Principal Components, Classical Multidimensional Scaling, and Factor Analysis

This chapter introduces the theory and application of principal components, classical multidimensional scaling, and factor analysis. Principal components seek to effectively summarize high dimensional data as lower dimensional scores. Multidimensional scaling gives a visual representation of points when all we know about the points are the distances separating them. Classical multidimensional scaling is seen to be an application of principal components when the distances are standard Euclidean distances. Principal components and factor analysis are often used for similar purposes but their theoretical background is quite different.