Table of Contents Summary Maximum Variance Formulation Motivating Example Noise and Redundancy Covariance Matrix Summary If we have some measurements of data, but do not know the underlying dynamics, PCA can resolve this by producing a change of basis such that the dynamics are reflected upon the eigenvectors.
Maximum Variance Formulation Although there are several derivations of PCA. I really like the approach of projecting the data onto a lower dimensional space in order to maximize the variance of the projected data.