The DO Loop
Statistical programming in SAS with an emphasis on SAS/IML programs
A previous article describes the nonnegative matrix factorization (NMF). You can use the NMF to reveal important features in data that can be used to reduce the dimensionality of the problem. NMF is useful when the data are nonnegative, such as counts or pixel values in an image. The goal
In his 2004 paper, "Non-negative Matrix Factorization with Sparseness Constraints," Patrick Hoyer introduced a function that measures the sparseness of a nonzero vector. The paper does not explain or motivate the formula, so this article describes the geometry and intuition behind Hoyer's formula, along with a visualization and examples. Hoyer's
A previous article discusses the problem of fitting a kernel density estimate (KDE) to data that are strictly positive. If you use a standard KDE, the resulting density curve might estimate non-zero probability for negative values. This is unsatisfactory because quantities like lengths and mass cannot be negative. The previous