Uniqueness
The factorization is not unique: A matrix and its inverse can be used to transform the two factorization matrices by, e.g.,
If the two new matrices and are non-negative they form another parametrization of the factorization.
The non-negativity of and applies at least if B is a non-negative monomial matrix. In this simple case it will just correspond to a scaling and a permutation.
More control over the non-uniqueness of NMF is obtained with sparsity constraints.
Read more about this topic: Non-negative Matrix Factorization
Famous quotes containing the word uniqueness:
“Until now when we have started to talk about the uniqueness of America we have almost always ended by comparing ourselves to Europe. Toward her we have felt all the attraction and repulsions of Oedipus.”
—Daniel J. Boorstin (b. 1914)
“Somehow we have been taught to believe that the experiences of girls and women are not important in the study and understanding of human behavior. If we know men, then we know all of humankind. These prevalent cultural attitudes totally deny the uniqueness of the female experience, limiting the development of girls and women and depriving a needy world of the gifts, talents, and resources our daughters have to offer.”
—Jeanne Elium (20th century)