Hierarchical ALS Algorithms for Nonnegative Matrix and 3D Tensor Factorization

By Andrzej S. Cichocki, Rafal Zdunek, Shun-ichi Amari. International Conference on Agents, 2007

317 citations recorded by the source corpus.

Subfields: Computational Mechanics, Signal Processing

View Paper: https://www.semanticscholar.org/paper/92d66f4ccac67581e19ff5f5707fb16a932240e5

How researchers see this paper

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

In Computational Mechanics

In Signal Processing

Citations in the corpus

Algorithms for nonnegative matrix and tensor factorizations: a unified view based on block coordinate descent framework (2013, methodology): “To prevent zero columns, a small positive number could be used for the maximum operator in (13): That is, max(·, ) with a small positive number such as 10−16 is used instead of max(·, 0) [20,35].”
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].”
Fast Local Algorithms for Large Scale Nonnegative Matrix and Tensor Factorizations (2009, methodology): “We refer to these update rules as the HALS algorithm which we first introduced in [3].”
On the Geometric Interpretation of the Nonnegative Rank (2010, methodology): “The solutions of the above nonnegative rank problems have been computedwith standard nonnegative matrix factorization algorithms [35,13,25] and, in general, the optimal solution is found after 10 to 100 restarts of these algorithms(15) .”
Fast Nonnegative Matrix Factorization: An Active-Set-Like Method and Comparisons (2011, methodology): “Their multiplicative updating algorithm [23] has been one of the most commonly used for NMF, but some issues related to its performance [26, 15, 17] and problems with convergence [11] were reported.”
Provable Alternating Gradient Descent for Non-negative Matrix Factorization with Strong Correlations (2017, unknown): “HALS converges on the DIR and CTM datasets, but the convergence is in slower rates.”
Efficient and accurate extraction of in vivo calcium signals from microendoscopic video data (2018, unknown): “HALS stands for hierarchical alternating least squares (Cichocki et al. 2007).”
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 ”
CaImAn an open source tool for scalable calcium imaging data analysis (2019, methodology): “8: repeat Optionally keep updating A; C; b; f using HALS (Cichocki et al., 2007).”