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 principles 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)

• Publications (DBLP pdf BibTeX), and videos
• Activities
• Forthcoming program committees (past PC):
  • Workshop on Computational Information Geometry for Image and Signal Processing (CIGISP), 21-25 September 2015, funded by the International Center of Mathematical Sciences (ICMS) (UK).
    Organizers: Kit Dodson, Frank Critchley and Frank Nielsen.
  • S+SSPR 2014: Structural and Syntactic Pattern Recognition and Statistical Techniques in Pattern Recognition, August 20-22, 2014, Joensuu, Finland.
  • MAHI workshop: Methodological Aspects of Hyperspectral Imaging, October 2013
• 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) paper
    • 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 (paper poster, IAPR ICPR 2012 )
    • Jensen Divergence Based SPD Matrix Means and Applications (paper 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)
    • more...
  • Visual computing (including HCI, UI, Graphics and Vision):
    • Consensus Region Merging for Image Segmentation, IAPR ACPR, 2013. paper
    • Fast Newton Nearest Neighbors Boosting For Image Classification, IEEE MLSP, 2013.
    • Perspective click-and-drag area selections in pictures (MVA 2013, video slides)
      Best practical paper award.
    • Logging safely in public spaces using color PINs (arXiv 1304.6499 video)
  • 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 english-french-japanese dictionary of computational information geometry terms.
• A poster on taxonomy of principal distances.
• Some notes
  • 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)
• 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