**Non-negative matrix factorization** (**NMF**) relies heavily on linear algebra. It factorizes an input matrix, **V**, into a product of two smaller matrices, **W** and **H**, in such a way that these three matrices have no negative values. In the context of NLP, these three matrices have the following meanings:

- The input matrix
**V**is the term counts or tf-idf matrix of size*n***m*, where*n*is the number of documents or samples, and*m*is the number of terms. - The first decomposition output matrix W is the feature matrix of size
*t***m*, where*t*is the number of topics specified. Each row of**W**represents a topic with each element in the row representing the rank of a term in the topic. - The second decomposition output matrix H is the coefficient ...