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Toward Faster Nonnegative Matrix Factorization: A New Algorithm and Comparisons

Jingu Kim, Haesun Park
2008 2008 Eighth IEEE International Conference on Data Mining  
Nonnegative Matrix Factorization (NMF) is a dimension reduction method that has been widely used for various tasks including text mining, pattern analysis, clustering, and cancer class discovery.  ...  Comparisons of algorithms using datasets that are from real life applications as well as those artificially generated show that the proposed new algorithm outperforms existing ones in computational speed  ...  Acknowledgments The work of authors was supported in part by the National Science Foundation grants CCF-0732318 and CCF-0808863, and the Samsung Scholarship awarded to Jingu Kim.  ... 
doi:10.1109/icdm.2008.149 dblp:conf/icdm/KimP08 fatcat:ubq4sb3o7fa55lgpiqxpvixtuu

Decoding neural events from fMRI BOLD signal: A comparison of existing approaches and development of a new algorithm

Keith Bush, Josh Cisler
2013 Magnetic Resonance Imaging  
We test and compare this new algorithm against three other recent deconvolution algorithms under varied levels of autocorrelated and Gaussian noise, hemodynamic response function (HRF) misspecification  ...  Here, we develop and test a new algorithm for performing semiblind (i.e., no knowledge of stimulus timings) deconvolution of the BOLD signal that treats the neural event as an observable, but intermediate  ...  Toward the larger goal of reducing bias when making inferences about neural processes in neuroimaging analyses, the purpose of the present experiments was to (a) develop a new deconvolution algorithm and  ... 
doi:10.1016/j.mri.2013.03.015 pmid:23602664 pmcid:PMC3738068 fatcat:ls7wh6uemrdmjl4ggvpmwxhg4a

Compressed Nonnegative Matrix Factorization Is Fast and Accurate

Mariano Tepper, Guillermo Sapiro
2016 IEEE Transactions on Signal Processing  
Nonnegative matrix factorization (NMF) has an established reputation as a useful data analysis technique in numerous applications.  ...  In separable NMF (SNMF) the left factors are a subset of the columns of the input matrix.  ...  ACKNOWLEDGMENTS The authors would like to thank Mauricio Delbracio for many useful scientific discussions and Matthew Rocklin for his help and technical support with the dask and into libraries.  ... 
doi:10.1109/tsp.2016.2516971 fatcat:w3k4ocypsjaxvecvot6qfcjo3a

Kullback-Leibler Divergence for Nonnegative Matrix Factorization [chapter]

Zhirong Yang, He Zhang, Zhijian Yuan, Erkki Oja
2011 Lecture Notes in Computer Science  
are well-scaled and thus lead to a new projected gradient method for NMF which runs faster or yields better approximation than three other widely used NMF algorithms. ⋆ Supported by the Academy of Finland  ...  We show that using KL-divergence takes the normalization structure into account in a very natural way and brings improvements for nonnegative matrix factorizations: the gradients of the normalized KL-divergence  ...  such as additional L1 or L2 norms of the factorizing matrices.  ... 
doi:10.1007/978-3-642-21735-7_31 fatcat:khntcrb52bfd5jlsqmi6b4z7pi

Adaptive Nonnegative Matrix Factorization and Measure Comparisons for Recommender Systems [article]

Gianna M. Del Corso, Francesco Romani
2018 arXiv   pre-print
In this paper we propose new methods based on the NMF of the rating matrix and we compare them with some classical algorithms such as the SVD and the regularized and unregularized non-negative matrix factorization  ...  The Nonnegative Matrix Factorization (NMF) of the rating matrix has shown to be an effective method to tackle the recommendation problem.  ...  In this paper we propose new methods based on the Nonnegative Matrix Factorization (NMF) of the rating matrix and we compare them with some classical algorithms such as the SVD and the regularized and  ... 
arXiv:1607.07607v2 fatcat:rcinypa7g5grhmyfquw3gr457y

Fast Nonnegative Matrix Factorization and Applications to Pattern Extraction, Deconvolution and Imputation [article]

Xihui Lin, Paul C. Boutros
2018 bioRxiv   pre-print
Nonnegative matrix factorization (NMF) is a technique widely used in various fields, including artificial intelligence (AI), signal processing and bioinformatics.  ...  Our NMF algorithm thus handles missing values naturally and integrates prior knowledge to guide NMF towards a more meaningful decomposition.  ...  Kenneth 241 Chu and Dr. Catalina Anghel.  ... 
doi:10.1101/321802 fatcat:w6ozrne5wbd23dje5z2nd5mlwy

Newton-based optimization for Kullback–Leibler nonnegative tensor factorizations

Samantha Hansen, Todd Plantenga, Tamara G. Kolda
2015 Optimization Methods and Software  
Tensor factorizations with nonnegative constraints have found application in analyzing data from cyber traffic, social networks, and other areas.  ...  Our new methods exploit structure and reformulate the optimization problem as small independent subproblems. We employ bound-constrained Newton and quasi-Newton methods.  ...  We thank the anonymous referees for clarifying some of our arguments, and for suggesting additional experiments.  ... 
doi:10.1080/10556788.2015.1009977 fatcat:voox4r6tonhungkakb35bdzfue

Joint Majorization-Minimization for Nonnegative Matrix Factorization with the β-divergence [article]

Arthur Marmin and José Henrique de Morais Goulart and Cédric Févotte
2021 arXiv   pre-print
This article proposes new multiplicative updates for nonnegative matrix factorization (NMF) with the β-divergence objective function.  ...  Our new updates are derived from a joint majorization-minimization (MM) scheme, in which an auxiliary function (a tight upper bound of the objective function) is built for the two factors jointly and minimized  ...  Oja, “Unified development of multiplicative algorithms for linear and quadratic nonnegative matrix factorization,” IEEE Trans.  ... 
arXiv:2106.15214v2 fatcat:agbyg2ds65c3lmgxwxep24odda

Text Mining using Nonnegative Matrix Factorization and Latent Semantic Analysis [article]

Ali Hassani, Amir Iranmanesh, Najme Mansouri
2020 arXiv   pre-print
As a result, we propose a new feature agglomeration method based on Nonnegative Matrix Factorization, which is employed to separate the terms into groups, and then each group's term vectors are agglomerated  ...  Nevertheless, text data require tokenization which usually yields a very large and highly sparse term-document matrix, which is usually difficult to process using conventional machine learning algorithms  ...  Nonnegative Matrix Factorization Nonnegative Matrix Factorization (NMF) is a matrix analysis method, which attempts to represent each matrix in the following format: X n×m = W n×k H k×m (4) This representation  ... 
arXiv:1911.04705v3 fatcat:kkegojl2kffohl65isw7unttom

Algorithms for positive semidefinite factorization

Arnaud Vandaele, François Glineur, Nicolas Gillis
2018 Computational optimization and applications  
Given an m-by-n nonnegative matrix X and an integer k, the PSD factorization problem consists in finding, if possible, symmetric k-by-k positive semidefinite matrices {A^1,...,A^m} and {B^1,...  ...  This paper considers the problem of positive semidefinite factorization (PSD factorization), a generalization of exact nonnegative matrix factorization.  ...  of the 24-gon 24 24 6 slack matrix of the 28-gon 28 28 E(0) = 1 and E(t) → t→∞ 0 if the corresponding algorithm converges towards an exact factorization.  ... 
doi:10.1007/s10589-018-9998-x fatcat:rixnn24y3fecnbqvtndt27becu

Algorithms for nonnegative matrix factorization with the beta-divergence [article]

Cédric Févotte
2011 arXiv   pre-print
This paper describes algorithms for nonnegative matrix factorization (NMF) with the beta-divergence (beta-NMF).  ...  Simulations on synthetic and real data illustrate the faster convergence of the ME approach.  ...  This work is supported by project ANR-09-JCJC-0073-01 TANGERINE (Theory and applications of nonnegative matrix factorization).  ... 
arXiv:1010.1763v3 fatcat:4qcxgxb4cnd2jgwho3mhbs6rny

Novel Algorithms based on Majorization Minimization for Nonnegative Matrix Factorization [article]

R. Jyothi, P. Babu, R. Bahl
2019 arXiv   pre-print
Under matrix decomposition, nonnegative matrix factorization is used to decompose a nonnegative matrix into a product of two nonnegative matrices which gives some meaningful interpretation of the data.  ...  The first algorithm-Iterative Nonnegative Matrix Factorization (INOM) sequentially updates the two nonnegative matrices while the second algorithm-Parallel Iterative Nonnegative Matrix Factorization (PARINOM  ...  The authors are with CARE, IIT Delhi, New Delhi, 110016, India.(email: jyothi.r@care.iitd.ac.in, prabhubabu@care.iitd.ac.in, rbahl@care.iitd.ac.in)  ... 
arXiv:1905.04529v1 fatcat:ginhrwvqrjgnhivub7s45wptke

Optimization and expansion of non-negative matrix factorization

Xihui Lin, Paul C. Boutros
2020 BMC Bioinformatics  
Non-negative matrix factorization (NMF) is a technique widely used in various fields, including artificial intelligence (AI), signal processing and bioinformatics.  ...  We show through complexity analysis and experiments that our implementation converges faster than well-known methods.  ...  Kenneth Chu and Dr. Catalina Anghel.  ... 
doi:10.1186/s12859-019-3312-5 pmid:31906867 pmcid:PMC6945623 fatcat:gauldinpcbbync24whyny2dt3e

Novel Algorithms based on Majorization Minimization for Nonnegative Matrix Factorization

R. Jyothi, P. Babu, R. Bahl
2019 IEEE Access  
Under matrix decomposition, nonnegative matrix factorization is used to decompose a nonnegative matrix into a product of two nonnegative matrices which gives some meaningful interpretation of the data.  ...  The first algorithm -Iterative Nonnegative Matrix Factorization (INOM) sequentially updates the two nonnegative matrices while the second algorithm -Parallel Iterative Nonnegative Matrix Factorization  ...  We address this algorithm as Parallel Iterative Nonnegative Matrix Factorization (PARINOM).  ... 
doi:10.1109/access.2019.2933845 fatcat:lyly3ayvnnhx5kybgciksgoeuy

Robust Near-Separable Nonnegative Matrix Factorization Using Linear Optimization [article]

Nicolas Gillis, Robert Luce
2013 arXiv   pre-print
In this paper, we generalize Hottopixx in order to resolve these two drawbacks, that is, we propose a new LP model which does not require normalization and detects the factorization rank automatically.  ...  Bittorf, Recht, R\'e and Tropp ('Factoring nonnegative matrices with linear programs', NIPS 2012) proposed a linear programming (LP) model, referred to as Hottopixx, which is robust under any small perturbation  ...  Given n nonnegative m-dimensional vectors gathered in a nonnegative matrix M ∈ R m×n + and a factorization rank r, NMF computes two nonnegative matrices W ∈ R m×r + and H ∈ R r×n + such that M ≈ W H.  ... 
arXiv:1302.4385v2 fatcat:7sdsgaf7hffarjt4xsyofzckme
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