Mathematics
Principal Component Analysis for Dimensionality Reduction
Quick fact
PCA transforms correlated variables into a new set of uncorrelated variables, called principal components, which are ordered by how much of the original variance they capture. The first principal component alone accounts for the largest possible share of total variation, often more than any single original variable.
Why this is interesting
How can you compress a dataset with hundreds of columns into just two or three numbers per row, losing as little information as possible? That is exactly what Principal Component Analysis (PCA) does.