Frank NIELSEN (PhD'96, HDR'06)
@FrnkNlsn
Blog
ACM SM,
IEEE SM,
ELLIS
Sony CSL
LIX
Main fields of interest:
- Geometric science of information
- Computational information geometry
- Theory of (dis)similarities and aggregators
- Machine learning and artificial intelligence
- Visual computing and computational photography
- Computational mathematics
Editor:
- Information geometry (Springer INGE)
- Entropy (MDPI).
- Past: Journal of Mathematical Imaging and Vision (Springer JMIV)
- Publications
- Some introductory and overview papers:
- Cramer-Rao lower bound and information geometry
→ A first read introducing the Fisher information matrix, the CRLB, and the differential-geometrization of statistics - An elementary introduction to information geometry
→ Learn what is the fundamental theorem of information geometry! - Introduction to Bregman manifolds
→ Learn the dually flat spaces of exponential families and mixture families, and the dual generalized Pythagorean theorems - What is... an information projection?
→ Projection along geodesics, projection as divergence minimization, cases where we have uniqueness of projections - Slides and video:
- Five selected publications:
- Bregman Voronoi diagrams, Discrete and Computational Geometry, 2010.
- The Burbea-Rao and Bhattacharyya centroids, IEEE Transactions on Information Theory, 2011.
- An information-geometric characterization of Chernoff information, IEEE Signal Processing Letters, 2013.
- On the chi square and higher-order chi distances for approximating f-divergences, IEEE Signal Processing Letters, 2013.
- Generalized Bhattacharyya and Chernoff upper bounds on Bayes error using quasi-arithmetic means, Pattern Recognition Letters, 2014.
- Five selected collaborative publications tackling various applications:
- Imaging: Statistical region merging, IEEE Transactions on pattern analysis and machine intelligence, 2014.
- Music: DeepBach: a Steerable Model for Bach Chorales Generation, ICML 2017.
- Computer graphics: Volumetric illustration: designing 3D models with internal textures, SIGGRAPH, 2004.
- Computer vision: Shape retrieval using hierarchical total Bregman soft clustering, IEEE transactions on pattern analysis and machine intelligence, 2012.
- Telecommunications: Combinatorial optimization algorithms for radio network planning, Theoretical Computer Science 2001.
- Some research cards
- Cramer-Rao lower bound and information geometry
- Textbooks (AMZ book author web page):
- Introduction to HPC with MPI for Data Science, Springer, 2016. (also translated in Chinese)
- A Concise and Practical Introduction to Programming Algorithms in Java, Springer, 2009. (also translated in Chinese)
- Visual Computing: Geometry, Graphics, and Vision, Charles River Media, 2005.