多项式欧拉形分布
Polynomial Eulerian shape distributions
摘要：
在本文中，一个新的方法是来自形状理论的背景下。所实施的方法是出于在\citet{GM93}中提出的一个公开问题，关于涉及矩阵参数的欧拉超几何函数的某些形状密度的建设。相关联的分布是通过建立所需的形状不变量和一个已知的结果之间的连接典型的相关性自1963年以来，通常在统计形状理论和解决的结果，密度表示在无穷级数的带状多项式，其中涉及相当大的困难推断。然后，工作进行到解析地解决计算的问题，通过使用欧拉矩阵关系的两个矩阵参数导出相应的多项式分布在一定的参数空间，允许执行精确的推理的基础上，精确的分布特征的多项式的非常低的程度。提出了一种比较相关形状结构的方法，并将其应用于手写体识别。
英文摘要：
In this paper a new approach is derived in the context of shape theory. The implemented methodology is motivated in an open problem proposed in \citet{GM93} about the construction of certain shape density involving Euler hypergeometric functions of matrix arguments. The associated distribution is obtained by establishing a connection between the required shape invariants and a known result on canonical correlations available since 1963; as usual in statistical shape theory and the addressed result, the densities are expressed in terms of infinite series of zonal polynomials which involves considerable difficulties in inference. Then the work proceeds to solve analytically the problem of computation by using the Eulerian matrix relation of two matrix argument for deriving the corresponding polynomial distribution in certain parametric space which allows to perform exact inference based on exact distributions characterized for polynomials of very low degree. A methodology for comparing correlation shape structure is proposed and applied in handwritten differentiation.
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