Generalized Nonnegative Matrix Approximations with Bregman Divergences

By Inderjit S. Dhillon, Suvrit Sra. Neural Information Processing Systems, 2005

517 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/12565866e56e2b1781ef698eb0cb2d8ddcb8c5a7

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Robust nonnegative matrix factorization using L21-norm (2011, background): “Algorithmic extensions of NMF also have been developed to accommodate a variety of objective functions [4, 7] into different data analysis problems, including classification [21] collaborative filtering [22], and constrained clustering [15, 23].”
Embedding Networks with Edge Attributes (2018, methodology): “We apply NMF [26] on the set of abstracts to get topic distribution for each abstract.”
Collaborative matrix factorization with multiple similarities for predicting drug-target interactions (2013, background): “Another series of related work are “nonnegative” matrix factorization (NMF) [6, 7], in which factorized matrices must keep the elements nonnegative.”
Nonnegative Matrix Factorization: A Comprehensive Review (2013, unknown): “Csiszár’s ’-divergence [51], Bregman divergence [52], and”
Families of Alpha- Beta- and Gamma- Divergences: Flexible and Robust Measures of Similarities (2010, methodology): “Until now the Beta-divergence has been successfully applied for robust PCA (Principal Component Analysis) and clustering [71], robust ICA (Independent Component Analysis) [15,68,69], and robust NMF/NTF [30,70,73–76].”
Density-ratio matching under the Bregman divergence: a unified framework of density-ratio estimation (2012, methodology): “Note that the Bregman divergence has been widely used in machine learning literature so far (Collins et al., 2002; Murata et al., 2004; Tsuda et al., 2005; Dhillon and Sra, 2006; Cayton, 2008; Wu et al., 2009), and the current paper explores a new application of the Bregman divergence in the framewo”
Convex and Semi-Nonnegative Matrix Factorizations (2010, background): “Algorithmic extensions of NMF have been developed to accommodate a variety of objective functions [ 12 ], [13] and a variety of data analysis problems, including classification [14] and collaborative filtering [15].”
Hierarchical ALS Algorithms for Nonnegative Matrix and 3D Tensor Factorization (2007, methodology): “Nonnegative Matrix Factorization (NMF) and its multi-way extensions: Nonnegative Tensor Factorization (NTF) and Parallel Factor analysis (PARAFAC) models with sparsity and/or non-negativity constraints have been recently proposed as promising and quite efficient tools for processing sparse signals, ”
On Tensors, Sparsity, and Nonnegative Factorizations (2011, unknown): “We note that generalizations of KL divergence have have also been proposed in the literature, including Bregman divergence [7] and beta divergence [6].”
Fast Nonnegative Matrix Factorization: An Active-Set-Like Method and Comparisons (2011, background): “Frobenius norm, Kullback–Leibler divergence [23], and Bregman divergence [9, 25].”
SVD based initialization: A head start for nonnegative matrix factorization (2008, methodology): “even though an acronym such as NMA might be more appropriate [ 1 ].”
Algorithms for Nonnegative Matrix Factorization with the β-Divergence (2010, unknown): “NMF with Bregman divergences has been considered by Dhillon and Sra (2005), where the lack of results about the monotonicity of multiplicative algorithms in general has been noted.”
Algorithms for nonnegative matrix and tensor factorizations: a unified view based on block coordinate descent framework (2013, methodology): “Matrices W and H are found by solving an optimization problem defined with Frobenius norm, Kullback-Leibler divergence [67,68], or other divergences [24,68].”
Geospatial Area Embedding Based on the Movement Purpose Hypothesis Using Large-Scale Mobility Data from Smart Card (2016, methodology): “In the context of the graph theory, adjacency matrix factorization techniques like singular value decompositon (SVD) and non-negative matrix factorization (NMF) are the prototype [21].”
Nonnegative Matrix Factorization with the Itakura-Saito Divergence: With Application to Music Analysis (2009, methodology): “Thus, the gradient descent multiplicative rules given in Dhillon and Sra (2005) and Cichocki, Zdunek et al.”