Principal component analysis (PCA) is a classical machine learning technique. The goal of PCA is to transform a dataset into one with fewer columns. This is called dimensionality reduction. The ...

Mathematics of Computation, Vol. 87, No. 309 (January 2018), pp. 237-259 (23 pages) Abstract This paper is concerned with computations of a few smallest eigenvalues (in absolute value) of a large ...

Transforming a dataset into one with fewer columns is more complicated than it might seem, explains Dr. James McCaffrey of Microsoft Research in this full-code, step-by-step machine learning tutorial.

Two methods are presented for efficiently computing the eigenvalues of the finite-difference Laplacian. One method embeds the region considered in a rectangle. The other method is applicable when the ...