# PCA

## Principal Component Analysis

Principal component analysis (PCA) is a
type of factor analysis which can be used to generate a simplified view
of a multi-dimensional data set, such as those from descriptive
analysis. The data set is reduced to a smaller set of underlying
factors based on the correlations of the original variables. PCA
uses linear transformation to generate a set of uncorrelated principal
components (PCs). Each principal component is a linear combination of
the original variables. The largest amount of variation in the data set
is aligned with the first PC, the next greatest amount of variation is
assigned to the second PC, and so on^{1} .

Because PCA involves a linear transformation, it merely involves a change in the viewpoint of the data, as opposed to creating something new. PCA generates factor loadings, representing the correlation of attributes to the new dimensions (PCs), and factor scores which represent the values of the samples in the new space.

PCA is commonly used to provide a way to visualize the relationships among products and attributes. It can also be applied to a set of consumer liking data to generate an internal preference map.

## Notes

^{1} Lawless, H. and H. Heymann (1998). **Sensory Evaluation of Food: Principles and Practices**. New York, Kluwer Academic/Plenum Publishers.