Fast Local Algorithms for Large Scale Nonnegative Matrix and Tensor Factorizations

By Andrzej S. Cichocki, Anh Huy Phan. IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences, 2009

607 citations recorded by the source corpus.

Subfields: Computational Mathematics, Signal Processing

View Paper: https://www.semanticscholar.org/paper/4229f467b059188fc7a1234016a3c80557fa7df0

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Citations in the corpus

Bayesian tuning and bandits : an extensible, open source library for AutoML (2018, methodology): “We can set the ranges for search at [4, 8], and [7, 20] respectively.”
Efficient and accurate extraction of in vivo calcium signals from microendoscopic video data (2018, positive): “(Friedrich et al., 2017b) modified the fastHALS algorithm (Cichocki and Phan, 2009) to estimate the nonnegative spatial components A;b and the nonnegative temporal activity C; f in the CNMF model Y ¼ A Cþ bf T þE by including sparsity and localization constraints.”
PadChest: A large chest x-ray image dataset with multi-label annotated reports (2019, neutral): “Non-negative Matrix Factorization (NMF), [26].”
Fast Nonnegative Matrix Factorization: An Active-Set-Like Method and Comparisons (2011, methodology): “Unlike the active set method, in which typically only one variable is exchanged between working sets, the block principal pivoting method allows the exchanges of multiple variables with a goal of finding the optimal active and passive sets faster.”
Algorithms for nonnegative matrix and tensor factorizations: a unified view based on block coordinate descent framework (2013, methodology): “[19,20] and the rank-one residue iteration (RRI) independently by Ho [44].”
Explaining Distributed Neural Activations via Unsupervised Learning (2017, methodology): “In short, given a pretrained CNN and an input image, we apply elastic NMF [2, 7] to the activation patterns (i.”
Nonnegative Matrix Factorization: A Comprehensive Review (2013, methodology): “Cichocki and Phan suggested similar FASTHALS algorithm [65].”
Scalable Coordinate Descent Approaches to Parallel Matrix Factorization for Recommender Systems (2012, methodology): “Recently, [9] and [10] have showed that coordinate descent methods are effective for nonnegative matrix factorization (NMF).”
A Systematic Review of Compressive Sensing: Concepts, Implementations and Applications (2018, neutral): “[130].”
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].”
Outlier Detection for Text Data (2017, methodology): “,···,r, and h⊺ i ←argmin h⊺ i ≥0 f(w1,···,wr,h ⊺ 1,···,h ⊺ r) for i = 1,···,r. The 2K-block BCD algorithm has been studied as Hierarchical Alternating Least Squares (HALS) proposed by Cichocki et al. [10, 9] and independently by Ho et al. [17] as rank-one residue iteration (RRI). 3.1.3 BCD with k(n ”
A Block Coordinate Descent Method for Regularized Multiconvex Optimization with Applications to Nonnegative Tensor Factorization and Completion (2013, methodology): “where r is a speciﬁed order and the Frobenius norm of a tensor Similar models based on the CP decomposition can be found in [19,31,33].”
The Why and How of Nonnegative Matrix Factorization (2014, background): “For ℓ = 1 , 2 , . . . , r : HALS has been rediscovered several times, originally in [27] (see also [25]), then as the rank-one residue iteration (RRI) in [63], as FastNMF in [84], and also in [89].”
SUSTain: Scalable Unsupervised Scoring for Tensors and its Application to Phenotyping (2018, methodology): “HALS fitting algorithms: Our fitting algorithms follow the intuition of Hierarchical Alternating Least Squares (HALS) framework [12] (aka rank-one residue iteration [23]), which enables formulating the solution for each k-th rank-1 component separately.”
Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 1 Low-Rank Tensor Decompositions (2016, neutral): “The Alternating Least Squares (ALS) based algorithms minimize the cost function iteratively by individually optimizing each component (factor matrix, B(n), while keeping the other component matrices fixed [52,59,105,119].”