Hands-On Unsupervised Learning with Python

Non-Negative Matrix Factorization

When the dataset, X, is non-negative, it is possible to apply a factorization technique, which has been proven (for example, in Learning the parts of objects by non-negative matrix factorization, Lee D. D., and Seung, S. H., Nature, 401, 10/1999) to be more reliable when the goal of the task is to extract atoms that correspond to the structural parts of the samples. For example, in the case of images, they are supposed to be geometrical elements or even more complex parts. The main condition imposed by Non-Negative Matrix Factorization (NNMF) is that all of the matrices involved must be non-negative and X = UV. Hence, once a norm, N, has been defined (for example, Frobenius), the simple objective becomes ...