Seite - 364 - in Differential Geometrical Theory of Statistics

Entropy2016,18, 396 17. Chevallier, E.; Barbaresco, F.; Angulo, J. Probabilitydensity estimationon thehyperbolic space applied to radar processing. InGeometric Science of Information; Springer: Berlin/Heidelberg, Germany, 2015; pp.753–761. 18. Said,S.;Bombrun,L.;Berthoumieu,Y.NewRiemannianPriorsontheUnivariateNormalModel.Entropy 2014,16, 4015–4031. 19. Said,S.;Hatem,H.;Bombrun,L.;Baba,C.;Vemuri,B.C.GaussiandistributionsonRiemanniansymmetric spaces: Statistical learningwithstructuredcovariancematrices. 2016,arXiv:1607.06929. 20. Terras, A. Harmonic Analysis on Symmetric Spaces and Applications II; Springer: Berlin/Heidelberg, Germany,2012. 21. Siegel,C.L.Symplecticgeometry.Am. J.Math. 1943,65,doi:10.2307/2371774. 22. Helgason, S.Differential Geometry, Lie Groups, and Symmetric Spaces; Academic Press: Cambridge, MA, USA,1979. 23. Cannon, J.W.; Floyd, W.J.; Kenyon, R.; Parry, W.R. Hyperbolic geometry. In Flavors of Geometry; CambridgeUniversityPress:Cambridge,UK,1997;Volume31,pp. 59–115. 24. Bhatia,R.MatrixAnalysis. InGraduateTexts inMathematics-169; Springer: Berlin/Heidelberg,Germany,1997. 25. Kim, P.; Richards, D. Deconvolution density estimation on the space of positive definite symmetric matrices. InNonparametricStatisticsandMixtureModels:AFestschrift inHonorofThomasP.Hettmansperger; WorldScientificPublishing: Singapore,2008;pp. 147–168. 26. Loubes, J.-M.;Pelletier,B.Akernel-basedclassifieronaRiemannianmanifold.Stat.Decis. 2016,26, 35–51. 27. Gangolli,R.;Varadarajan,V.S.HarmonicAnalysis ofSphericalFunctionsonRealReductiveGroups; Springer: Berlin/Heidelberg,Germany,1988. 28. Decurninge,A.;Barbaresco,F.RobustBurgEstimationofRadarScatterMatrix forMixturesofGaussian StationaryAutoregressiveVectors. 2016,arxiv:1601.02804. 29. Barbaresco,F.EddyDissipationRate(EDR)retrievalwithultra-fasthighrangeresolutionelectronic-scanning X-bandairport radar: ResultsofEuropeanFP7UFOToulouseAirport trials. InProceedingsof the201516th InternationalRadarSymposium,Dresden,Germany,24–26 June2015. 30. OudeNijhuis,A.C.P.;Thobois,L.P.;Barbaresco,F.MonitoringofWindHazardsandTurbulenceatAirportswith Lidar andRadarSensors andMode-SDownlinks: TheUFOProject;Bulletinof theAmericanMeteorological Society,2016, submittedforpublication. 31. Barbaresco,F.;Forget,T.;Chevallier,E.;Angulo, J.Dopplerspectrumsegmentationofradarseaclutterby mean-shiftandinformationgeometrymetric. InProceedingsof the17thInternationalRadarSymposium (IRS),Krakow,Poland,10–12May2016;pp. 1–6. 32. Fukunaga,K.;Hostetler,L.D.TheEstimationof theGradientofaDensityFunction,withApplications in PatternRecognition.Proc. IEEETrans. Inf. Theory1975,21, 32–40. 33. Arias-Castro, E.; Mason, D.; Pelletier, B. On the estimation of the gradient lines of a density and the consistencyof themean-shiftalgorithm. J.Mach. Learn.Res. 2000,17, 1–28. 34. Subbarao, R.;Meer, P.NonlinearMeanShift overRiemannianManifolds. Int. J. Comput. Vis. 2009, 84, doi:10.1007/s11263-008-0195-8. 35. Wang, Y.H.; Han, C.Z. PolSAR Image Segmentation by Mean Shift Clustering in the Tensor Space. ActaAutom.Sin. 2010,36, 798–806. 36. Rousseeuw,P.Silhouettes:Agraphicalaid to the interpretationandvalidationofclusteranalysis. J.Comput. Appl.Math. 1987,1, 53–65. 37. Barbaresco,F.GeometricTheoryofHeat fromSouriauLieGroupsThermodynamicsandKoszulHessian Geometry:Applications in InformationGeometry forExponentialFamilies.Entropy2016,18, 386. 38. Wanga,Y.;Huang,X.;Wua,L.ClusteringviageometricmedianshiftoverRiemannianmanifolds. Inf. Sci. 2013,220, 292–305. 39. Munkres, J.R.ElementaryDifferentialTopology. InAnnalsofMathematicsStudies-54;PrincetonUniversity Press: Princeton,NJ,USA,1967. c©2016bytheauthors. LicenseeMDPI,Basel,Switzerland. Thisarticle isanopenaccess articledistributedunder the termsandconditionsof theCreativeCommonsAttribution (CCBY) license (http://creativecommons.org/licenses/by/4.0/). 364