Principal component analysis (PCA) is a mainstay
of modern data analysis - a black box that is widely
used but poorly understood. The goal of this paper is
to dispel the magic behind this black box. This tutorial
focuses on building a solid intuition for how and why
principal component analysis works; furthermore, it
crystallizes this knowledge by deriving from first principals,
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 the power of PCA as well as the when, the how
and the why of applying this technique.