ABSTRACT
Principal component analysis and independent component analysis fall within a branch of statistics known as multivariate analysis. As the name implies, multivariate analysis is concerned with the analysis of multiple variables (or measurements), but treats them as a single entity (for example, variables from multiple measurements made on the same process or system). In multivariate analysis, these multiple variables are often represented as a single vector variable that includes the different variables:
x=[x1(t), x2(t).… xm(t)]T For 1≤m≤M (1)
The ‘T’ stands for transposed and represents the matrix operation of switching rows and columns.* In this case, x is composed of M variables, each containing N (t=1,…, N) observations. In signal processing, the observations are time samples, while in image processing they are pixels. Multivariate data, as represented by x above can also be considered to reside in M-dimensional space, where each spatial dimension contains one signal (or image).
