7.2 Non-normalized Principal Component Analysis

Active variables

• Distance between variables: based on the covariances of the variables

\[ d^2(j,l) = var(j) + var(h) - 2 cov(j,h) \]

• Distance between individuals: classic (squared) euclidean distance (sum of the squares of the differences with centered data).

Interpretation

Factorial Planes for Variables: This has to do with the representation of the variances as well as the association among variables. We can interpret the directions in the plane in terms of the covariances between the variables and the axes.

Factorial Planes for Individuals: This has to do with the representation of the similarities between individuals. We interpret the positions of the individuals on the factorial plane in terms of their values, and taking into account the meaning assigned to the axes.

Supplementary Variables

• Continuous: we pay attention to the covariances of the continuous variables with the factorial axes.

• Categorical: representation of each category in the cloud of row-points as the center of gravity of the individuals having such category. We use the v-test to assess their “characterization power.”