Single author publications (Frank Nielsen)

Incomplete list (in construction...)
  1. Approximation and bounding techniques for the Fisher-Rao distances between parametric statistical models, Handbook of Statistics (Editor(s): Arni S.R. Srinivasa Rao, Zhidong Bai, C.R. Rao), Elsevier, Volume 51, 2024, Pages 67-116, ISBN 9780443293283.
  2. Fast Proxy Centers for the Jeffreys Centroid: The Jeffreys–Fisher–Rao Center and the Gauss–Bregman Inductive Center. Entropy 26.12 (2024): 1008.
  3. Symplectic Bregman divergences, 2024
  4. Divergences Induced by the Cumulant and Partition Functions of Exponential Families and Their Deformations Induced by Comparative Convexity. Entropy 26(3): 193 (2024)
  5. What is.. .an Inductive Mean?. AMS Notices, 1852-1855 (2023)
  6. A Simple Approximation Method for the Fisher-Rao Distance between Multivariate Normal Distributions. Entropy 25(4): 654 (2023)
  7. Quasi-arithmetic Centers, Quasi-arithmetic Mixtures, and the Jensen-Shannon ∇-Divergences. GSI (1) 2023: 147-156
  8. Fisher-Rao and pullback Hilbert cone distances on the multivariate Gaussian manifold with applications to simplification and quantization of mixtures. TAG-ML 2023: 488-504
  9. The many faces of information geometry, Notices of the AMS, 69.1 (2022): 36-45.
  10. The Kullback–Leibler divergence between lattice Gaussian distributions, Journal of the Indian Institute of Science 102.4 (2022): 1177-1188.
  11. The analytic dually flat space of the mixture family of two prescribed distinct Cauchy distributions, Handbook of Statistics (Editor(s): Frank Nielsen, Arni S.R. Srinivasa Rao, C.R. Rao), Elsevier, Volume 46, 2022, Pages 225-256, ISBN 9780323913454.
  12. Onicescu’s informational energy and correlation coefficient in exponential families. Foundations 2.2 (2022): 362-376.
  13. Generalizing the Alpha-Divergences and the Oriented Kullback-Leibler Divergences with Quasi-Arithmetic Means. Algorithms 15(11): 435 (2022)
  14. Statistical Divergences between Densities of Truncated Exponential Families with Nested Supports: Duo Bregman and Duo Jensen Divergences. Entropy 24(3): 421 (2022)
  15. Revisiting Chernoff Information with Likelihood Ratio Exponential Families. Entropy 24(10): 1400 (2022)
  16. Comparing the Zeta Distributions with the Pareto Distributions from the Viewpoint of Information Theory and Information Geometry: Discrete versus Continuous Exponential Families of Power Laws, Physical Sciences Forum. Vol. 5. No. 1. MDPI, 2022.
  17. Progress in Information Geometry, Springer Nature, Switzerland, 2021.
  18. On a Variational Definition for the Jensen-Shannon Symmetrization of Distances Based on the Information Radius. Entropy 23(4): 464 (2021)
  19. On geodesic triangles with right angles in a dually flat space, Progress in Information Geometry: Theory and Applications. Cham: Springer International Publishing, 2021. 153-190.
  20. Fast Approximations of the Jeffreys Divergence between Univariate Gaussian Mixtures via Mixture Conversions to Exponential-Polynomial Distributions. Entropy 23(11): 1417 (2021)
  21. On a Generalization of the Jensen-Shannon Divergence and the Jensen-Shannon Centroid. Entropy 22(2): 221 (2020)
  22. On Voronoi Diagrams on the Information-Geometric Cauchy Manifolds. Entropy 22(7): 713 (2020)
  23. The Siegel-Klein Disk: Hilbert Geometry of the Siegel Disk Domain. Entropy 22(9): 1019 (2020)
  24. An Elementary Introduction to Information Geometry. Entropy 22(10): 1100 (2020)
  25. On the Jensen-Shannon Symmetrization of Distances Relying on Abstract Means. Entropy 21(5): 485 (2019)
  26. The Statistical Minkowski Distances: Closed-Form Formula for Gaussian Mixture Models. GSI 2019: 359-367
  27. What is an information projection, Notices of the AMS 65.3 (2018): 321-324.
  28. The Chord Gap Divergence and a Generalization of the Bhattacharyya Distance. IEEE ICASSP 2018: 2276-2280
  29. Introduction to HPC with MPI for Data Science, Undergraduate Topics in Computer Science, Springer 2016, ISBN 978-3-319-21902-8, pp. 3-259
  30. Image and Information, arXiv:1602.01228 (2016).
  31. Geometric science of information, Springer International Publishing, 2015.
  32. On learning statistical mixtures maximizing the complete likelihood, AIP Conference Proceedings. Vol. 1641. No. 1. American Institute of Physics, 2015.
  33. Generalized Bhattacharyya and Chernoff upper bounds on Bayes error using quasi-arithmetic means. Pattern Recognit. Lett. 42: 25-34 (2014)
  34. Geometric Theory of Information, Berlin, Germany:: Springer, 2014.
  35. An Information-Geometric Characterization of Chernoff Information. IEEE Signal Process. Lett. 20(3): 269-272 (2013)
  36. Jeffreys Centroids: A Closed-Form Expression for Positive Histograms and a Guaranteed Tight Approximation for Frequency Histograms. IEEE Signal Process. Lett. 20(7): 657-660 (2013)
  37. Cramér-Rao lower bound and information geometry. Connected at Infinity II: A Selection of Mathematics by Indians (2013): 18-37.
  38. Hypothesis Testing, Information Divergence and Computational Geometry. GSI 2013: 241-248
  39. Perspective click-and-drag area selections in pictures. MVA 2013: 29-32
  40. Pattern Learning and Recognition on Statistical Manifolds: An Information-Geometric Review. SIMBAD 2013: 1-25
  41. Logging safely in public spaces using color PINs, arXiv:1304.6499 (2013).
  42. K-MLE: A fast algorithm for learning statistical mixture models. ICASSP 2012: 869-872
  43. Closed-form information-theoretic divergences for statistical mixtures. ICPR 2012: 1723-1726
  44. Perspective dragging: quick area selection in photos. SIGGRAPH ASIA Posters 2012: 18
  45. Chernoff information of exponential families, 2011.
  46. A family of statistical symmetric divergences based on Jensen's inequality, arXiv:1009.4004 (2010).
  47. Computational Information Geometry-Pursing the Meaning of Distances, Open Systems Science. IOS Press, 2010. 217-249.
  48. A Concise and Practical Introduction to Programming Algorithms in Java, Undergraduate Topics in Computer Science, Springer 2009, ISBN 978-1-84882-338-9
  49. Technical opinion: Steering self-learning distance algorithms. Communications of the ACM 52(11): 150-152 (2009)
  50. Opinion on open, closed, or clopen access, Communications of the ACM (CACM) (2009).
  51. Harris-Stephens' combined corner/edge detector, in unpublished computer vision textbook (2009).
  52. A volume shader for quantum voronoi diagrams inside the 3d bloch ball, ShaderX7: Advanced Rendering Techniques. Charles River Media/Thomson Publishing (2009).
  53. Emerging Trends in Visual Computing: LIX Fall Colloquium, ETVC 2008, Palaiseau, France, November 18-20, 2008, Revised Selected and Invited Papers. (2009).
  54. An interactive tour of Voronoi diagrams on the GPU. In ShaderX6, pages 539–556. Charles River Media, February 2008. Section 9.1 (Beyond Pixels and Triangles).
  55. Visual computing: Geometry, graphics, and vision (graphics series), Charles River Media, Inc., 2005.
  56. The Digital Chameleon Principle: Computing Invisibility by Rendering Transparency. IEEE Computer Graphics and Applications 27(1): 90-96 (2007) 2005
  57. Surround video: a multihead camera approach. Vis. Comput. 21(1-2): 92-103 (2005)
  58. A GPU panorama viewer for generic camera models. In ShaderX5: Advanced Rendering Techniques, pages 543–552. Charles River Media/Thomson Publishing, December 2005.
  59. Interactive image segmentation based on GPU cellular automata. In ShaderX5: Advanced Rendering Techniques, pages 511–518. Charles River Media/Thomson Publishing, December 2005.
  60. Plenoptic path and its applications. IEEE ICIP (1) 2003: 793-796
  61. High Resolution Full Spherical Videos. IEEE ITCC 2002: 260-267 2001
  62. On point covers of c-oriented polygons. Theor. Comput. Sci. 263(1-2): 17-29 (2001) 2000
  63. On Representing Spherical Videos, IEEE Conference on Computer Vision and Pattern Recognition (CVPR). 2001.
  64. Fast stabbing of boxes in high dimensions. Theor. Comput. Sci. 246(1-2): 53-72 (2000)
  65. Randomized adaptive algorithms for mosaicing systems. IEICE TRANSACTIONS on Information and Systems 83.7 (2000): 1386-1394.
  66. On point covers of c-oriented polygons. CCCG 1998
  67. Grouping and Querying: A Paradigm to Get Output-Sensitive Algorithms. JCDCG 1998: 250-257
  68. Randomized Adaptive Algorithms for Mosaicing Systems. MVA 1998: 11-14 1996
  69. Output-Sensitive Peeling of Convex and Maximal Layers. Inf. Process. Lett. 59(5): 255-259 (1996)
  70. Fast Stabbing of Boxes in High Dimensions. CCCG 1996: 87-92