[…] The classical singular value decomposition (SVD) has a long and venerable history. I have described it as a fundamental theorem of linear algebra. Nevertheless, the mathematical property that makes it so useful in general (namely, the orthogonality of the matrix factors) also makes it less useful for certain applications. In response, researchers developed the nonnegative matrix factorization (NMF), which removes the requirement of orthogonality and replaces it with a requirement that the elements in the matrix factors be nonnegative. …