6 Principal component analysis for perceptual maps (toothpaste dataset)

In this chapter, you will learn how to carry out a principal component analysis and visualize the results in a perceptual map.

Say we have a set of observations that differ from each other on a number of dimensions, for example, we have a number of whiskey brands (observations) that are rated on a number of attributes such as body, sweetness, fruitiness, etc (dimensions). If some of those dimensions are strongly correlated then it should be possible to describe the observations by a smaller (than original) number of dimensions without losing too much information. For example, sweetness and fruitness could be highly correlated and could therefore be replaced by one variable. Such dimensionality reduction is the goal of principal component analysis.