Nonnegative Matrix Factorization (NMF)

Breaking down complicated data into a small set of nonnegative building blocks that reveal how it works.

Given a data matrix X, the goal of NMF is to approximate it as the product of two lower-dimensional matrices U and V, where none of the entries in U or V can be negative. NMF can be seen as the nonnegative variant of PCA.

Geometrically, NMF is equivalent to finding the simplest polyhedral cone that encapsulates X. The challenge is that there exist infinitely many feasible cones. We aim to find the widest.