@inproceedings{Lee1999,
author = {Lee, Daniel D and Seung, H Sebastian},
booktitle = {Advances in Neural Information Processing Systems},
editor = {Leen, T and Dietterich, T and Tresp, V},
mendeley-groups = {jrsicklsnmfpackagecitations},
publisher = {MIT Press},
title = {{Algorithms for Non-negative Matrix Factorization}},
url = {https://proceedings.neurips.cc/paper/2000/file/f9d1152547c0bde01830b7e8bd60024c-Paper.pdf},
volume = {13},
year = {2000}
}
@article{Eddelbuettel2011,
author = {Eddelbuettel, Dirk and Fran{\c{c}}ois, Romain},
doi = {10.18637/jss.v040.i08},
journal = {Journal of Statistical Software},
mendeley-groups = {jrsicklsnmfpackagecitations},
number = {8},
pages = {1--18},
title = {{Rcpp: Seamless R and C++ Integration}},
volume = {40},
year = {2011}
}
@article{Lun2016,
abstract = {Single-cell RNA sequencing (scRNA-seq) is widely used to profile the transcriptome of individual cells. This provides biological resolution that cannot be matched by bulk RNA sequencing, at the cost of increased technical noise and data complexity. The differences between scRNA-seq and bulk RNA-seq data mean that the analysis of the former cannot be performed by recycling bioinformatics pipelines for the latter. Rather, dedicated single-cell methods are required at various steps to exploit the cellular resolution while accounting for technical noise. This article describes a computational workflow for low-level analyses of scRNA-seq data, based primarily on software packages from the open-source Bioconductor project. It covers basic steps including quality control, data exploration and normalization, as well as more complex procedures such as cell cycle phase assignment, identification of highly variable and correlated genes, clustering into subpopulations and marker gene detection. Analyses were demonstrated on gene-level count data from several publicly available datasets involving haematopoietic stem cells, brain-derived cells, T-helper cells and mouse embryonic stem cells. This will provide a range of usage scenarios from which readers can construct their own analysis pipelines.},
author = {Lun, Aaron T.L. and McCarthy, Davis J. and Marioni, John C.},
doi = {10.12688/F1000RESEARCH.9501.2/DOI},
issn = {1759796X},
journal = {F1000Research},
keywords = {Bioconductor,Bioinformatics,RNA-seq,Single cell,Workflow},
mendeley-groups = {jrsicklsnmfpackagecitations},
pmid = {27909575},
publisher = {F1000 Research Ltd},
title = {{A step-by-step workflow for low-level analysis of single-cell RNA-seq data with Bioconductor}},
url = {https://pubmed.ncbi.nlm.nih.gov/27909575/},
volume = {5},
year = {2016}
}

@techreport{halfbakednmf,
address = {Cambridge},
author = {{Le Roux}, Jonathan and Weniger, Felix and Hershey, John R.},
institution = {Mitsubishi Electric Research Laboratories (MERL)},
mendeley-groups = {jrsicklsnmfpackagecitations},
title = {{Sparse NMF: half-baked or well done?}},
year = {2015}
}
@inproceedings{jNMF2011,
address = {Mitterberg, Austria},
author = {Akata, Zeynep and Thurau, Christian and Bauckhage, Christian},
booktitle = {16th Computer Vision Winter Workshop},
file = {:C\:/Users/Dorothy Ellis/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Akata, Thurau, Bauckhage - 2011 - Non-negative matrix factorization in multi-modality data for segmentation and label Prediction.pdf:pdf},
mendeley-groups = {jrsicklsnmfpackagecitations},
month = {feb},
pages = {652879},
title = {{Non-negative matrix factorization in multi-modality data for segmentation and label Prediction.}},
url = {https://hal.inria.fr/hal-00652879},
year = {2011}
}
@article{Liu2013,
author = {Liu, Jialu and Wang, Chi and Gao, Jing and Han, Jiawei},
doi = {10.1137/1.9781611972832.28},
file = {:C\:/Users/Dorothy Ellis/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Liu et al. - 2013 - Multi-View Clustering via Joint Nonnegative Matrix Factorization.pdf:pdf},
journal = {Proceedings of the 2013 SIAM International Conference on Data Mining},
mendeley-groups = {jrsicklsnmfpackagecitations},
pages = {252--260},
title = {{Multi-view clustering via joint nonnegative matrix factorization}},
year = {2013}
}
@article{Cai2008,
abstract = {Recently Non-negative Matrix Factorization (NMF) has received a lot of attentions in information retrieval, computer vision and pattern recognition. NMF aims to find two non-negative matrices whose product can well approximate the original matrix. The sizes of these two matrices are usually smaller than the original matrix. This results in a compressed version of the original data matrix. The solution of NMF yields a natural parts-based representation for the data. When NMF is applied for data representation, a major disadvantage is that it fails to consider the geometric structure in the data. In this paper, we develop a graph based approach for parts-based data representation in order to overcome this limitation. We construct an affinity graph to encode the geometrical information and seek a matrix factorization which respects the graph structure. We demonstrate the success of this novel algorithm by applying it on real world problems.},
author = {Cai, Deng and He, Xiaofei and Wu, Xiaoyun and Han, Jiawei},
doi = {10.1109/ICDM.2008.57},
isbn = {9780769535029},
issn = {15504786},
journal = {Proceedings - IEEE International Conference on Data Mining, ICDM},
mendeley-groups = {jrsicklsnmfpackagecitations},
pages = {63--72},
title = {{Non-negative matrix factorization on manifold}},
year = {2008}
}
@article{Elyanow2020,
abstract = {Single-cell RNA-sequencing (scRNA-seq) enables high-throughput measurement of RNA expression in single cells. However, because of technical limitations, scRNA-seq data often contain zero counts for many transcripts in individual cells. These zero counts, or dropout events, complicate the analysis of scRNA-seq data using standard methods developed for bulk RNA-seq data. Current scRNA-seq analysis methods typically overcome dropout by combining information across cells in a lower-dimensional space, leveraging the observation that cells generally occupy a small number of RNA expression states. We introduce netNMF-sc, an algorithm for scRNA-seq analysis that leverages information across both cells and genes. netNMF-sc learns a low-dimensional representation of scRNA-seq transcript counts using network-regularized non-negative matrix factorization. The network regularization takes advantage of prior knowledge of gene-gene interactions, encouraging pairs of genes with known interactions to be nearby each other in the low-dimensional representation. The resulting matrix factorization imputes gene abundance for both zero and nonzero counts and can be used to cluster cells into meaningful subpopulations. We show that netNMF-sc outperforms existing methods at clustering cells and estimating gene-gene covariance using both simulated and real scRNA-seq data, with increasing advantages at higher dropout rates (e.g., >60%). We also show that the results from netNMF-sc are robust to variation in the input network, with more representative networks leading to greater performance gains.},
author = {Elyanow, Rebecca and Dumitrascu, Bianca and Engelhardt, Barbara E. and Raphael, Benjamin J.},
doi = {10.1101/gr.251603.119},
file = {:C\:/Users/Dorothy Ellis/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Elyanow et al. - 2020 - NetNMF-SC Leveraging gene-gene interactions for imputation and dimensionality reduction in single-cell expres(2).pdf:pdf;:C\:/Users/Dorothy Ellis/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Elyanow et al. - 2020 - NetNMF-SC Leveraging gene-gene interactions for imputation and dimensionality reduction in single-cell expres(3).pdf:pdf},
issn = {15495469},
journal = {Genome Research},
mendeley-groups = {jrsicklsnmfpackagecitations},
month = {feb},
number = {2},
pages = {195--204},
pmid = {31992614},
publisher = {Cold Spring Harbor Laboratory Press},
url={https://pubmed.ncbi.nlm.nih.gov/31992614/},
title = {{NetNMF-SC: Leveraging gene-gene interactions for imputation and dimensionality reduction in single-cell expression analysis}},
volume = {30},
year = {2020}
}
@article{Eddelbuettel2014,
author = {Eddelbuettel, Dirk and Sanderson, Conrad},
journal = {Computational	Statistics and Data Analysis},
mendeley-groups = {jrsicklsnmfpackagecitations},
month = {mar},
pages = {1054--1063},
title = {{RcppArmadillo: Accelerating R with high-performance C++ linear algebra}},
url = {http://dx.doi.org/10.1016/j.csda.2013.02.005},
volume = {71},
year = {2014}
}
@article{jnmf2009,
abstract = {In many domains there will exist different representations or "views" describing the same set of objects. Taken alone, these views will often be deficient or incomplete. Therefore a key problem for exploratory data analysis is the integration of multiple views to discover the underlying structures in a domain. This problem is made more difficult when disagreement exists between views. We introduce a new unsupervised algorithm for combining information from related views, using a late integration strategy. Combination is performed by applying an approach based on matrix factorization to group related clusters produced on individual views. This yields a projection of the original clusters in the form of a new set of "meta-clusters" covering the entire domain. We also provide a novel model selection strategy for identifying the correct number of meta-clusters. Evaluations performed on a number of multi-view text clustering problems demonstrate the effectiveness of the algorithm. {\textcopyright} 2009 Springer.},
author = {Greene, Derek and Cunningham, P{\'{a}}draig},
doi = {10.1007/978-3-642-04180-8_45/COVER},
file = {:C\:/Users/Dorothy Ellis/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Greene, Cunningham - 2009 - A matrix factorization approach for integrating multiple data views.pdf:pdf},
isbn = {3642041795},
issn = {03029743},
journal = {Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)},
mendeley-groups = {jrsicklsnmfpackagecitations},
number = {PART 1},
pages = {423--438},
publisher = {Springer, Berlin, Heidelberg},
title = {{A matrix factorization approach for integrating multiple data views}},
url = {https://link.springer.com/chapter/10.1007/978-3-642-04180-8_45},
volume = {5781 LNAI},
year = {2009}
}
@article{louvain,
abstract = {We propose a simple method to extract the community structure of large networks. Our method is a heuristic method that is based on modularity optimization. It is shown to outperform all other known community detection methods in terms of computation time. Moreover, the quality of the communities detected is very good, as measured by the so-called modularity. This is shown first by identifying language communities in a Belgian mobile phone network of 2 million customers and by analysing a web graph of 118 million nodes and more than one billion links. The accuracy of our algorithm is also verified on ad hoc modular networks. {\textcopyright} 2008 IOP Publishing Ltd.},
archivePrefix = {arXiv},
arxivId = {0803.0476},
author = {Blondel, Vincent D. and Guillaume, Jean Loup and Lambiotte, Renaud and Lefebvre, Etienne},
doi = {10.1088/1742-5468/2008/10/P10008},
eprint = {0803.0476},
issn = {1742-5468},
journal = {Journal of Statistical Mechanics: Theory and Experiment},
keywords = {Networks,New applications of statistical mechanics,Random graphs},
mendeley-groups = {jrsicklsnmfpackagecitations},
month = {oct},
number = {10},
pages = {P10008},
publisher = {IOP Publishing},
url={https://iopscience.iop.org/article/10.1088/1742-5468/2008/10/P10008},
title = {{Fast unfolding of communities in large networks}},
volume = {2008},
year = {2008}
}
@article{NMFinR,
abstract = {Background: Nonnegative Matrix Factorization (NMF) is an unsupervised learning technique that has been applied successfully in several fields, including signal processing, face recognition and text mining. Recent applications of NMF in bioinformatics have demonstrated its ability to extract meaningful information from high-dimensional data such as gene expression microarrays. Developments in NMF theory and applications have resulted in a variety of algorithms and methods. However, most NMF implementations have been on commercial platforms, while those that are freely available typically require programming skills. This limits their use by the wider research community.Results: Our objective is to provide the bioinformatics community with an open-source, easy-to-use and unified interface to standard NMF algorithms, as well as with a simple framework to help implement and test new NMF methods. For that purpose, we have developed a package for the R/BioConductor platform. The package ports public code to R, and is structured to enable users to easily modify and/or add algorithms. It includes a number of published NMF algorithms and initialization methods and facilitates the combination of these to produce new NMF strategies. Commonly used benchmark data and visualization methods are provided to help in the comparison and interpretation of the results.Conclusions: The NMF package helps realize the potential of Nonnegative Matrix Factorization, especially in bioinformatics, providing easy access to methods that have already yielded new insights in many applications. Documentation, source code and sample data are available from CRAN. {\textcopyright} 2010 Gaujoux and Seoighe; licensee BioMed Central Ltd.},
author = {Gaujoux, Renaud and Seoighe, Cathal},
doi = {10.1186/1471-2105-11-367/FIGURES/5},
file = {:C\:/Users/Dorothy Ellis/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Gaujoux, Seoighe - 2010 - A flexible R package for nonnegative matrix factorization.pdf:pdf},
issn = {14712105},
journal = {BMC Bioinformatics},
keywords = {Algorithms,Bioinformatics,Computational Biology/Bioinformatics,Computer Appl. in Life Sciences,Microarrays},
mendeley-groups = {jrsicklsnmfpackagecitations},
month = {jul},
number = {1},
pages = {1--9},
pmid = {20598126},
publisher = {BioMed Central},
title = {{A flexible R package for nonnegative matrix factorization}},
url = {https://bmcbioinformatics.biomedcentral.com/articles/10.1186/1471-2105-11-367},
volume = {11},
year = {2010}
}
@article{Zheng2017,
abstract = {Characterizing the transcriptome of individual cells is fundamental to understanding complex biological systems. We describe a droplet-based system that enables 3′ mRNA counting of tens of thousands of single cells per sample. Cell encapsulation, of up to 8 samples at a time, takes place in ∼6 min, with ∼50% cell capture efficiency. To demonstrate the system's technical performance, we collected transcriptome data from ∼250k single cells across 29 samples. We validated the sensitivity of the system and its ability to detect rare populations using cell lines and synthetic RNAs. We profiled 68k peripheral blood mononuclear cells to demonstrate the system's ability to characterize large immune populations. Finally, we used sequence variation in the transcriptome data to determine host and donor chimerism at single-cell resolution from bone marrow mononuclear cells isolated from transplant patients.},
author = {Zheng, Grace X.Y. and Terry, Jessica M. and Belgrader, Phillip and Ryvkin, Paul and Bent, Zachary W. and Wilson, Ryan and Ziraldo, Solongo B. and Wheeler, Tobias D. and McDermott, Geoff P. and Zhu, Junjie and Gregory, Mark T. and Shuga, Joe and Montesclaros, Luz and Underwood, Jason G. and Masquelier, Donald A. and Nishimura, Stefanie Y. and Schnall-Levin, Michael and Wyatt, Paul W. and Hindson, Christopher M. and Bharadwaj, Rajiv and Wong, Alexander and Ness, Kevin D. and Beppu, Lan W. and Deeg, H. Joachim and McFarland, Christopher and Loeb, Keith R. and Valente, William J. and Ericson, Nolan G. and Stevens, Emily A. and Radich, Jerald P. and Mikkelsen, Tarjei S. and Hindson, Benjamin J. and Bielas, Jason H.},
doi = {10.1038/NCOMMS14049},
file = {:C\:/Users/Dorothy Ellis/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Zheng et al. - 2017 - Massively parallel digital transcriptional profiling of single cells.pdf:pdf},
issn = {20411723},
journal = {Nature Communications},
mendeley-groups = {jrsicklsnmfpackagecitations},
month = {jan},
pmid = {28091601},
publisher = {Nature Publishing Group},
url={https://pubmed.ncbi.nlm.nih.gov/28091601/},
title = {{Massively parallel digital transcriptional profiling of single cells}},
volume = {8},
year = {2017}
}
@article{Boutsidis2008,
abstract = {We describe Nonnegative Double Singular Value Decomposition (NNDSVD), a new method designed to enhance the initialization stage of nonnegative matrix factorization (NMF). NNDSVD can readily be combined with existing NMF algorithms. The basic algorithm contains no randomization and is based on two SVD processes, one approximating the data matrix, the other approximating positive sections of the resulting partial SVD factors utilizing an algebraic property of unit rank matrices. Simple practical variants for NMF with dense factors are described. NNDSVD is also well suited to initialize NMF algorithms with sparse factors. Many numerical examples suggest that NNDSVD leads to rapid reduction of the approximation error of many NMF algorithms. {\textcopyright} 2007 Elsevier Ltd. All rights reserved.},
author = {Boutsidis, C. and Gallopoulos, E.},
doi = {10.1016/J.PATCOG.2007.09.010},
file = {:C\:/Users/Dorothy Ellis/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Boutsidis, Gallopoulos - 2008 - SVD based initialization A head start for nonnegative matrix factorization.pdf:pdf},
issn = {00313203},
journal = {Pattern Recognition},
keywords = {Low rank,NMF,Nonnegative matrix factorization,Perron-Frobenius,SVD,Singular value decomposition,Sparse NMF,Sparse factorization,Structured initialization},
mendeley-groups = {jrsicklsnmfpackagecitations},
month = {apr},
number = {4},
pages = {1350--1362},
title = {{SVD based initialization: A head start for nonnegative matrix factorization}},
volume = {41},
year = {2008}
}

@article{UMAP,
abstract = {UMAP (Uniform Manifold Approximation and Projection) is a novel manifold learning technique for dimension   reduction. UMAP is constructed from a theoretical framework based in Riemannian geometry and algebraic topology. The result is a practical scalable algorithm that applies to real world data. The UMAP algorithm is competitive with t-SNE for visualization quality, and arguably preserves more of the global structure with superior run time performance. Furthermore, UMAP has no computational restrictions on embedding dimension, making it viable as a general purpose dimension reduction technique for machine learning.},
author = {McInnes, Leland and Healy, John and Saul, Nathaniel and Gro{\ss}berger, Lukas},
doi = {10.21105/JOSS.00861},
file = {:C\:/Users/Dorothy Ellis/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/McInnes et al. - 2018 - UMAP Uniform Manifold Approximation and Projection.pdf:pdf},
issn = {2475-9066},
journal = {Journal of Open Source Software},
mendeley-groups = {jrsicklsnmfpackagecitations},
month = {sep},
number = {29},
pages = {861},
publisher = {The Open Journal},
title = {{UMAP: Uniform Manifold Approximation and Projection}},
url = {https://joss.theoj.org/papers/10.21105/joss.00861},
volume = {3},
year = {2018}
}
@book{ggplot2,
address = {Cham, Switzerland},
author = {Wickham, Hadley},
doi = {https://doi.org/10.1007/978-3-319-24277-4},
edition = {2},
isbn = {978-3-319-24277-4},
mendeley-groups = {jrsicklsnmfpackagecitations},
month = {jun},
publisher = {Springer International Publishing},
title = {{ggplot2: Elegant Graphics for Data Analysis}},
url = {https://ggplot2.tidyverse.org/},
year = {2016}
}

@inproceedings{Ng2001,
abstract = {Despite many empirical successes of spectral clustering methods— algorithms that cluster points using eigenvectors of matrices derived from the data—there are several unresolved issues. First. there are a wide variety of algorithms that use the eigenvectors in slightly different ways. Second, many of these algorithms have no proof that they will actually compute a reasonable clustering. In this paper, we present a simple spectral clustering algorithm that can be implemented using a few lines of Matlab. Using tools from matrix perturbation theory, we analyze the algorithm, and give conditions under which it can be expected to do well. We also show surprisingly good experimental results on a number of challenging clustering problems.},
address = {Cambridge, MA, USA},
author = {Ng, Andrew Y and Jordan, Michael I and Weiss, Yair},
booktitle = {Proceedings of the 14th International Conference on Neural Information Processing Systems: Natural and Synthetic},
pages = {849--856},
publisher = {MIT Press},
series = {NIPS'01},
title = {{On spectral clustering: analysis and an algorithm}},
year = {2001}
}

@article{maxcluster,
abstract = {Nonnegative matrix factorization (NMF) has been successfully applied to many areas for classification and clustering. Commonly-used NMF algorithms mainly target on minimizing the $l_2$ distance or Kullback-Leibler (KL) divergence, which may not be suitable for nonlinear case. In this paper, we propose a new decomposition method by maximizing the correntropy between the original and the product of two low-rank matrices for document clustering. This method also allows us to learn the new basis vectors of the semantic feature space from the data. To our knowledge, we haven't seen any work has been done by maximizing correntropy in NMF to cluster high dimensional document data. Our experiment results show the supremacy of our proposed method over other variants of NMF algorithm on Reuters21578 and TDT2 databasets.},
author = {Xu, Wei and Liu, Xin and Gong, Yihong},
doi = {10.1145/860435.860485},
journal = {SIGIR '03: Proceedings of the 26th annual international ACM SIGIR conference on research and development in information retrieval},
month = {jul},
pages = {267--273},
publisher = {Association for Computing Machinery (ACM)},
title = {{Document clustering based on non-negative matrix factorization}},
url = {https://dl.acm.org/doi/10.1145/860435.860485},
year = {2003}
}
@misc{Schliep2016,
author = {Schliep, Klaus and Hechenbichler, Klaus},
mendeley-groups = {jrsicklsnmfpackagecitations},
title = {{kknn: Weighted k-Nearest Neighbors}},
url = {https://cran.r-project.org/package=kknn},
year = {2016}
}

@article{irlba,
abstract = {New restarted Lanczos bidiagonalization methods for the computation of a few of the largest or smallest singular values of a large matrix are presented. Restarting is carried out by augmentation of...},
author = {Baglama, James and Reichel, Lothar},
doi = {10.1137/04060593X},
file = {:C\:/Users/Dorothy Ellis/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Baglama, Reichel - 2005 - Augmented Implicitly Restarted Lanczos Bidiagonalization Methods.pdf:pdf},
issn = {10648275},
journal = {SIAM Journal on Scientific Computing},
keywords = {15A18,65F15,65F50,iterative method,large-scale computation,partial singular value decomposition,singular value computation},
mendeley-groups = {jrsicklsnmfpackagecitations},
month = {jul},
number = {1},
pages = {19--42},
publisher = {Society for Industrial and Applied Mathematics},
title = {{Augmented Implicitly Restarted Lanczos Bidiagonalization Methods}},
volume = {27},
year = {2005}
}
@article{Beheshti2012,
abstract = {Identifying the skills that determine the success or failure to exercises and question items is a difficult task. Multiple skills may be involved at various degree of importance, and skills may overlap and correlate. In an effort towards the goal of finding the skills behind a set of items, we investigate two techniques to determine the number of dominant latent skills. The Singular Value Decomposition (SVD) is a known technique to find latent factors. The singular values represent direct evidence of the strength of latent factors. Application of SVD to finding the number of latent skills is explored. We introduce a second technique based on a},
author = {Beheshti, Behzad and Desmarais, Michel C. and Naceur, Rhouma},
file = {:C\:/Users/Dorothy Ellis/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Beheshti, Desmarais, Naceur - 2012 - Methods to Find the Number of Latent Skills.pdf:pdf},
journal = {International Educational Data Mining Society},
keywords = {Algebra,Data,Equations (Mathematics),Evaluation,Experiments,Mathematics,Models,Prediction,Simulation},
mendeley-groups = {jrsicklsnmfpackagecitations},
month = {jun},
publisher = {International Educational Data Mining Society. e-mail: admin@educationaldatamining.org; Web site: http://www.educationaldatamining.org},
title = {{Methods to Find the Number of Latent Skills}},
year = {2012}
}
@article{clValid,
author = {Brock, Guy and Pihur, Vasyl and Datta, Susmita and Datta, Somnath},
journal = {Journal of Statistical Software},
mendeley-groups = {jrsicklsnmfpackagecitations},
number = {4},
pages = {1--22},
title = {{{clValid}: An {R} Package for Cluster Validation}},
url = {https://www.jstatsoft.org/v25/i04/},
volume = {25},
year = {2008}
}

@Manual{factoextra,
    title = {factoextra: Extract and Visualize the Results of Multivariate Data Analyses},
    author = {Kassambara, Alboukadel and Mundt, Fabian},
    year = {2020},
    note = {R package version 1.0.7},
    url = {https://CRAN.R-project.org/package=factoextra},
