Properties and applications of Fisher distribution on the rotation group
Properties and applications of Fisher distribution on the rotation group
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旋转群上Fisher分布的性质及应用
DOI：
10.1016/j.jmva.2013.01.010
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发表时间：
2013
影响因子：
1.6
通讯作者：
Katsuyoshi Ohara and Nobuki Takayama
中科院分区：
文献类型：
--
作者：
Tomonari Sei;Hiroki Shibata;A. Takemura;Katsuyoshi Ohara and Nobuki Takayama
研究了旋转群SO（3）上Fisher分布（von Mises-Fisher分布，矩阵Langevin分布）的性质.特别是我们应用完整梯度下降，介绍了中山等人。（2011）[16]，以及用于评估分布的归一化常数和用于计算最大似然估计的级数展开方法。旋转群可以用两个正交向量的Stiefel流形来识别。因此，从统计建模的角度来看，比较这些流形上的Fisher分布是有意义的。我们说明了一个例子，近地天体数据的差异。
We study properties of Fisher distribution (von Mises–Fisher distribution, matrix Langevin distribution) on the rotation group SO(3). In particular we apply the holonomic gradient descent, introduced by Nakayama et al. (2011) [16], and a method of series expansion for evaluating the normalizing constant of the distribution and for computing the maximum likelihood estimate. The rotation group can be identified with the Stiefel manifold of two orthonormal vectors. Therefore from the viewpoint of statistical modeling, it is of interest to compare Fisher distributions on these manifolds. We illustrate the difference with an example of near-earth objects data.