Keep a useful lower-dimensional view

THE IDEA

Read the example.

A one-dimensional projection assigns each centred observation a coordinate along a chosen direction. PCA chooses a direction with maximum sample variance, then further orthogonal directions for remaining variance.

z = Xv, with ‖v‖₂ = 1

Use it well

High variance is not the same as high predictive value. Fit the transformation on training data and evaluate the retained representation on the actual task.