Principal Component Analysis Algorithm

Principal component analysis reduces the dimensionality of a dataset by computing a new set of axes, the principal components, ordered so the first captures the greatest possible variance in the data, the second the greatest remaining variance orthogonal to the first, and so on, typically found by computing the eigenvectors and eigenvalues of the data's covariance matrix. Projecting the data onto the first few principal components lets a smaller number of dimensions represent most of the dataset's variation, useful for visualization, noise reduction and speeding up other algorithms. Karl Pearson described the underlying idea in 1901, and Harold Hotelling developed the modern statistical formulation in the 1930s.