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Geometry and Fixed-Rate Quantization in Riemannian Metric Spaces Induced by Separable Bregman Divergences

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Part of the Lecture Notes in Computer Science book series (LNIP,volume 11712)


Dual separable Bregman divergences induce dual Riemannian metric spaces which are isometric to the Euclidean space after non-linear monotone embeddings. We investigate fixed-rate quantization and the induced Voronoi diagrams in those metric spaces.


  • Bregman divergence
  • Riemannian metric
  • Legendre transformation
  • Voronoi diagram
  • Quantization

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Correspondence to Frank Nielsen .

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Gomes-Gonçalves, E., Gzyl, H., Nielsen, F. (2019). Geometry and Fixed-Rate Quantization in Riemannian Metric Spaces Induced by Separable Bregman Divergences. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2019. Lecture Notes in Computer Science(), vol 11712. Springer, Cham.

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-26979-1

  • Online ISBN: 978-3-030-26980-7

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