e-DAS

Principal Component Analysis (PCA)

The Principal Component Analysis is a mathematical method which is used to transform a number of correlated variables into a smaller number of uncorrelated variables, the so called "Principal Components".
The principal components are constructed with declining importance: the first principal component comprises the as much of the total variability of all variables as possible, the second principal component as much of remaining variability and so on.

One widely used algortihm for PCA is the NIPALS (Nonlinear Iterative
Partial Least Squares) algorithm.

Figure 1:	The mathematical approach for PCA is to approximate the data matrix X, which has n objects and p variables, by two smaller matrices: the scores matrix T (n objects and d variables) and the loadings matrix L (d objects and p variables), where (see Figure 1). One widely used algortihm for PCA is the NIPALS (Nonlinear Iterative Partial Least Squares) algorithm.

A detailed description of the NIPALS algorithm is given here: