Non-Negative Matrix Factorization (NNMF) Algorithm

A Non-Negative Matrix Factorization (NNMF) Algorithm is a matrix factorization algorithm that can be applied by a non-negative matrix factorization system (to solve a non-negative matrix factorization task).

• Example(s):
  • NNMF Alternating Least Squares (Paatero, 1994).
  • NNMF Multiplicative update rules (Lee-Seung, 2000, Hoyer 2002).
  • NNMF Gradient Descent (Hoyer, 2004, Berry-Plemmons, 2004).
  • …
• Counter-Example(s):
  • Positive Matrix Factorization Algorithm.
  • SVD Matrix Factorization Algorithm.
• See: Matrix Factorization-based Recommendation Algorithm.

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References

2005

• (2005). “ALS Algorithms for the Nonnegative Matrix Factorization inText Mining." Presentation at SAS NMF Day 6
  • QUOTE: Outline
    • Nonnegative Matrix Factorization replaces LSI.
    • Alternating Least Squares Algorithm.
    • Multiplicative Update Algorithms.
    • Our ALS Algorithms: ACLS and AHCLS

2001

• (Lee & Seung, 2001) ⇒ Daniel D. Lee and H. Sebastian Seung. (2001). “Algorithms for Non-negative Matrix Factorization.” In: Advances in Neural Information Processing Systems 13: Proceedings of the 2000 Conference.

1999

• (Lee & Seung, 1999) ⇒ Daniel D. Lee, and H. Sebastian Seung. (1999). “Learning the Parts of Objects by Non-Negative Matrix Factorization." Nature, 401(6755).

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