Principal points for an allometric extension model
Principal points for an allometric extension model
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DOI：
10.1007/s00362-013-0532-z
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发表时间：
2013-05
影响因子：
1.3
通讯作者：
S. Matsuura;H. Kurata
中科院分区：
文献类型：
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作者：
S. Matsuura;H. Kurata
a维分布的一组主点是该分布在平方误差损失方面的最佳点近似。一般来说，很难导出主点的显式表达式。因此，我们可能需要在整个空间中寻找主点。许多努力已经致力于建立结果，指定一个线性子空间中的主要点。然而，以往的研究主要集中在椭圆对称分布和球对称分布的位置混合，这可能不适合于许多实际情况。在本文中，我们处理的混合椭圆对称分布，形成异速生长扩展模型，已被广泛应用于主成分分析的背景下。给出了主点位于前几个主成分所张成的线性子空间中的条件。
A set of-principal points of a-dimensional distribution is an optimal-point-approximation of the distribution in terms of a squared error loss. It is in general difficult to derive an explicit expression of principal points. Hence, we may have to search the whole spacefor-principal points. Many efforts have been devoted to establish results that specify a linear subspace in which principal points lie. However, the previous studies focused on elliptically symmetric distributions and location mixtures of spherically symmetric distributions, which may not be suitable to many practical situations. In this paper, we deal with a mixture of elliptically symmetric distributions that form an allometric extension model, which has been widely used in the context of principal component analysis. We give conditions under which principal points lie in the linear subspace spanned by the first several principal components.