Csiszár's Divergences for Non-negative Matrix Factorization: Family of New Algorithms

By Andrzej S. Cichocki, Rafal Zdunek, Shun-ichi Amari. International Conference on Agents, 2006

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Nonnegative Matrix Factorization with the Itakura-Saito Divergence: With Application to Music Analysis (2009, methodology): “These update rules were also obtained by Abdallah and Plumbley (2004), prior to (Dhillon and Sra, 2005; Cichocki et al., 2006).”
Algorithms for Nonnegative Matrix Factorization with the β-Divergence (2010, methodology): “…by Basu et al. (1998) and Eguchi and Kano (2001) and can be deﬁned as  (5) Basu et al. (1998) and Eguchi and Kano (2001) assume β > 1, but the deﬁnition domain can be extended to β ∈ R , as suggested by Cichocki et al. (2006), which is the deﬁnition domain that is considered in this paper.”
Nonnegative Matrix Factorization: A Comprehensive Review (2013, background): “Other cost functions consist of Minkowski family of metrics known as p-norm, Earth Mover’s distance metric [18], αdivergence [17], β-divergence [49], γ-divergence [50], Csiszár’s φ-divergence [51], Bregman divergence [52], and α-β-divergence [53].”
Algorithms and applications for approximate nonnegative matrix factorization (2007, methodology): “For example, (Cichocki et al., 2006) have proposed cost functions based on Csiszár’s φ-divergence.”