Machine Learning Algorithms

Non-negative matrix factorization

When the dataset is made up of non-negative elements, it's possible to use non-negative matrix factorization (NNMF) instead of standard PCA. The algorithm optimizes a loss function (alternatively on W and H) based on the Frobenius norm:

If dim(X) = n x m, then dim(W) = n x p and dim(H) = p x m with p equal to the number of requested components (the n_components parameter), which is normally smaller than the original dimensions n and m.

The final reconstruction is purely additive and it has been shown that it's particularly efficient for images or text where there are normally no non-negative elements. In the ...