Frank NIELSEN / フランク・ニールセン Sony Computer Science Laboratories Inc, Tokyo, contact Senior Researcher, Fellow Biography, research overview A more detailed home page, a blog

• Research: Geometric structures of learning, geometric computing for ML and AI and Information Theory with Applications. Dissimilarities and divergences including Bregman divergences
  
• Principal interests:

  Information Geometry, pyBregMan library for Bregman Manifolds Distances, divergences, and mutual information Geometric Science of Information (GSI), biannual conference and satellite events Information Theory Visual Computing Machine Learning Parallel computing and High Performance Computing, HPC

[+] Publication list (reverse chronological) and Slides
  Some selected works:

• pdf The Many Faces of Information Geometry, AMS Notices, 2022. 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)
• 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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