TY - GEN

T1 - Algorithms for non-negative matrix factorization

AU - Lee, Daniel D.

AU - Seung, Hyunjune Sebastian

PY - 2001/1/1

Y1 - 2001/1/1

N2 - Non-negative matrix factorization (NMF) has previously been shown to be a useful decomposition for multivariate data. Two different multiplicative algorithms for NMF are analyzed. They differ only slightly in the multiplicative factor used in the update rules. One algorithm can be shown to minimize the conventional least squares error while the other minimizes the generalized Kullback-Leibler divergence. The monotonic convergence of both algorithms can be proven using an auxiliary function analogous to that used for proving convergence of the Expectation-Maximization algorithm. The algorithms can also be interpreted as diagonally rescaled gradient descent, where the rescaling factor is optimally chosen to ensure convergence.

AB - Non-negative matrix factorization (NMF) has previously been shown to be a useful decomposition for multivariate data. Two different multiplicative algorithms for NMF are analyzed. They differ only slightly in the multiplicative factor used in the update rules. One algorithm can be shown to minimize the conventional least squares error while the other minimizes the generalized Kullback-Leibler divergence. The monotonic convergence of both algorithms can be proven using an auxiliary function analogous to that used for proving convergence of the Expectation-Maximization algorithm. The algorithms can also be interpreted as diagonally rescaled gradient descent, where the rescaling factor is optimally chosen to ensure convergence.

UR - http://www.scopus.com/inward/record.url?scp=84898964201&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84898964201&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84898964201

SN - 0262122413

SN - 9780262122412

T3 - Advances in Neural Information Processing Systems

BT - Advances in Neural Information Processing Systems 13 - Proceedings of the 2000 Conference, NIPS 2000

PB - Neural information processing systems foundation

T2 - 14th Annual Neural Information Processing Systems Conference, NIPS 2000

Y2 - 27 November 2000 through 2 December 2000

ER -