PhD (1996) HDR (2006)
ACM senior member
IEEE senior member
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 scale-free properties of Nature.
In the digital world, geometry is data-driven and allows intrinsic data
analytics by capturing the very essence of data through invariance
without being biased by such or such particular data representation.
Information geometry portal
interests ::= ((computational | information) geometry) | (computer |
(graphics | vision)) | (machine | (learning|vision|teaching)) | 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)
A software package for manipulating statistical mixtures (jMEF in Java(TM)/Matlab(R)/Python(TM))
blog: Computational Information Geometry Wonderland and
A tiny english-french-japanese dictionary of computational information geometry terms.
A poster on taxonomy of principal distances.
- Forthcoming program committees (past PC):
- Forthcoming/recent invited talks:
Voronoi diagrams in information geometry, MaxEnt 2014 (September).
GSI 2013: Geometric Science of Information,
August 28-30, 2013, Paris, France.
International Workshop on Similarity-Based Pattern Analysis and Recognition,
July 3-5, 2013, York, UK.
Advanced School and Workshop on Matrix Geometries and Applications, July 1-12, 2013, Trieste, Italy.
A glance at information-geometric signal processing pdf,
MAHI, October 2012. (Invited talk)
- Recent suggested papers (copyright notice):
- Computational information geometry:
- Sided, symmetrized and mixed alpha-clustering, submitted.
- Geometric Theory of Information, Springer, 2014
(Table of contents).
- A note on the optimal scalar Bregman k-means 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 quasi-arithmetic means. Pattern Recognition Letters 42: 25-34 (2014)
- Gentle Nearest Neighbors Boosting over Proper Scoring Rules (IEEE TPAMI)
- Hartigan's method for k-MLE: Mixture modeling with Wishart distributions and its application to motion retrieval
(GTI chapter, Springer), 2014
- Total Jensen divergences: Definition, Properties and k-Means++ Clustering, preprint, [slides]
- On the Chi square and higher-order Chi distances for approximating f-divergences
, preprint, [slides]
- Information-Geometric Lenses for Multiple Foci+Contexts Interfaces
, technical brief, Siggraph Asia, 2013
- Jeffreys centroids: A closed-form 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 information-geometric characterization of Chernoff information (paper, IEEE Signal Processing Letters 2013)
- Non-linear book manifolds: learning from associations the dynamic geometry of digital libraries, JCDL 2013. paper
- On approximating the Riemannian 1-center (paper, Elsevier Computational Geometry: Theory and Applications 2013)
- Closed-form information-theoretic divergences for statistical mixtures
poster, IAPR ICPR 2012
Jensen Divergence Based SPD Matrix Means and Applications
poster, IAPR ICPR 2012)
- k-MLE for mixtures of generalized Gaussians
(paper slides, IAPR ICPR 2012)
- k-MLE: A fast algorithm for learning statistical mixture models (paper, IEEE ICASSP 2012)
- The hyperbolic Voronoi diagram in arbitrary dimension (paper)
- Cramer-Rao lower bound and information geometry
(paper, published as a chapter of the book
Connected at Infinity II)
- Visual computing (including HCI, UI, Graphics and Vision):
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
- α-centroids and α-barycenters 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)
- Harris-Stephens' combined corner/edge detector (note BibTeX)