Machine Learning Algorithms - Second Edition

Non-Negative Matrix Factorization

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

If dim(X) = n × m, then dim(W) = n × p and dim(H) = p × 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. In some implementations, the loss function is squared and L1/L2 penalties are applied to both the W and H matrices:

As we are going to discuss in the next chapter, Chapter ...