Page - 417 - in Differential Geometrical Theory of Statistics
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Entropy2016,18, 425
(a) (b) (c)
(d) (e) (f)
(g) (h) (i)
Figure5.MinimizingnormalMPPsbetweentwoïŹxedpoints (red/cyan). Fromisotropiccovariance
(top row, (a)) to anisotropic (top row, (c)) onS2. ComparewithminimizingRiemanniangeodesic
(blackcurve). TheMPPtravels longer in thedirectionsofhighvariance. Familiesofcurves (middle
row, (dâf)) andcorrespondinganti-development (bottomrow, (gâi))onthe threesurfaces inFigure4.
The familyof curves isgeneratedby rotating the covariancematrix as inFigure4. Noticehowthe
varyinganisotropyaffects theresultingminimizingcurves,andhowtheanti-developedcurvesendat
differentpoints inR2.
(a) (b) (c)
Figure6.Cont.
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Differential Geometrical Theory of Statistics
- Title
- Differential Geometrical Theory of Statistics
- Authors
- Frédéric Barbaresco
- Frank Nielsen
- Editor
- MDPI
- Location
- Basel
- Date
- 2017
- Language
- English
- License
- CC BY-NC-ND 4.0
- ISBN
- 978-3-03842-425-3
- Size
- 17.0 x 24.4 cm
- Pages
- 476
- Keywords
- Entropy, Coding Theory, Maximum entropy, Information geometry, Computational Information Geometry, Hessian Geometry, Divergence Geometry, Information topology, Cohomology, Shape Space, Statistical physics, Thermodynamics
- Categories
- Naturwissenschaften Physik