Non-Negative Matrix Factorization

Unlike LDA, Non-Negative Matrix Factorization (NMF) is not a probabilistic model. instead, it is, as the name implies, an approach involving linear algebra. Using matrix factorization as an approach to topic modeling was introduced by Daniel D. Lee and H. Sebastian Seung in 1999. The approach falls into the decomposition family of models that includes PCA, the modeling technique introduced in Chapter 4, Introduction to Dimensionality Reduction and PCA.

The major differences between PCA and NMF are that PCA requires components to be perpendicular while allowing them to be either positive or negative. NMF requires that matrix components be non-negative, which should make sense if you think of this requirement in the context of the data. Topics cannot be negatively related to documents, and words cannot be negatively related to topics.

If you are not convinced, try to interpret a negative weight associating a topic with a document. It would be...