GENERALIZED PROCRUSTES ANALYSIS
GENERALIZED PROCRUSTES ANALYSIS
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DOI：
10.1007/bf02291478
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发表时间：
1975-01-01
期刊：
影响因子：
3
通讯作者：
GOWER, JC
中科院分区：
文献类型：
--
作者：
GOWER, JC
假设Pi（i）（i = 1，2，.，m，j = 1，2，...，n）给出了p维空间中mn个点的位置。总的来说，这些可以被认为是m个配置或缩放，每个配置或缩放是p维中的n个点。研究了m个构形的平移、旋转、反射和缩放问题，以最小化拟合优度准则Pj（i），其中Gi是m个点Pi（i）（i = 1，2，…，m）。每个配置的旋转位置可以被视为单独的分析与质心配置代表一个共识，并讨论了这种关系与个人缩放分析。给出了一种计算方法，其结果可概括为方差分析形式。特殊情况m = 2对应于经典的Procrustes分析，但是选择将每个配置拟合到公共质心配置的标准避免了当一个集合拟合到另一个集合时出现的困难，被认为是固定的。
Suppose Pi(i) (i = 1, 2, ..., m, j = 1, 2, ..., n) give the locations of mn points in p-dimensional space. Collectively these may be regarded as m configurations, or scalings, each of n points in p-dimensions. The problem is investigated of translating, rotating, reflecting and scaling the m configurations to minimize the goodness-of-fit criterion Σi=1m Σi=1n Δ2(Pj(i)Gi), where Gi is the centroid of the m points Pi(i) (i = 1, 2, ..., m). The rotated positions of each configuration may be regarded as individual analyses with the centroid configuration representing a consensus, and this relationship with individual scaling analysis is discussed. A computational technique is given, the results of which can be summarized in analysis of variance form. The special case m = 2 corresponds to Classical Procrustes analysis but the choice of criterion that fits each configuration to the common centroid configuration avoids difficulties that arise when one set is fitted to the other, regarded as fixed.