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On Identifiability of Nonnegative Matrix Factorization

Xiao Fu, Kejun Huang, Nicholas D. Sidiropoulos
2018 IEEE Signal Processing Letters  
Specifically, using the proposed criterion, it suffices to identify the latent factors if the rows of one factor are sufficiently scattered over the nonnegative orthant, while no structural assumption  ...  In this letter, we propose a new identification criterion that guarantees the recovery of the low-rank latent factors in the nonnegative matrix factorization (NMF) model, under mild conditions.  ...  covers a much wider range of applications including the cases where one factor is not nonnegative.  ... 
doi:10.1109/lsp.2018.2789405 fatcat:gleu66jg45d77koco5nqyq5f7m

Date of publication xxxx 00, 0000, date of current version xxxx 00, 0000. Digital Object Identifier 10.1109/ACCESS.2017.Doi Number Adaptive Wiener Gain to Improve Sound Quality on Nonnegative Matrix Factorization-based Noise Reduction System

Ying-Hui Lai, Syu-Siang Wang, Chien-Hsun Chen, Sin-Hua Jhang
2019 IEEE Access  
One shortcoming of existing network-based time series prediction methods is time consuming.  ...  To address this issue, this paper proposes a new prediction algorithm based on visibility graph and markov chains.  ...  Where P V = V is the matrix form of the above formula.  ... 
doi:10.1109/access.2019.2907175 fatcat:tq7zxakzzzay7idks64do3jkly

Bayesian Semi-nonnegative Tri-matrix Factorization to Identify Pathways Associated with Cancer Types [article]

Sunho Park, Tae Hyun Hwang
2017 arXiv   pre-print
We propose a Bayesian (semi-)nonnegative matrix factorization model for human cancer genomic data, where the biological prior knowledge represented by a pathway database and a PPI network is taken into  ...  Identifying altered pathways that are associated with specific cancer types can potentially bring a significant impact on cancer patient treatment.  ...  In particular, in [7] the authors use the nonnegative tri-matrix factorization model to identify pathways that are relevant to human cancer, which is the same goal as ours.  ... 
arXiv:1712.00520v1 fatcat:jss77dm7mvcyzhws4q5bede3qe

Semidefinite Programming Based Preconditioning for More Robust Near-Separable Nonnegative Matrix Factorization

Nicolas Gillis, Stephen A. Vavasis
2015 SIAM Journal on Optimization  
Nonnegative matrix factorization (NMF) under the separability assumption can provably be solved efficiently, even in the presence of noise, and has been shown to be a powerful technique in document classification  ...  This problem is referred to as near-separable NMF and requires that there exists a cone spanned by a small subset of the columns of the input nonnegative matrix approximately containing all columns.  ...  INTRODUCTION Nonnegative matrix factorization (NMF) is a powerful dimensionality reduction technique as it automatically extracts sparse and meaningful features from a set of nonnegative data vectors.  ... 
doi:10.1137/130940670 fatcat:hr4epf4ozfckvbbewikb6vsny4

A Characterization of the Non-Uniqueness of Nonnegative Matrix Factorizations [article]

W. Pan, F. Doshi-Velez
2016 arXiv   pre-print
Nonnegative matrix factorization (NMF) is a popular dimension reduction technique that produces interpretable decomposition of the data into parts.  ...  While other studies have provide criteria under which NMF is identifiable, we present the first (to our knowledge) characterization of the non-identifiability of NMF.  ...  Brief Review of Nonnegative Matrix Factorization Let S be a nonnegative matrix in R M ×N + .  ... 
arXiv:1604.00653v1 fatcat:3m4dkklavzfpzjwtgzwiwk5ou4

A Flexible Modeling Framework For Coupled Matrix And Tensor Factorizations

Evrim Acar, Mattias Nilsson, Michael Saunders
2014 Zenodo  
Publication in the conference proceedings of EUSIPCO, Lisbon, Portugal, 2014  ...  In Figure 3 (a), we observe that shared/unshared factors can be successfully identified using only nonnegativity constraints on the factors.  ...  together with nonnegativity constraints on the factors.  ... 
doi:10.5281/zenodo.43779 fatcat:of6w2qyymndthi5ndlltq67q2i

Computing symmetric nonnegative rank factorizations

V. Kalofolias, E. Gallopoulos
2012 Linear Algebra and its Applications  
An algorithm is described for the nonnegative rank factorization (NRF) of some completely positive (CP) matrices whose rank is equal to their CP-rank.  ...  The algorithm can compute the symmetric NRF of any nonnegative symmetric rank-r matrix that contains a diagonal principal submatrix of that rank and size with leading cost O(rm 2 ) operations in the dense  ...  This work was based on a talk presented at the ALA2010 Conference in  ... 
doi:10.1016/j.laa.2011.03.016 fatcat:tcall7o6wndz3kxulto54i77pu

Factoring nonnegative matrices with linear programs [article]

Victor Bittorf and Benjamin Recht and Christopher Re and Joel A. Tropp
2013 arXiv   pre-print
This paper describes a new approach, based on linear programming, for computing nonnegative matrix factorizations (NMFs).  ...  An optimized C++ implementation can factor a multigigabyte matrix in a matter of minutes.  ...  A Proofs Let Y be a nonnegative matrix whose rows sum to one. Assume that Y admits an exact separable factorization of rank r.  ... 
arXiv:1206.1270v2 fatcat:gpscntojqjhmfdq57c2jgixms4

Advances in Nonnegative Matrix and Tensor Factorization

A. Cichocki, M. Mørup, P. Smaragdis, W. Wang, R. Zdunek
2008 Computational Intelligence and Neuroscience  
to ensure the high quality of this issue.  ...  Acknowledgments The guest editors of this special issue are extremely grateful to all the reviewers who took time to carefully read the submitted manuscripts and to provide critical comments which helped  ...  The sixth paper, entitled "Gene tree labeling using nonnegative matrix factorization on biomedical literature" by K. E.  ... 
doi:10.1155/2008/852187 pmid:18615193 pmcid:PMC2443422 fatcat:bbjdwfrcfzf57bulhukdilqa2i

People to People Recommendation using Coupled Nonnegative Boolean Matrix Factorization

Balasubramaniam Thirunavukarasu, Nayak Richi, Chau Yuen
2018 2018 International Conference on Soft-computing and Network Security (ICSNS)  
To overcome this, the ALS method is adopted in which one factor matrix is updated while all other factor matrices are fixed [4] .  ...  the user burden for identifying information of interest from the abundant amount of data available.  ... 
doi:10.1109/icsns.2018.8573623 fatcat:by6wd5cp7ndszlcnw345boutzy

On Large-Scale Dynamic Topic Modeling with Nonnegative CP Tensor Decomposition [article]

Miju Ahn, Nicole Eikmeier, Jamie Haddock, Lara Kassab, Alona Kryshchenko, Kathryn Leonard, Deanna Needell, R. W. M. A. Madushani, Elena Sizikova, Chuntian Wang
2020 arXiv   pre-print
Previous work on dynamic topic modeling primarily employ the method of nonnegative matrix factorization (NMF), where slices of the data tensor are each factorized into the product of lower-dimensional  ...  products of nonnegative vectors, thereby preserving the temporal information.  ...  NMF for Matrices Nonnegative matrix factorization (NMF) seeks to find an approximate factorization of a nonnegative data matrix X ∈ R n 1 ×n 2 ≥0 into a nonnegative features matrix A and a nonnegative  ... 
arXiv:2001.00631v2 fatcat:h5o3vgp6f5fjrfkfr46hyabiwm

Blind Source Separation by Fully Nonnegative Constrained Iterative Volume Maximization

Zuyuan Yang, Shuxue Ding, Shengli Xie
2010 IEEE Signal Processing Letters  
However, the algorithm that they have proposed can guarantee the nonnegativities of the sources only, but cannot obtain a nonnegative mixing matrix necessarily.  ...  Recently, under the assumption that both of the sources and the mixing matrix are nonnegative, Wang et al. develop an amazing BSS method by using volume maximization.  ...  Nonnegative matrix factorization (NMF) is a newly developed method which aims to Decompose a nonnegative matrix into the product of two nonnegative matrices or factors [8] .  ... 
doi:10.1109/lsp.2010.2055854 fatcat:uycofj5oirgf5kjjricdajai5u

Introduction to Nonnegative Matrix Factorization [article]

Nicolas Gillis
2017 arXiv   pre-print
In this paper, we introduce and provide a short overview of nonnegative matrix factorization (NMF).  ...  In order to put NMF into perspective, the more general problem class of constrained low-rank matrix approximation problems is first briefly introduced.  ...  The author would like to thank the editors of the SIAM Activity Group on Optimization's Views and News (see http://wiki.siam.org/siag-op/index.php/View_and_News), Stefan Wild and Jennifer Erway, for providing  ... 
arXiv:1703.00663v1 fatcat:vipa3xubrre3jjcg3gkvm3mbbq

On the nonnegative rank of Euclidean distance matrices

Matthew M. Lin, Moody T. Chu
2010 Linear Algebra and its Applications  
The Euclidean distance matrix for n distinct points in R r is generically of rank r + 2.  ...  It is shown in this paper via a geometric argument that its nonnegative rank for the case r = 1 is generically n.  ...  In particular, if Q 4 = UV is one of the two nontrivial standard nonnegative factorizations of Q 4 , i.e., columns of ϑ(U) (or ϑ(V )) are the four vertices of the quadrilateral, then q 5 is a nonnegative  ... 
doi:10.1016/j.laa.2010.03.038 pmid:23966751 pmcid:PMC3747005 fatcat:zkpvy7rgbzhyzj2smydhelidle

Nonnegative matrix partial co-factorization for drum source separation

Jiho Yoo, Minje Kim, Kyeongok Kang, Seungjin Choi
2010 2010 IEEE International Conference on Acoustics, Speech and Signal Processing  
Nonnegative matrix factorization (NMF) was successfully applied to spectrograms of music to learn basis vectors, followed by support vector machine (SVM) to classify basis vectors into ones associated  ...  To this end, we present nonnegative matrix partial co-factorization (NMPCF) where the target matrix (spectrograms of music) and drum-only-matrix (collected from various drums a priori) are simultaneously  ...  INTRODUCTION Nonnegative matrix factorization (NMF) is a low-rank approximation method where a nonnegative input data matrix (target matrix) is approximated as a product of two nonnegative factor matrices  ... 
doi:10.1109/icassp.2010.5495305 dblp:conf/icassp/YooKKC10 fatcat:jkwl5pciwvdbxcbyeghhhtzsgu
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