Home page of Frank NIELSEN | Geometric Science of Information (GSI)

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Frank NIELSEN
Sony Computer Science Laboratories, Inc (Tokyo), [contact]
Senior Researcher (Fellow), Biography [research overview], IEEE Fellow

Research:
- Geometric Science of Information (GSI'27, 24-27 August 2027, ENAC, Toulouse, France and related events)
- Information Geometry [pyBregMan library] Non-Euclidean Computational Geometry and Its Applications in Machine Learning
- Geometric structures of learning and dynamics of AI
- Distances, divergences, and mutual information , including Bregman divergences
- Information Theory , Visual Computing , Machine Learning , Parallel computing and High Performance Computing

[+] Recent publication list / Selected publications

pdf The Many Faces of Information Geometry, AMS Notices, 2022. MR 4353351. video tutorial, and a full-length review paper
Approximation and bounding techniques for the Fisher-Rao distances between parametric statistical models, Handbook of Statistics (51), Elsevier, 2024. (arXiv:2403.10089)
On a variational definition for the Jensen-Shannon symmetrization of distances based on the information radius, Entropy 23.4 (2021): 464. (arXiv:2102.09728)
Generalized Bhattacharyya and Chernoff upper bounds on Bayes error using quasi-arithmetic means, Pattern Recognition Letters 42, 2014. (arXiv:1401.4788)
pdf Revisiting Chernoff information with likelihood ratio exponential families, Entropy 24 (10), 1400, 2022. (arXiv:2207.03745)
pdf project Non-linear Embeddings in Hilbert Simplex Geometry, TAG-ML 2023. (arXiv:2302.09738)

Software

Slides

A more detailed home page, a blog, some research cards

Some recent technical reports (in preparation for peer-reviewed publications)

Dual-connection midpoint matrix means and their Gauss composition, arXiv:2609.07551
Minimum enclosing Bregman balls made easy, arXiv:2607.24197
Group invariance of f-divergences and the Fisher-Rao distance, arXiv:2606.25790
Neural Legendre-Fenchel transform with Hessian Preconditioning, arXiv:2606.09077
Generalising maximum mean discrepancy: kernelised functional Bregman divergences, arXiv:2604.24047
Quadratic polarity and polar Fenchel-Young divergences from the canonical Legendre polarity, arXiv:2603.04812
Geometric structures and deviations on James' symmetric positive-definite matrix bicone domain, arXiv:2603.02483
Scales of Fréchet means and Karcher quasi-arithmetic means, arXiv:2511.21173
pyBregMan: A Python library for Bregman Manifolds, arXiv:2408.04175
Tempered Calculus for ML: Application to Hyperbolic Model Embedding, arXiv:2402.04163

Some selected works

pdf The Many Faces of Information Geometry, AMS Notices, 2022. MR 4353351. Watch the video tutorial, and a full-length review paper
Approximation and bounding techniques for the Fisher-Rao distances between parametric statistical models, Handbook of Statistics (51), Elsevier, 2024. (arXiv)
On f-Divergences Between Cauchy Distributions, IEEE Transactions on Information Theory, 2023. (arXiv)
pdf Statistical divergences between densities of truncated exponential families with nested supports: Duo Bregman and duo Jensen divergences, Entropy 2022. (arXiv)
pdf On a Generalization of the Jensen–Shannon Divergence and the Jensen–Shannon Centroid, Entropy, 2022. (arXiv)
pdf Revisiting Chernoff information with likelihood ratio exponential families, Entropy 2022. (arXiv)
On conformal divergences and their population minimizers, IEEE Transactions on Information Theory 62 (1), 2015. (arXiv)
Generalized Bhattacharyya and Chernoff upper bounds on Bayes error using quasi-arithmetic means, Pattern Recognition Letters 42, 2014. (arXiv)
Optimal interval clustering: Application to Bregman clustering and statistical mixture learning, IEEE Signal Processing Letters 21 (10), 2014. (arXiv)
On the chi square and higher-order chi distances for approximating f-divergences, IEEE Signal Processing Letters, 2013. (arXiv)
Jeffreys centroids: A closed-form expression for positive histograms and a guaranteed tight approximation for frequency histograms, IEEE Signal Processing Letters 20 (7), 2013. (arXiv)
Shape retrieval using hierarchical total Bregman soft clustering, IEEE Transactions on Pattern Analysis and Machine Intelligence 2012.
The Burbea-Rao and Bhattacharyya centroids, IEEE Transactions on Information Theory, 2011. (arXiv)
pdf Hierarchical clustering, chapter 8 of Introduction to HPC with MPI for Data Science, Springer, 2016.
A closed-form expression for the Sharma–Mittal entropy of exponential families, Journal of Physics A: Mathematical and Theoretical 45 (3), 2011. (arXiv)
Bregman Voronoi diagrams, Discrete & Computational Geometry 44, 2010. (arXiv). Conference: On Bregman Voronoi diagrams, Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms (SODA 2007).
Hyperbolic Voronoi diagrams made easy, IEEE International Conference on Computational Science and Its Applications, 2010. (arXiv)
Approximating smallest enclosing balls with applications to machine learning, International Journal of Computational Geometry & Applications 19 (05), 2009.

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