Python Data Analysis Cookbook

Applying principal component analysis for dimension reduction

Principal component analysis (PCA), invented by Karl Pearson in 1901, is an algorithm that transforms data into uncorrelated orthogonal features called principal components. The principal components are the eigenvectors of the covariance matrix.

Sometimes, we get better results by scaling the data prior to applying PCA, although this is not strictly necessary. We can interpret PCA as projecting data to a lower dimensional space. Some of the principal components contribute relatively little information (low variance); therefore, we can omit them. We have the following transformation: