Please send me your favorite application of information geometry.
Happy new year to all of you. Frank
Digital cameras are quickly merging with smart phones, and
visual computing applications  that support computational
photography and augmented reality applications are flourishing at a
By 2013, the annual worldwide IP traffic is predicted to be a zettabyte:
90% of consumer IP traffic and 60% of
mobile IP traffic will be video.
How do we extract and use rich information from those massive data sets?
As visual data abound, computer vision and computer graphics are
increasingly relying on machine learning and information-theoretic methods.
Computational Information Geometry is a novel paradigm to perform high-fidelity data analysis using the language and thinking of geometry.
Geometry allows us to map the data in space for efficient processing and retrieval of intrinsic information.
Geometry is in essence coordinate-free and allows one to extract the very information from data.
Geometrization of statistics has provided novel algorithms for manipulating statistical mixture models
such as Gaussian mixture models  that are commonly used in image processing:
An image pixel at position (x,y) with color attributes (red, green,
blue) is embedded into a 5D space so that a 2D color image is
interpreted as a 5D spatial point cloud. We then seek for a compact
generative statistical representation of the image point set.
Such statistical methods are useful for explaning human cognitive
and learning skills , and analyzing emerging phenomena of complex
systems using hierarchical Bayesian models.
Geometry is well alive and continue to play a crucial role in natural
sciences. For example, the propagation of seismic waves from an
epicenter follows Fermat's principle of shortest paths (minimum arrival
time). Since the Earth is made of anisotropic media such as the
peridotite, shortest paths are not line segments: The geometry is not
Euclidean. Seismic wave propagation is currently best modeled using
Finsler geometry that extends Riemmanian geometry by taking into account
the anisotropic direction of materials. In , we recently show how to
aggregate and cluster information in such Finslerian spaces.
Finsler geometry is also considered for advanced medical imaging of
Last but not least, the theory of portfolio allocation has been traditionally carried out using the mean-variance method of Markowitz.
Considering universal statistical distributions (exponential families) allows one to bypass the Gaussian assumption,
and to derive the exact expression of the risk premium (a Bregman divergence) and certainty equivalent .
Moreover, we design an on-line learning algorithm with guaranteed lower bounds on its cumulated certainty equivalents .
It is interesting to note that portfolio theory has also been considered to explain robustness trade-offs of cells in biology  (bioeconomics).
 Hiroaki Kitano: Violations of robustness trade-offs
Mol Syst Biol. 2010; 6: 384. 10.1038/msb.2010.40
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