Principal Component Analysis
Principal Component Analysis
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DOI：
10.1007/978-1-4757-1904-8
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发表时间：
1986
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影响因子：
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通讯作者：
I. Jolliffe
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文献类型：
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作者：
I. Jolliffe
本文大部分内容的观点是，PCA主要是一种描述性工具，不需要严格的分布或模型假设。这意味着它可以用于大范围的数据，这可能与多元正态性的“理想”大相径庭。但是，在执行PCA时，需要对某些类型的数据进行一些修改或特别注意。我们已经遇到了一些这样的例子，例如在第9章中，数据按照观察值或变量分组，在第12章中，观察值是非独立的。本章描述了一些其他特殊类型的数据，标准PCA应该以某种方式进行修改，或者相关技术可能相关。第13.1节介绍了离散数据中涉及PCA的一些想法。特别是，在第5.4节中作为图形技术介绍的对应分析，将进一步讨论，并且还描述了处理以排名形式给出的数据的程序。当数据包括对动物或植物的测量时，确定量化大小和形状的各个方面的变化的“组成部分”有时很有趣。第13.2节检查了试图找到这些成分的PCA的修改。在第13.3节中，讨论了所有观测值中x的p个元素被限制求和为相同常数（通常为1或100）的组成数据，并在第13.4节中描述了PCA在分析设计实验数据中的rôle。
The viewpoint taken in much of this text is that PCA is mainly a descriptive tool with no need for rigorous distributional or model assumptions. This implies that it can be used on a wide range of data, which can diverge considerably from the ‘ideal’of multivariate normality. There are, however, certain types of data where some modification or special care is desirable when performing PCA. Some instances of this have been encountered already, for example in Chapter 9 where the data are grouped either by observations or by variables, and in Chapter 12 where observations are non-independent. The present chapter describes a number of other special types of data for which standard PCA should be modified in some way, or where related techniques may be relevant. Section 13.1 looks at a number of ideas involving PCA for discrete data. In particular, correspondence analysis, which was introduced as a graphical technique in Section 5.4, is discussed further, and procedures for dealing with data given as ranks are also described. When data consist of measurements on animals or plants it is sometimes of interest to identify ‘components’ of variation that quantify size and various aspects of shape. Section 13.2 examines modifications of PCA that attempt to find such components.In Section 13.3, compositional data in which the p elements of x are constrained to sum to the same constant (usually 1 or 100) for all observations are discussed, and in Section 13.4 the rôle of PCA in analysing data from designed experiments is described.