Seonglae ChoNon-negative matrix factorization or NNMF
Alternating algorithm converges to a local minimum of
Pros
- Natural fit for positive-valued data
- Can be interpreted (meaningful signs)
Cons
- Only applicable to non-negative data
- Optimization procedure is non-convex; requires initialization
- “Interpretability” is unreliable (reducing can completely change the basis function rather than select a subset)
- Learned components are not orthogonal nor naturally ordered
Non-negative matrix factorization
Non-negative matrix factorization (NMF or NNMF), also non-negative matrix approximation[1][2] is a group of algorithms in multivariate analysis and linear algebra where a matrix V is factorized into (usually) two matrices W and H, with the property that all three matrices have no negative elements. This non-negativity makes the resulting matrices easier to inspect. Also, in applications such as processing of audio spectrograms or muscular activity, non-negativity is inherent to the data being considered. Since the problem is not exactly solvable in general, it is commonly approximated numerically.
https://en.wikipedia.org/wiki/Non-negative_matrix_factorization