Principal Component Analysis

Principal component analysis (PCA) is a powerful technique for using the data to choose good bases. In this lesson you will learn how PCA chooses bases to minimize the mean-square error between the $N$-dimensional signal and a representation using $p<N$ bases. That is, PCA finds the best $p<N$ bases for explaining the variance of the data. The PCA bases are the eigenvectors of a covariance matrix formed from the data. You will also learn how the PCA bases provide a significant reduction in noise when the signal of interest is inherently low dimensional.