R package for Non-negative Tensor Decomposition

```
git clone https://github.com/rikenbit/nnTensor/
R CMD INSTALL nnTensor
```

or type the code below in the R console window ~~~~ library(devtools) devtools::install_github(“rikenbit/nnTensor”) ~~~~

**Non-negative Matrix Factorization (NMF)**: Nonnegative Matrix and Tensor Factorizations, Andrzej CICHOCK, et. al., 2009, A Study on Efficient Algorithms for Nonnegative Matrix/Tensor Factorization, Keigo Kimura, 2017**Projected NMF****Nonnegative Hebbian Rule (NHR)****Ding-Ti-Peg-Park (DTPP) algorithm****(Column vector-wise) Orthogonal NMF**- Algorithms for Orthogonal Nonnegative Matrix Factorization, Seungjin Choi, 2008

**(Column vector-wise) Orthogonality-regularized NMF**- Orthogonal matrix factorization enables integrative analysis of multiple RNA binding proteins, Martin Stražar, Marinka Žitnik, Blaž Zupan, Jernej Ule, Tomaž Curk, Bioinformatics, 15;32(10):1527-35, 2016

**Non-negative Matrix Tri-Factorization (NMTF)**: Fast Optimization of Non-Negative Matrix Tri-Factorization: Supporting Information, Andrej Copar, et. al., PLOS ONE, 14(6), e0217994, 2019, Co-clustering by Block Value Decomposition, Bo Long et al., SIGKDD’05, 2005**Simultaneous Non-negative Matrix Factorization (siNMF)**: Extracting Gene Expression Profiles Common to Colon and Pancreatic Adenocarcinoma using Simultaneous nonnegative matrix factorization, Liviu Badea, Pacific Symposium on Biocomputing, 13:279-290, 2009, Discovery of multi-dimensional modules by integrative analysis of cancer genomic data. Shihua Zhang, et al., Nucleic Acids Research, 40(19), 9379-9391, 2012, Probabilistic Latent Tensor Factorization, International Conference on Latent Variable Analysis and Signal Separation, Y. Kenan Yilmaz et al., 346-353, 2010**Joint Non-negative Matrix Factorization (jNMF)**: A non-negative matrix factorization method for detecting modules in heterogeneous omics multi-modal data, Zi Yang, et al., Bioinformatics, 32(1), 1-8, 2016**Non-negative CP Decomposition (NTF)***α-Divergence (KL, Pearson, Hellinger, Neyman) / β-Divergence (KL, Frobenius, IS)*: Non-negative Tensor Factorization using Alpha and Beta Divergence, Andrzej CICHOCKI et. al., 2007, TensorKPD.R (gist of mathieubray)*Fast HALS*: Multi-way Nonnegative Tensor Factorization Using Fast Hierarchical Alternating Least Squares Algorithm (HALS), Anh Huy PHAN et. al., 2008*α-HALS/β-HALS*: Fast Local Algorithms for Large Scale Nonnegative Matrix and Tensor Factorizations, Andrzej CICHOCKI et. al., 2008

**Non-negative Tucker Decomposition (NTD)***KL, Frobenius*: Nonnegative Tucker Decomposition, Yong-Deok Kim et. al., 2007*α-Divergence (KL, Pearson, Hellinger, Neyman) / β-Divergence (KL, Frobenius, IS)*: Nonneegative Tucker Decomposition With Alpha-Divergence, Yong-Deok Kim et. al., 2008, Fast and efficient algorithms for nonnegative Tucker decomposition, Anh Huy Phan, 2008*Fast HALS*: Extended HALS algorithm for nonnegative Tucker decomposition and its applications for multiway analysis and classification, Anh Hyu Phan et. al., 2011

**Rank estimation of NMF**- Jean-Philippe Brunet. et. al., (2004). Metagenes and molecular pattern discovery using matrix factorization. PNAS
- Xiaoxu Han. (2007). CANCER MOLECULAR PATTERN DISCOVERY BY SUBSPACE CONSENSUS KERNEL CLASSIFICATION
- Attila Frigyesi. et. al., (2008). Non-Negative Matrix Factorization for the Analysis of Complex Gene Expression Data: Identification of Clinically Relevant Tumor Subtypes. Cancer Informatics
- Haesun Park. et. al., (2019). Lecture 3: Nonnegative Matrix Factorization: Algorithms and Applications. SIAM Gene Golub Summer School, Aussois France, June 18, 2019
- Chunxuan Shao. et. al., (2017). Robust classification of single-cell transcriptome data by nonnegative matrix factorization. Bioinformatics
- Paul Fogel (2013). Permuted NMF: A Simple Algorithm Intended to Minimize the Volume of the Score Matrix
- Philip M. Kim. et. al., (2003). Subsystem Identification Through Dimensionality Reduction of Large-Scale Gene Expression Data. Genome Research
- Lucie N. Hutchins. et. al., (2008). Position-dependent motif characterization using non-negative matrix factorization. Bioinformatics
- Patrik O. Hoyer (2004). Non-negative Matrix Factorization with Sparseness Constraints. Journal of Machine Learning 5
- N. Fujita et al., (2018) Biomarker discovery by integrated joint non-negative matrix factorization and pathway signature analyses, Scientific Report
- Art B. Owen et. al., (2009). Bi-Cross-Validation of the SVD and the Nonnegative Matrix Factorization. The Annals of Applied Statistics

**Exponent term depending on Beta parameter**- M. Nakano et al., (2010). Convergence-guaranteed multiplicative algorithms for nonnegative matrix factorization with Beta-divergence. IEEE Workshop on Machine Learning for Signal Processing

Copyright (c) 2018 Koki Tsuyuzaki and Laboratory for Bioinformatics Research, RIKEN Center for Biosystems Dynamics Reseach Released under the Artistic License 2.0.

- Koki Tsuyuzaki
- Manabu Ishii
- Itoshi Nikaido