TY - GEN

T1 - A modified multiplicative update algorithm for euclidean distance-based nonnegative matrix factorization and its global convergence

AU - Hibi, Ryota

AU - Takahashi, Norikazu

PY - 2011/11/28

Y1 - 2011/11/28

N2 - Nonnegative matrix factorization (NMF) is to approximate a given large nonnegative matrix by the product of two small nonnegative matrices. Although the multiplicative update algorithm is widely used as an efficient computation method for NMF, it has a serious drawback that the update formulas are not well-defined because they are expressed in the form of a fraction. Furthermore, due to this drawback, the global convergence of the algorithm has not been guaranteed. In this paper, we consider NMF in which the approximation error is measured by the Euclidean distance between two matrices. We propose a modified multiplicative update algorithm in order to overcome the drawback of the original version and prove its global convergence.

AB - Nonnegative matrix factorization (NMF) is to approximate a given large nonnegative matrix by the product of two small nonnegative matrices. Although the multiplicative update algorithm is widely used as an efficient computation method for NMF, it has a serious drawback that the update formulas are not well-defined because they are expressed in the form of a fraction. Furthermore, due to this drawback, the global convergence of the algorithm has not been guaranteed. In this paper, we consider NMF in which the approximation error is measured by the Euclidean distance between two matrices. We propose a modified multiplicative update algorithm in order to overcome the drawback of the original version and prove its global convergence.

KW - Euclidean distance

KW - global convergence

KW - multiplicative update

KW - nonnegative matrix factorization

UR - http://www.scopus.com/inward/record.url?scp=81855227209&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=81855227209&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-24958-7_76

DO - 10.1007/978-3-642-24958-7_76

M3 - Conference contribution

AN - SCOPUS:81855227209

SN - 9783642249570

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 655

EP - 662

BT - Neural Information Processing - 18th International Conference, ICONIP 2011, Proceedings

T2 - 18th International Conference on Neural Information Processing, ICONIP 2011

Y2 - 13 November 2011 through 17 November 2011

ER -