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广义Beta Ⅱ分布子流形的几何结构 被引量：2

Geometric Structure of Sub-manifolds of the Generalized Beta Type Ⅱ Distribution
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摘要 研究分布流形的几何结构是信息几何的一项重要课题。本文给出了基于信息几何的角度广义Beta Ⅱ分布子流形的几何结构;计算出此流形的Fisher信息阵和黎曼联络,进而求出高斯曲率;并在该流形上定义Kullback-Leibler散度及J-散度,并说明散度之间的关系以及各种特殊情况下的散度;最后给出流形上的测地线方程。 Investigating the geometric structures of the distribution manifolds is a basic task in information geometry. In this paper, the submanifolds of the generalized beta type Ⅱ distribution and obtain is investigated its geometric structure. The Fish information matrix, Riemannian connections and Gaussian curvatures of the submanifolds of the generalized beta type Ⅱ distribution are given. At last, Kullback-Leibler divergence, J-divergence and geodesic equations are obtained.
作者 吴利萍 曹丽梅 田敏
机构地区 北京理工大学理学院数学系
出处 《科技导报》 CAS CSCD 2008年第22期34-37,共4页 Science & Technology Review
关键词 流形 高斯曲率 散度 信息几何 manifold Gaussian curvature divergence information geometry
分类号 O186.1 [理学—基础数学]
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参考文献8

  • 1Amari S, Nagaoka H. Metbods of information geometry [M]. London: Oxford University Press, 2000.
  • 2Amari S. Differential geometrical methods in statistics [M]. Germany: Springer Lecture Notes in Statistics, 1985.
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  • 7仲锋惟,孙华飞,张真宁.Fisher Z分布流形的几何结构[J].科技导报,2007,25(9):33-36. 被引量：6
  • 8Zhong F, Sun H, Zhang Z. The geometry of the dirichlet manifold [J]. Journal of the Korean Mathematical Society, 2008, 45(3): 859-870.

二级参考文献6

  • 1AMARI S. Differential geometrical methods in statistics[M]. Germany:Springer lecture Notes in Statistics, 1985.
  • 2AMARI S. Methods of information geometry [M]. England: Oxford University Press, 2000.
  • 3DODSON C T. Gamma manifolds and stochastic geometry[C]// Proceedings of the workshop on recent topics in differential geometry. Santiago de Compostela, 1997: 16- 19.
  • 4AMARI S. Differential geometry of a parametric family of invertible linear systems Riemannian metric, dual affine connections and divergence [J]. Mathematical Systems Theory, 1987(20): 53-82.
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  • 6DODSON C T, MATSUZOE H. An affine embedding of the gamma manifold[J]. Appl Sci, 2003(5): 1-6.

共引文献5

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科技导报
2008年 第22期

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