Principal component analysis #

Principal component analysis (PCA) is a commonly used dimensionality reduction technique.

There are two interesting ways of thinking about it:

1. The principal components of a dataset are the eigenvectors of its covariance matrix.
2. (From a great paper on generalised low rank models): PCA aims to solve

\[ \min \left\|A-Z\right\| _F^2 \] subject to \(\mathrm{rank}(Z) \leq k\).