% NMF and NTF
@book{amari,
  title={Nonnegative Matrix and Tensor Factorizations},
  author={CICHOCK, A. et al.},
  year={2009},
  publisher={Wiley}
}

% NMF
@article{nmf,
  author = {Lee, D. and Seung, H.},
  journal = {Nature},
  title = {Learning the parts of objects by non-negative matrix factorization},
  volume = {401},
  pages = {788-791},
  year = {1999}}

% Kimura
@article{kimura,
  author = {Kimura, K.},
  journal = {Ph.D. Thesis},
  title = {A Study on Efficient Algorithms for Nonnegative Matrix/Tensor Factorization},
  year = {2017}}

% Orthogonal NMF
@article{orthogonal1,
  author = {Choi, S.},
  journal = {IEEE World Congress on Computational Intelligence},
  title = {Algorithms for Orthogonal Nonnegative Matrix Factorization},
  pages = {1828-1832},
  year = {2008}}

% Orthogonal NMF
@article{orthogonal2,
  author = {Stražar, M. et al.},
  journal = {Bioinformatics},
  title = {Orthogonal matrix factorization enables integrative analysis of multiple RNA binding proteins},
  volume = {32(10)},
  pages = {1527-1535},
  year = {2016}}

% NMTF
@article{nmtf1,
  author = {Copar, A. et al.},
  journal = {PLOE ONE},
  title = {Fast Optimization of Non-Negative Matrix Tri-Factorization: Supporting Information},
  volume = {14(6)},
  pages = {e0217994},
  year = {e2019}}

% NMTF
@article{nmtf2,
  author = {Long, B. et al.},
  journal = {SIGKDD'05},
  title = {Co-clustering by Block Value Decomposition},
  pages = {635–640},
  year = {2005}}

% NMTF
@article{nmtf3,
  author = {Ding, C. et al.},
  journal = {SIGKDD'06},
  title = {Orthogonal Nonnegative Matrix Tri-Factorizations for Clustering},
  pages = {126–135},
  year = {2006}}

% siNMF
@article{sinmf1,
  author = {Badea, L.},
  journal = {Pacific Symposium on Biocomputing},
  title = {Extracting Gene Expression Profiles Common to Colon and Pancreatic Adenocarcinoma using Simultaneous nonnegative matrix factorization},
  pages = {279-290},
  year = {2008}}

% siNMF
@article{sinmf2,
  author = {Zhang, S. et al.},
  journal = {Nucleic Acids Research},
  title = {Discovery of multi-dimensional modules by integrative analysis of cancer genomic data},
  volume = {40(19)},
  pages = {9379-9391},
  year = {2012}}

% siNMF
@article{sinmf3,
  author = {Yilmaz, Y. K. et al.},
  journal = {IVA/ICA 2010},
  title = {Probabilistic Latent Tensor Factorization},
  pages = {346-353},
  year = {2010}}

% jNMF
@article{jnmf,
  author = {Yang, Z. et al.},
  journal = {Bioinformatics},
  title = {A non-negative matrix factorization method for detecting modules in heterogeneous omics multi-modal data},
  volume = {32(1)},
  pages = {1-8},
  year = {2016}}

% NTF
@article{ntf1,
  author = {Cichocki, A. et al.},
  journal = {ICASSP'07},
  title = {Non-negative Tensor Factorization using Alpha and Beta Divergence},
  pages = {III-1393-III-1396},
  year = {2007}}

% NTF
@article{ntf2,
  author = {Phan, A. H. et al.},
  journal = {NOLTA 2008},
  title = {Multi-way Nonnegative Tensor Factorization Using Fast Hierarchical Alternating Least Squares Algorithm (HALS)},
  year = {2008}}

% NTF
@article{ntf3,
  author = {Cichocki, A. et al.},
  journal = {IEICE Transactions},
  title = {Fast Local Algorithms for Large Scale Nonnegative Matrix and Tensor Factorizations},
  volume = {92-A},
  pages = {708-721},
  year = {2009}}

% NTD
@article{ntd1,
  author = {Kim, Y.-D. et al.},
  journal = {IEEE CVPR},
  title = {Nonnegative Tucker Decomposition},
  pages = {1-8},
  year = {2017}}

% NTD
@article{ntd2,
  author = {Kim, Y.-D. et al.},
  title = {Nonneegative Tucker Decomposition with Alpha-Divergence},
  year = {2008}}

% NTD
@article{ntd3,
  author = {Phan, A. H. et al.},
  journal = {ISNN 2008},
  title = {Fast and efficient algorithms for nonnegative Tucker decomposition},
  pages = {772-782},
  year = {2008}}

% NTD
@article{ntd4,
  author = {Phan, A. H. et al.},
  journal = {Neurocomputing},
  title = {Extended HALS algorithm for nonnegative Tucker decomposition and its applications for multiway analysis and classification},
  volume = {74(11)},
  pages = {1956-1969},
  year = {2011}}

% Rank Estimation (Cophenetic Correlation Coefficient)
@article{ccc,
  author = {Brunet, J.-P. et al.},
  journal = {PNAS},
  title = {Metagenes and molecular pattern discovery using matrix factorization},
  volume = {101(12)},
  pages = {4164-4169},
  year = {2004}}

% Rank Estimation (Matrix condition)
@article{condition,
  author = {Han, X.},
  journal = {CSB 2007},
  title = {Cancer Molecular Pattern Discovery by Subspace Consensus Kernel Classification},
  volume = {6},
  pages = {55-65},
  year = {2007}}

% Rank Estimation (Permutated data)
@article{perm,
  author = {Frigyesi, A. et al.},
  journal = {Cancer Informatics},
  title = {Non-Negative Matrix Factorization for the Analysis of Complex Gene Expression Data: Identification of Clinically Relevant Tumor Subtypes},
  year = {2008}}

% Rank Estimation (Dispersion coefficient of consensus matrix)
@article{dispersion,
  author = {Park, H. et al.},
  journal = {SIAM Gene Golub Summer School},
  title = {Lecture 3: Nonnegative Matrix Factorization: Algorithms and Applications},
  year = {2019}}

% Rank Estimation (Cell sparsensss & Entropy)
@article{sparseness1,
  author = {Shao, C. et al.},
  journal = {Bioinformatics},
  title = {Robust classification of single-cell transcriptome data by nonnegative matrix factorization},
  volume = {33(2)},
  pages = {235-242},
  year = {2017}}

% Rank Estimation (Volume of reconstructed matrix)
@article{volume,
  author = {Fogel, P.},
  journal = {arXiv},
  title = {Permuted NMF: A Simple Algorithm Intended to Minimize the Volume of the Score Matrix},
  year = {2013}}

% Rank Estimation (SVD)
@article{singular,
  author = {Kim, P. M. et al.},
  journal = {Genome Research},
  title = {Subsystem Identification Through Dimensionality Reduction of Large-Scale Gene Expression Data},
  volume = {13(7)},
  pages = {1706-1718},
  year = {2003}}

% Rank Estimation (RSS)
@article{rss,
  author = {Hutchins, L. N. et al.},
  journal = {Bioinformatics},
  title = {Position-dependent motif characterization using non-negative matrix factorization},
  volume = { 24(23)},
  pages = {2684-2690},
  year = {2008}}

% Rank Estimation (Sparseness)
@article{sparseness2,
  author = {Hoyer, P. O.},
  journal = {JMLR 5},
  title = {Non-negative Matrix Factorization with Sparseness Constraints},
  pages = {1457-1469},
  year = {2004}}

% Rank Estimation (Mask matrix)
@article{mask1,
  author = {Fujita, N. et al.},
  journal = {Scientific Report},
  title = {Biomarker discovery by integrated joint non-negative matrix factorization and pathway signature analyses},
  volume = {8(1)},
  pages = {9743},
  year = {2018}}

% Rank Estimation (Mask matrix)
@article{mask2,
  author = { Owen, A. B. et al.},
  journal = {The Annals of Applied Statistics},
  title = {Bi-Cross-Validation of the SVD and the Nonnegative Matrix Factorization},
  volume = {3(2)},
  pages = {564-594},
  year = {2009}}

% Exponent term depending on Beta parameter
@article{exp,
  author = {Nakano, M. et al.},
  journal = {IEEE MLSP},
  title = {Convergence-guaranteed multiplicative algorithms for nonnegative matrix factorization with Beta-divergence},
  pages = {283-288},
  year = {2010}}
