You can think of it as “PCA where all the principal component entries and loadings must be positive”. Harder optimization problem to solve though due to that c

You can think of it as “PCA where all the principal component entries and loadings must be positive”. Harder optimization problem to solve though due to that constraint. The connection is especially clear when looking at the projected least squares algorithms for NMF — plain PCA minimizes the Euclidean reconstruction loss, while NMF algorithms alternates gradient descent steps to do that with projection steps to force everything positive.