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 on1 .

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.