Principal component analysis

This chapter introduces linear dimension reduction based on principal component analysis. It first explains when principal component analysis is effective, and what potential issues you might look for by visualising data in a tour. The first section then shows how we can determine how many principal components are needed to describe data based on a scree plot. It also discusses the interpretation of the coefficients, using two data examples. The second section illustrates the difference between showing the data in the model space and showing the model in the data spacs. In this case a biplot shows the data in the model space, while we can use a wire-frame display within a grand tour of the data to show the model in the data space. The final section shows examples where interesting relationships beween variables is not linear: when there are outlying points, or when there is non-linear association between variables.