Frank NIELSEN
PhD (1996) HDR (2006)
ACM senior member
IEEE senior member
5793b870

Computational information geometry for Imaging and Intelligence
Dreaming digital worlds... My research aims at understanding the nature and structure of
information and randomness in data,
and exploiting algorithmically this knowledge in innovative imaging applications.
For that purpose, I coined the field of computational information geometry (computational differential geometry) to extract information as regular structures whilst
taking into account variability in datasets by grounding them in geometric spaces. Geometry beyond Euclidean spaces has a long history of revolutionizing
the way we perceived reality: Curved spacetime geometry sustained relativity theory and fractal geometry unveiled the scalefree properties of Nature.
In the digital world, geometry is datadriven and allows intrinsic data
analytics by capturing the very essence of data through invariance
principles
without being biased by such or such particular data representation.
Information geometry portal
interests ::= ((computational  information) geometry)  (computer 
(graphics  vision))  (machine  (learningvisionteaching))  optimization
Essentially, all models are wrong, but some are useful George E. P. Box (Statistician)
One geometry cannot be more true than another; it can only be more convenient
Jules H. Poincaré (Universalist)

Publications
(DBLP
pdf BibTeX),
and videos

Activities
 Forthcoming program committees (past PC):
 Forthcoming/recent invited talks:

Voronoi diagrams in information geometry, MaxEnt 2014 (September).

GSI 2013: Geometric Science of Information,
August 2830, 2013, Paris, France.

International Workshop on SimilarityBased Pattern Analysis and Recognition,
July 35, 2013, York, UK.

Advanced School and Workshop on Matrix Geometries and Applications, July 112, 2013, Trieste, Italy.

A glance at informationgeometric signal processing pdf,
MAHI, October 2012. (Invited talk)
 Recent suggested papers (copyright notice):
 Computational information geometry:
 Sided, symmetrized and mixed alphaclustering, submitted.
 Geometric Theory of Information, Springer, 2014
(Table of contents).
 A note on the optimal scalar Bregman kmeans clustering with an application to learning best statistical mixtures (recent result session at ISIT'14)
 Further results on the hyperbolic Voronoi diagrams (ISVD 2014, postponed to 2015)
 Visualizing hyperbolic Voronoi diagrams (ACM SoCG 2014, video track):
view on utube, mp4 video, paper
 Generalized Bhattacharyya and Chernoff upper bounds on Bayes error using quasiarithmetic means. Pattern Recognition Letters 42: 2534 (2014)
paper
 Gentle Nearest Neighbors Boosting over Proper Scoring Rules (IEEE TPAMI)
 Hartigan's method for kMLE: Mixture modeling with Wishart distributions and its application to motion retrieval
(GTI chapter, Springer), 2014
 Total Jensen divergences: Definition, Properties and kMeans++ Clustering, preprint, [slides]
 On the Chi square and higherorder Chi distances for approximating fdivergences
, preprint, [slides]
 InformationGeometric Lenses for Multiple Foci+Contexts Interfaces
, technical brief, Siggraph Asia, 2013
 Jeffreys centroids: A closedform expression for
positive histograms and a guaranteed tight
approximation for frequency histograms (paper slides
IEEE Xplore(R) )
 Hypothesis testing, information divergence and computational geometry (paper,
slides, Geometric Sciences of Information, GSI 2013)
 An informationgeometric characterization of Chernoff information (paper, IEEE Signal Processing Letters 2013)
 Nonlinear book manifolds: learning from associations the dynamic geometry of digital libraries, JCDL 2013. paper
 On approximating the Riemannian 1center (paper, Elsevier Computational Geometry: Theory and Applications 2013)
 Closedform informationtheoretic divergences for statistical mixtures
(paper
poster, IAPR ICPR 2012
)

Jensen Divergence Based SPD Matrix Means and Applications
(paper
poster, IAPR ICPR 2012)
 kMLE for mixtures of generalized Gaussians
(paper slides, IAPR ICPR 2012)
 kMLE: A fast algorithm for learning statistical mixture models (paper, IEEE ICASSP 2012)
 The hyperbolic Voronoi diagram in arbitrary dimension (paper)
 CramerRao lower bound and information geometry
(paper, published as a chapter of the book
Connected at Infinity II)

more...
 Visual computing (including HCI, UI, Graphics and Vision):

more...
 A software package for manipulating statistical mixtures (jMEF in Java(TM)/Matlab(R)/Python(TM))
 blog: Computational Information Geometry Wonderland and
tweets: @FrnkNlsn

A tiny englishfrenchjapanese dictionary of computational information geometry terms.

A poster on taxonomy of principal distances.
 Some notes
 αcentroids and αbarycenters of probability measures (note)
 Legendre transformation and information geometry (note)
 Limits from l'Hôpital rule: Shannon entropy as
limit cases of Rényi and Tsallis entropies (note)
 HarrisStephens' combined corner/edge detector (note BibTeX)
 IEEE member of
Computer Society (CS) ,
Signal Processing Society (SPS),
IEEE Information Theory Society (IT), and
member of the Technical Committees on Computer Pattern Analysis and Machine Intelligence and on
Mathematical Foundations of Computing
