ABSTRACT
Principal component analysis and independent component analysis fall within a branch of statistics known as multivariate analysis. In general, multivariate analysis seeks to produce results that take into account the relationship between multiple variables and within the variables; so, it uses tools that operate on all the data. A major concern of multivariate analysis is to find transformations of the multivariate data that make the data set smaller or easier to understand. Linear transformations are frequently applied to multivariate data to produce new data sets that are more meaningful or can be condensed into fewer variables. There are a number of techniques that can be used to find the principal components of a data set, but the most commonly used is based on singular-value decomposition. Many multivariate techniques rotate the data set as part of their operation. The analyses presented in the chapter use linear transformations applied to multivariate data: multiple signals or data that relate to each other.
