How many principal components? stopping rules for determining the number of non-trivial axes revisited
How many principal components? stopping rules for determining the number of non-trivial axes revisited
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DOI：
10.1016/j.csda.2004.06.015
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发表时间：
2005-06-15
影响因子：
1.8
通讯作者：
Somers, KM
中科院分区：
文献类型：
--
作者：
Peres-Neto, PR;Jackson, DA;Somers, KM
主成分分析是应用最广泛的工具之一，用来总结变量之间的共同变化模式。一些研究已经调查了单个方法的能力，或者比较了一些方法在确定描述模拟数据集的共同方差的分量数量方面的性能。我们找出了与这些研究相关的一些不足之处，并进行了广泛的模拟研究，比较了大量可用的规则，并开发了一些新的方法。总而言之，我们比较了20条停止规则，并提出了一种似乎非常有效的两步法。首先，使用Bartlett检验来检验第一主成分的重要性，以表明在整个数据集中是否有至少两个变量具有共同的变异。如果有意义，可以应用许多不同的规则来估计要保留的非平凡成分的数量。然而，这些方法的相对优劣取决于数据是否包含强相关变量。我们还估计了一些现场数据集的非平凡分量的数量，以便我们可以基于模拟数据来评估我们结论的适用性。(C)2004爱思唯尔B.V.保留所有权利。
Principal component analysis is one of the most widely applied tools in order to summarize common patterns of variation among variables. Several studies have investigated the ability of individual methods, or compared the performance of a number of methods, in determining the number of components describing common variance of simulated data sets. We identify a number of shortcomings related to these studies and conduct an extensive simulation study where we compare a larger number of rules available and develop some new methods. In total we compare 20 stopping rules and propose a two-step approach that appears to be highly effective. First, a Bartlett's test is used to test the significance of the first principal component, indicating whether or not at least two variables share common variation in the entire data set. If significant, a number of different rules can be applied to estimate the number of non-trivial components to be retained. However, the relative merits of these methods depend on whether data contain strongly correlated or uncorrelated variables. We also estimate the number of non-trivial components for a number of field data sets so that we can evaluate the applicability of our conclusions based on simulated data. (c) 2004 Elsevier B.V. All rights reserved.