Non-negative matrix factorization: A useful method for two-way life tables

摘要

In statistical applications, two-way tables of numeric data, samples by variables, are often analyzed using principal component analysis (PCA), a special case of singular value decomposition (SVD). The scores from PCA are often useful for helping to understand relationships among the samples of the table. We would also like to understand the relationships among the variables and for that purpose PCA loadings are usually difficult to interpret. If the entries in the table are positive or zero, then non-negative matrix factorization (NMF) allows better interpretations of the variables. In this paper, we compare PCA, SVD, and NMF using USA mortality data covering the years 1968 to 2010. The goal is to explicate negative matrix factorization using a data set familiar to actuaries.