Graphical Representation of Data Using Principal Components
The main objective of a PCA is to reduce the dimensionality of a set of data. This is particularly advantageous if a set of data with many variables lies, in reality, close to a two-dimensional subspace (plane). In this case the data can be plotted with respect to these two dimensions, thus giving a straightforward visual representation of what the data look like, instead of having a large mass of numbers to digest. If the data fall close to a three-dimensional subspace it is still possible, with a little effort, to gain a good visual impression of the data, especially if a computer is available with interactive graphics. Even with slightly more dimensions it is possible, with some degree of ingenuity, to get a ‘picture’ of the data—see, for example, Chapters 10–12 (by Tukey and Tukey) in Barnett (1981)—although we shall concentrate almost entirely on two-dimensional representations in the present chapter.
KeywordsSingular Value Decomposition Correspondence Analysis Minimum Span Tree Mahalanobis Distance Greylag Goose
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