  Principal component analysis (PCA) is a mainstay of modern data analysis - a
black box that is widely used but (sometimes) poorly understood. The goal of
this paper is to dispel the magic behind this black box. This manuscript
focuses on building a solid intuition for how and why principal component
analysis works. This manuscript crystallizes this knowledge by deriving from
simple intuitions, the mathematics behind PCA. This tutorial does not shy away
from explaining the ideas informally, nor does it shy away from the
mathematics. The hope is that by addressing both aspects, readers of all levels
will be able to gain a better understanding of PCA as well as the when, the how
and the why of applying this technique.
