Outlier detection by rotation to principal components

This demonstration illustrates why multivariate outliers might not be apparent in univariate views, but become readily apparent on the smallest principal component.

For bivariate data, principal component scores are equivalent to a rotation of the data to a view whose coordinate axes are aligned with the major-minor axes of the data ellipse. It is shown here by linear iterpolation between the original data, XY, and PCA scores, of the form

  xy <- XY + α * (PCA-XY)
where α ranges from 0 to 1.

The data shown here were genereated as 100 obsservations on two correlated normal variables with two bivariate outliers near (2,2), (-2, -2).