arXiv: Fast proxy centers for Jeffreys centroids via Fisher-Rao midpoints
FrnkNlsn · x · 2026-08-22
Frank Nielsen's paper (arXiv:2410.14326) tackles the Jeffreys centroid — the centroid minimizing average symmetrized KL divergence, useful in clustering, information retrieval and fusion — which lacks a closed form for categorical and normal distributions.
Two fast proxies are proposed:
- The Jeffreys-Fisher-Rao center, defined as the Fisher-Rao midpoint of the sided KL centroids. It admits a generic formula for uni-parameter exponential families and closed forms for categorical/normal distributions, matching the exact Jeffreys centroid for same-mean normals.
- An inductive Gauss-Bregman center, generalizing the Gauss arithmetic-geometric double-sequence mean, which experimentally approximates the Jeffreys centroid very well.
Both are computationally fast plug-in replacements for symmetric-divergence clustering and retrieval pipelines.
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