding of network-\n and distance-based data

2019/03/21 by Martin Keller‐Ressel, Keller-Ressel, Martin, Stephanie Nargang +1 · 2 citations
Computer Science · Engineering · #51M10 #68Wxx #Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #G.2.2 #G.3 #Human Pose and Action Recognition #Machine Learning (cs.LG) #Metric Geometry (math.MG) #Neural Networks and Applications #Traffic Prediction and Management Techniques

paper · pdf · doi:10.48550/arxiv.1903.08977

openalex publication_date 2019/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce hydra (hyperbolic distance recovery and approximation), a new\nmethod for embedding network- or distance-based data into hyperbolic space. We\nshow mathematically that hydra satisfies a certain optimality guarantee: It\nminimizes the `hyperbolic strain' between original and embedded data points.\nMoreover, it recovers points exactly, when they are located on a hyperbolic\nsubmanifold of the feature space. Testing on real network data we show that the\nembedding quality of hydra is competitive with existing hyperbolic embedding\nmethods, but achieved at substantially shorter computation time. An extended\nmethod, termed hydra+, outperforms existing methods in both computation time\nand embedding quality.\n

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