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Entropy2016,18, 98 8. Arnaudon,M.;Barbaresco,F.;Yang,L.RiemannianMediansandMeansWithApplications toRadarSignal Processing. IEEEJ.Sel. Top. SignalProcess. 2013,7, 595–604. 9. Arnaudon,M.;Yang,L.;Barbaresco,F.Stochasticalgorithmsforcomputingp-meansofprobabilitymeasures, GeometryofRadarToeplitzcovariancematricesandapplications toHRDopplerprocessing. InProceedings of International InternationalRadarSymposium(IRS),Leipzig,Germany,7–9September2011;pp. 651–656. 10. Terras,A.HarmonicAnalysis onSymmetricSpacesandApplications; Springer-Verlag:NewYork,NY,USA,1988; VolumeII. 11. Atkinson,C.;Mitchell,A.Rao’sdistancemeasure.SankhyaSer.A1981,43, 345–365. 12. Pennec,X.ProbabilitiesandstatisticsonRiemannianmanifolds: Basic tools forgeometricmeasurements. InProcedingsof the IEEEWorkshoponNonlinearSignalandImageProcessing,Antalya,Turkey,20–23June 1999;pp. 194–198. 13. Pennec,X. IntrinsicstatisticsonRiemannianmanifolds: Basic tools forgeometricmeasurements. J.Math. ImagingVis. 2006,25, 127–154. 14. Guang,C.;BabaC.V.ANovelDynamicSystemintheSpaceofSPDMatriceswithApplicationstoAppearance Tracking.SIAMJ. ImagingSci. 2013,6, 592–615. 15. Said, S.; Bombrun, L.; Berthoumieu, Y.; Manton, J. RiemannianGaussiandistributions on the space of symmetricpositivedefinitematrices. 2015,arXiv:1507.01760. 16. Schwarz,G.EstimatingtheDimensionofaModel.Ann. Stat. 1978,6, 461–464. 17. Lee, J.S.;Grunes,M.R.;Ainsworth,T.L.;Du,L.J.; Schuler,D.L.;Cloude, S.R.Unsupervisedclassification usingpolarimetricdecompositionandthecomplexWishart classifier. IEEETrans.Geosci. RemoteSens. 1999, 37, 2249–2258. 18. Berezin,F.A.Quantization incomplexsymmetric spaces. Izv.Akad.NaukSSSRSer.Mat. 1975,39, 363–402. 19. Malliavin, P. Invariant or quasi-invariant probabilitymeasures for infinite dimensional groups, Part II: UnitarizingmeasuresorBerezinianmeasures. Jpn. J.Math. 2008,3, 19–47. 20. Barbaresco, F. Information Geometry of Covariance Matrix: Cartan-Siegel Homogeneous Bounded Domains, Mostow/BergerFibrationandFréchetMedian,Matrix InformationGeometry;Bhatia,R.,Nielsen,F.,Eds.; Springer: NewYork,NY,USA,2012;pp. 199–256. 21. Barbaresco,F. InformationgeometrymanifoldofToeplitzHermitianpositivedefinitecovariancematrices: Mostow/Berger fibration and Berezin quantization of Cartan-Siegel domains. Int. J. Emerg. Trends SignalProcess. 2013,1, 1–11. 22. Jeuris, B.; Vandebril, R.Averagingblock-ToeplitzmatriceswithpreservationofToeplitzblock structure. In Proceedings of the SIAM Conference on Applied Linear Algebra (ALA), Atlanta, GA, USA, 20–26October2015. 23. Jeuris,B.;Vandebril,R.TheKählerMeanofBlock-ToeplitzMatriceswithToeplitzStructuredBlock.Available online: http://www.cs.kuleuven.be/publicaties/rapporten/tw/TW660.pdf (accessedon10March2016). 24. Jeuris,B.RiemannianOptimizationforAveragingPositiveDefiniteMatrices. Ph.D.Thesis,Universityof Leuven,Leuven,Belgium,2015. 25. Maass,H.Siegel’smodular formsandDirichlet series. InLectureNotes inMathematics; Springer-Verlag:New York,NY,USA,1971;Volume216. 26. Higham,N.J.FunctionsofMatrices,TheoryandComputation; Society for IndustrialandAppliedMathematics: Philadelphia,PA,USA,2008. 27. Helgason, S. Differential Geometry, Lie Groups, and Symmetric Spaces; American Mathematical Society: Providence,RI,USA,2001. 28. Afsari,B.RiemannianLp centerofmass: Existence,uniquenessandconvexity.Proc.Am.Math. Soc. 2011, 139, 655–673. 29. Muirhead,R.J.Aspects ofMultivariateStatisticalTheory; JohnWiley&Sons:NewYork,NY,USA,1982. 30. Robert,C.P.;Casella,G.MonteCarloStatisticalMethods; Springer-Verlag: Berlin,Germany,2004. 31. Udriste, C. Convex Functions and Optimization Methods on Riemannian Manifolds; Mathematics and Its Applications;KluwerAcademicPublishers:Dordrecht,TheNetherlands,1994. 32. Chavel, I.RiemannianGeometry, aModern Introduction;CambridgeUniversityPress:Cambridge,UK,2006. 33. Yang,L.MédianesdeMesuresdeProbabilitédans lesVariétésRiemanniennesetApplicationsà laDétection deCiblesRadar. Ph.D.Thesis,L’universitédePoitiers,Poitiers,France,2011. (InFrench) 382
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Differential Geometrical Theory of Statistics
Titel
Differential Geometrical Theory of Statistics
Autoren
Frédéric Barbaresco
Frank Nielsen
Herausgeber
MDPI
Ort
Basel
Datum
2017
Sprache
englisch
Lizenz
CC BY-NC-ND 4.0
ISBN
978-3-03842-425-3
Abmessungen
17.0 x 24.4 cm
Seiten
476
Schlagwörter
Entropy, Coding Theory, Maximum entropy, Information geometry, Computational Information Geometry, Hessian Geometry, Divergence Geometry, Information topology, Cohomology, Shape Space, Statistical physics, Thermodynamics
Kategorien
Naturwissenschaften Physik
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Differential Geometrical Theory of Statistics