Abstract
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.
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Hibi, R., Takahashi, N. (2011). A Modified Multiplicative Update Algorithm for Euclidean Distance-Based Nonnegative Matrix Factorization and Its Global Convergence. In: Lu, BL., Zhang, L., Kwok, J. (eds) Neural Information Processing. ICONIP 2011. Lecture Notes in Computer Science, vol 7063. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24958-7_76
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DOI: https://doi.org/10.1007/978-3-642-24958-7_76
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-24957-0
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