PCA and PCoA

Andreas Tilevik
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Andreas Tilevik: University of Skövde

Chapter Chapter 6 in Multivariate Statistics and Machine Learning in R For Beginners, 2025, pp 83-109 from Springer

Abstract: Abstract This chapter focuses on principal component analysis (PCA) and principal coordinate analysis (PCoA), two of the most fundamental methods in multivariate statistics. It begins by introducing simple methods for combining variables and then explains how PCA can be used for this purpose. This chapter also illustrates how to determine an appropriate number of principal components using a scree plot and Kaiser’s criterion. The difference between loadings and weights is discussed, along with how Varimax rotation can enhance the interpretability of PCA, before introducing PCoA. Although PCA and PCoA both simplify complex datasets, they are based on different mathematical principles and are suited to different types of data and distance measures. By the end of this chapter, you will see that these two methods yield the same results when PCoA is based on Euclidean distances.

Date: 2025
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DOI: 10.1007/978-3-032-01851-9_6

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