Machine Learning

19.7 Nonnegative Matrix Factorization

The strong connection between dimensionality reduction and low-rank matrix factorization has already been stressed while discussing PCA. ICA can also be considered as a low-rank matrix factorization, if a smaller number, compared to the l observed random variables, of independent components is retained (e.g., selecting the m < l least Gaussian ones).

An alternative to the previously discussed low-rank matrix factorization schemes was suggested in [135, 136], which guarantees the nonnegativity of the elements of the resulting matrix factors. Such a constraint is enforced in certain applications because negative elements contradict physical reality. For example, in image analysis, the intensity values of ...