Jolliffe I. Principal Component Analysis (2ed., Springer, 2002)(518s)

234 10. Outlier Detection, Influential Observations and Robust EstimationFigure 10.1. Example of an outlier that is not detectable by looking at one variableat a time.that outliers will manifest themselves in directions other than those whichare detectable from simple plots of pairs of the original variables.Outliers can be of many types, which complicates any search for directionsin which outliers occur. However, there are good reasons for lookingat the directions defined by either the first few or the last few PCs in orderto detect outliers. The first few and last few PCs will detect different typesof outlier, and in general the last few are more likely to provide additionalinformation that is not available in plots of the original variables.As discussed in Gnanadesikan and Kettenring (1972), the outliers thatare detectable from a plot of the first few PCs are those which inflatevariances and covariances. If an outlier is the cause of a large increasein one or more of the variances of the original variables, then it must beextreme on those variables and thus detectable by looking at plots of singlevariables. Similarly, an observation that inflates a covariance or correlationbetween two variables will usually be clearly visible on a plot of these two