| Title: | Non-Negative Tensor Decomposition |
|---|---|
| Description: | Some functions for performing non-negative matrix factorization, non-negative CANDECOMP/PARAFAC (CP) decomposition, non-negative Tucker decomposition, and generating toy model data. See Andrzej Cichock et al (2009) and the reference section of GitHub README.md <https://github.com/rikenbit/nnTensor>, for details of the methods. |
| Authors: | Koki Tsuyuzaki [aut, cre], Itoshi Nikaido [aut] |
| Maintainer: | Koki Tsuyuzaki <[email protected]> |
| License: | MIT + file LICENSE |
| Version: | 1.3.0 |
| Built: | 2025-02-07 05:00:37 UTC |
| Source: | https://github.com/rikenbit/nntensor |
Some functions for performing non-negative matrix factorization, non-negative CANDECOMP/PARAFAC (CP) decomposition, non-negative Tucker decomposition, and generating toy model data. See Andrzej Cichock et al (2009) and the reference section of GitHub README.md <https://github.com/rikenbit/nnTensor>, for details of the methods.
The DESCRIPTION file:
| Package: | nnTensor |
| Type: | Package |
| Title: | Non-Negative Tensor Decomposition |
| Version: | 1.3.0 |
| Authors@R: | c(person("Koki", "Tsuyuzaki", role = c("aut", "cre"), email = "[email protected]"), person("Itoshi", "Nikaido", role = "aut")) |
| Depends: | R (>= 3.4.0) |
| Imports: | methods, MASS, fields, rTensor, plot3D, tagcloud, ggplot2 |
| Suggests: | knitr, rmarkdown, testthat, dplyr |
| Description: | Some functions for performing non-negative matrix factorization, non-negative CANDECOMP/PARAFAC (CP) decomposition, non-negative Tucker decomposition, and generating toy model data. See Andrzej Cichock et al (2009) and the reference section of GitHub README.md <https://github.com/rikenbit/nnTensor>, for details of the methods. |
| License: | MIT + file LICENSE |
| URL: | https://github.com/rikenbit/nnTensor |
| VignetteBuilder: | knitr |
| Repository: | https://rikenbit.r-universe.dev |
| RemoteUrl: | https://github.com/rikenbit/nntensor |
| RemoteRef: | HEAD |
| RemoteSha: | 034d190f69830ec11ff4cdf75dbbfe2d649e88f0 |
| Author: | Koki Tsuyuzaki [aut, cre], Itoshi Nikaido [aut] |
| Maintainer: | Koki Tsuyuzaki <[email protected]> |
Index of help topics:
GabrielNMF Gabriel-type Bi-Cross-Validation for
Non-negative Matrix Factorization
NMF Non-negative Matrix Factorization Algorithms
(NMF)
NMTF Non-negative Matrix Tri-Factorization
Algorithms (NMTF)
NTD Non-negative Tucker Decomposition Algorithms
(NTD)
NTF Non-negative CP Decomposition Algorithms (NTF)
jNMF Joint Non-negative Matrix Factorization
Algorithms (jNMF)
kFoldMaskTensor Mask tensors generator to perform k-fold cross
validation
nnTensor-package Non-Negative Tensor Decomposition
plot.NMF Plot function of the result of NMF function
plotTensor2D Plot function for visualization of matrix data
structure
plotTensor3D Plot function for visualization of tensor data
structure
recTensor Tensor Reconstruction from core tensor (S) and
factor matrices (A)
siNMF Simultaneous Non-negative Matrix Factorization
Algorithms (siNMF)
toyModel Toy model data for using NMF, NTF, and NTD
Koki Tsuyuzaki [aut, cre], Itoshi Nikaido [aut]
Maintainer: Koki Tsuyuzaki <[email protected]>
Andrzej CICHOCK, et. al., (2009). Nonnegative Matrix and Tensor Factorizations. John Wiley & Sons, Ltd
Keigo Kimura, (2017). A Study on Efficient Algorithms for Nonnegative Matrix/Tensor Factorization. Hokkaido University Collection of Scholarly and Academic Papers
Andrzej CICHOCKI et. al., (2007). Non-negative Tensor Factorization using Alpha and Beta Divergence. IEEE ICASSP 2007
Anh Huy PHAN et. al., (2008). Multi-way Nonnegative Tensor Factorization Using Fast Hierarchical Alternating Least Squares Algorithm (HALS). NOLTA2008
Andrzej CICHOCKI et. al., (2008). Fast Local Algorithms for Large Scale Nonnegative Matrix and Tensor Factorizations. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Yong-Deok Kim et. al., (2007). Nonnegative Tucker Decomposition. IEEE Conference on Computer Vision and Pattern Recognition
Yong-Deok Kim et. al., (2008). Nonneegative Tucker Decomposition With Alpha-Divergence. IEEE International Conference on Acoustics, Speech and Signal Processing
Anh Huy Phan, (2008). Fast and efficient algorithms for nonnegative Tucker decomposition. Advances in Neural Networks - ISNN2008
Anh Hyu Phan et. al. (2011). Extended HALS algorithm for nonnegative Tucker decomposition and its applications for multiway analysis and classification. Neurocomputing
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
toyModel,NMF,NTF,NTD,recTensor,plotTensor3D
ls("package:nnTensor")ls("package:nnTensor")
The input data is assumed to be non-negative matrix. GabrielNMF devides the input file into four matrices (A, B, C, and D) and perform cross validation by the prediction of A from the matrices B, C, and D.
GabrielNMF(X, J = 3, nx = 5, ny = 5, ...)GabrielNMF(X, J = 3, nx = 5, ny = 5, ...)
X |
The input matrix which has N-rows and M-columns. |
J |
The number of low-dimension (J < {N, M}). |
nx |
The number of hold-out in row-wise direction (2 < nx < N). |
ny |
The number of hold-out in row-wise direction (2 < ny < M). |
... |
Other parameters for NMF function. |
TestRecError : The reconstruction error calculated by Gabriel-style Bi-Cross Validation.
Koki Tsuyuzaki
Art B. Owen et. al., (2009). Bi-Cross-Validation of the SVD and the Nonnegative Matrix Factorization. The Annals of Applied Statistics
if(interactive()){ # Test data matdata <- toyModel(model = "NMF") # Bi-Cross-Validation BCV <- rep(0, length=5) names(BCV) <- 2:6 for(j in seq(BCV)){ print(j+1) BCV[j] <- mean(GabrielNMF(matdata, J=j+1, nx=2, ny=2)$TestRecError) } proper.rank <- as.numeric(names(BCV)[which(BCV == min(BCV))]) # NMF out <- NMF(matdata, J=proper.rank) }if(interactive()){ # Test data matdata <- toyModel(model = "NMF") # Bi-Cross-Validation BCV <- rep(0, length=5) names(BCV) <- 2:6 for(j in seq(BCV)){ print(j+1) BCV[j] <- mean(GabrielNMF(matdata, J=j+1, nx=2, ny=2)$TestRecError) } proper.rank <- as.numeric(names(BCV)[which(BCV == min(BCV))]) # NMF out <- NMF(matdata, J=proper.rank) }
The input data objects are assumed to be non-negative matrices. jNMF decompose the matrices to two low-dimensional factor matices simultaneously.
jNMF(X, M=NULL, pseudocount=.Machine$double.eps, initW=NULL, initV=NULL, initH=NULL, fixW=FALSE, fixV=FALSE, fixH=FALSE, L1_W=1e-10, L1_V=1e-10, L1_H=1e-10, L2_W=1e-10, L2_V=1e-10, L2_H=1e-10, J = 3, w=NULL, algorithm = c("Frobenius", "KL", "IS", "PLTF"), p=1, thr = 1e-10, num.iter = 100, viz = FALSE, figdir = NULL, verbose = FALSE)jNMF(X, M=NULL, pseudocount=.Machine$double.eps, initW=NULL, initV=NULL, initH=NULL, fixW=FALSE, fixV=FALSE, fixH=FALSE, L1_W=1e-10, L1_V=1e-10, L1_H=1e-10, L2_W=1e-10, L2_V=1e-10, L2_H=1e-10, J = 3, w=NULL, algorithm = c("Frobenius", "KL", "IS", "PLTF"), p=1, thr = 1e-10, num.iter = 100, viz = FALSE, figdir = NULL, verbose = FALSE)
X |
A list containing input matrices (X_k, <N*Mk>, k=1..K). |
M |
A list containing the mask matrices (X_k, <N*Mk>, k=1..K). If the input matrix has missing values, specify the element as 0 (otherwise 1). |
pseudocount |
The pseudo count to avoid zero division, when the element is zero (Default: Machine Epsilon). |
initW |
The initial values of factor matrix W, which has N-rows and J-columns (Default: NULL). |
initV |
A list containing the initial values of multiple factor matrices (V_k, <N*J>, k=1..K, Default: NULL). |
initH |
A list containing the initial values of multiple factor matrices (H_k, <Mk*J>, k=1..K, Default: NULL). |
fixW |
Whether the factor matrix W is updated in each iteration step (Default: FALSE). |
fixV |
Whether the factor matrices Vk are updated in each iteration step (Default: FALSE). |
fixH |
Whether the factor matrices Hk are updated in each iteration step (Default: FALSE). |
L1_W |
Paramter for L1 regularitation (Default: 1e-10). This also works as small positive constant to prevent division by zero, so should be set as 0. |
L1_V |
Paramter for L1 regularitation (Default: 1e-10). This also works as small positive constant to prevent division by zero, so should be set as 0. |
L1_H |
Paramter for L1 regularitation (Default: 1e-10). This also works as small positive constant to prevent division by zero, so should be set as 0. |
L2_W |
Paramter for L2 regularitation (Default: 1e-10). |
L2_V |
Paramter for L2 regularitation (Default: 1e-10). |
L2_H |
Paramter for L2 regularitation (Default: 1e-10). |
J |
Number of low-dimension (J < N, Mk). |
w |
Weight vector (Default: NULL) |
algorithm |
Divergence between X and X_bar. "Frobenius", "KL", and "IS" are available (Default: "KL"). |
p |
The parameter of Probabilistic Latent Tensor Factorization (p=0: Frobenius, p=1: KL, p=2: IS) |
thr |
When error change rate is lower than thr, the iteration is terminated (Default: 1E-10). |
num.iter |
The number of interation step (Default: 100). |
viz |
If viz == TRUE, internal reconstructed matrix can be visualized. |
figdir |
the directory for saving the figure, when viz == TRUE. |
verbose |
If verbose == TRUE, Error change rate is generated in console windos. |
W : A matrix which has N-rows and J-columns (J < N, Mk). V : A list which has multiple elements containing N-rows and J-columns (J < N, Mk). H : A list which has multiple elements containing Mk-rows and J-columns matrix (J < N, Mk). RecError : The reconstruction error between data matrix and reconstructed matrix from W and H. TrainRecError : The reconstruction error calculated by training set (observed values specified by M). TestRecError : The reconstruction error calculated by test set (missing values specified by M). RelChange : The relative change of the error.
Koki Tsuyuzaki
Liviu Badea, (2008) Extracting Gene Expression Profiles Common to Colon and Pancreatic Adenocarcinoma using Simultaneous nonnegative matrix factorization. Pacific Symposium on Biocomputing 13:279-290
Shihua Zhang, et al. (2012) Discovery of multi-dimensional modules by integrative analysis of cancer genomic data. Nucleic Acids Research 40(19), 9379-9391
Zi Yang, et al. (2016) A non-negative matrix factorization method for detecting modules in heterogeneous omics multi-modal data, Bioinformatics 32(1), 1-8
Y. Kenan Yilmaz et al., (2010) Probabilistic Latent Tensor Factorization, International Conference on Latent Variable Analysis and Signal Separation 346-353
N. Fujita et al., (2018) Biomarker discovery by integrated joint non-negative matrix factorization and pathway signature analyses, Scientific Report
matdata <- toyModel(model = "siNMF_Hard") out <- jNMF(matdata, J=2, num.iter=2)matdata <- toyModel(model = "siNMF_Hard") out <- jNMF(matdata, J=2, num.iter=2)
The output multiple mask tensors can be immediately specified as the argument M for NTF() or NTD().
kFoldMaskTensor(X, k=3, seeds=123, sym=FALSE)kFoldMaskTensor(X, k=3, seeds=123, sym=FALSE)
X |
An rTensor object. |
k |
Number of split for k-fold cross validation (Default: 3). |
seeds |
Random seed to use for set.seed() (Default: 123). |
sym |
Data will be dropped symmetrically (available only when matrix is specified, Default: FALSE). |
Koki Tsuyuzaki
tensordata <- toyModel(model = "CP") str(kFoldMaskTensor(tensordata, k=5))tensordata <- toyModel(model = "CP") str(kFoldMaskTensor(tensordata, k=5))
The input data is assumed to be non-negative matrix. NMF decompose the matrix to two low-dimensional factor matices. This function is also used as initialization step of tensor decomposition (see also NTF and NTD).
NMF(X, M=NULL, pseudocount=.Machine$double.eps, initU=NULL, initV=NULL, fixU=FALSE, fixV=FALSE, L1_U=1e-10, L1_V=1e-10, L2_U=1e-10, L2_V=1e-10, J = 3, rank.method=c("all", "ccc", "dispersion", "rss", "evar", "residuals", "sparseness.basis", "sparseness.coef", "sparseness2.basis", "sparseness2.coef", "norm.info.gain.basis", "norm.info.gain.coef", "singular", "volume", "condition"), runtime=30, algorithm = c("Frobenius", "KL", "IS", "Pearson", "Hellinger", "Neyman", "Alpha", "Beta", "ALS", "PGD", "HALS", "GCD", "Projected", "NHR", "DTPP", "Orthogonal", "OrthReg"), Alpha = 1, Beta = 2, eta = 1e-04, thr1 = 1e-10, thr2 = 1e-10, tol = 1e-04, num.iter = 100, viz = FALSE, figdir = NULL, verbose = FALSE)NMF(X, M=NULL, pseudocount=.Machine$double.eps, initU=NULL, initV=NULL, fixU=FALSE, fixV=FALSE, L1_U=1e-10, L1_V=1e-10, L2_U=1e-10, L2_V=1e-10, J = 3, rank.method=c("all", "ccc", "dispersion", "rss", "evar", "residuals", "sparseness.basis", "sparseness.coef", "sparseness2.basis", "sparseness2.coef", "norm.info.gain.basis", "norm.info.gain.coef", "singular", "volume", "condition"), runtime=30, algorithm = c("Frobenius", "KL", "IS", "Pearson", "Hellinger", "Neyman", "Alpha", "Beta", "ALS", "PGD", "HALS", "GCD", "Projected", "NHR", "DTPP", "Orthogonal", "OrthReg"), Alpha = 1, Beta = 2, eta = 1e-04, thr1 = 1e-10, thr2 = 1e-10, tol = 1e-04, num.iter = 100, viz = FALSE, figdir = NULL, verbose = FALSE)
X |
The input matrix which has N-rows and M-columns. |
M |
The mask matrix which has N-rows and M-columns. If the input matrix has missing values, specify the elements as 0 (otherwise 1). |
pseudocount |
The pseudo count to avoid zero division, when the element is zero (Default: Machine Epsilon). |
initU |
The initial values of factor matrix U, which has N-rows and J-columns (Default: NULL). |
initV |
The initial values of factor matrix V, which has M-rows and J-columns (Default: NULL). |
fixU |
Whether the factor matrix U is updated in each iteration step (Default: FALSE). |
fixV |
Whether the factor matrix V is updated in each iteration step (Default: FALSE). |
L1_U |
Paramter for L1 regularitation (Default: 1e-10). This also works as small positive constant to prevent division by zero, so should be set as 0. |
L1_V |
Paramter for L1 regularitation (Default: 1e-10). This also works as small positive constant to prevent division by zero, so should be set as 0. |
L2_U |
Paramter for L2 regularitation (Default: 1e-10). |
L2_V |
Paramter for L2 regularitation (Default: 1e-10). |
J |
The number of low-dimension (J < {N, M}). If a numerical vector is specified (e.g. 2:6), the appropriate rank is estimated. |
rank.method |
The rank estimation method (Default: "all"). Only if the J option is specified as a numerical vector longer than two, this option will be active. |
runtime |
The number of trials to estimate rank (Default: 10). |
algorithm |
NMF algorithms. "Frobenius", "KL", "IS", "Pearson", "Hellinger", "Neyman", "Alpha", "Beta", "ALS", "PGD", "HALS", "GCD", "Projected", "NHR", "DTPP", "Orthogonal", and "OrthReg" are available (Default: "Frobenius"). |
Alpha |
The parameter of Alpha-divergence. |
Beta |
The parameter of Beta-divergence. |
eta |
The stepsize for PGD algorithm (Default: 0.0001). |
thr1 |
When error change rate is lower than thr1, the iteration is terminated (Default: 1E-10). |
thr2 |
If the minus-value is generated, replaced as thr2 (Default: 1E-10). This value is used within the internal function .positive(). |
tol |
The tolerance parameter used in GCD algorithm. |
num.iter |
The number of interation step (Default: 100). |
viz |
If viz == TRUE, internal reconstructed matrix can be visualized. |
figdir |
The directory for saving the figure, when viz == TRUE. |
verbose |
If verbose == TRUE, Error change rate is generated in console window. |
U : A matrix which has N-rows and J-columns (J < {N, M}). V : A matrix which has M-rows and J-columns (J < {N, M}). J : The number of dimension (J < {N, M}). RecError : The reconstruction error between data tensor and reconstructed tensor from U and V. TrainRecError : The reconstruction error calculated by training set (observed values specified by M). TestRecError : The reconstruction error calculated by test set (missing values specified by M). RelChange : The relative change of the error. Trial : All the results of the trials to estimate the rank. Runtime : The number of the trials to estimate the rank. RankMethod : The rank estimation method.
Koki Tsuyuzaki
Andrzej CICHOCK, et. al., (2009). Nonnegative Matrix and Tensor Factorizations. John Wiley & Sons, Ltd
Keigo Kimura, (2017). A Study on Efficient Algorithms for Nonnegative Matrix/ Tensor Factorization. Hokkaido University Collection of Scholarly and Academic Papers
if(interactive()){ # Test data matdata <- toyModel(model = "NMF") # Simple usage out <- NMF(matdata, J=5) # Rank estimation mode (single method) out2 <- NMF(matdata, J=2:10, rank.method="ccc", runtime=3) plot(out2) # Rank estimation mode (all method) out3 <- NMF(matdata, J=2:10, rank.method="all", runtime=10) plot(out3) }if(interactive()){ # Test data matdata <- toyModel(model = "NMF") # Simple usage out <- NMF(matdata, J=5) # Rank estimation mode (single method) out2 <- NMF(matdata, J=2:10, rank.method="ccc", runtime=3) plot(out2) # Rank estimation mode (all method) out3 <- NMF(matdata, J=2:10, rank.method="all", runtime=10) plot(out3) }
The input data is assumed to be non-negative matrix. NMTF decompose the matrix to three low-dimensional factor matices.
NMTF(X, M=NULL, pseudocount=.Machine$double.eps, initU=NULL, initS=NULL, initV=NULL, fixU=FALSE, fixS=FALSE, fixV=FALSE, L1_U=1e-10, L1_S=1e-10, L1_V=1e-10, L2_U=1e-10, L2_S=1e-10, L2_V=1e-10, orthU=FALSE, orthV=FALSE, rank = c(3, 4), algorithm = c("Frobenius", "KL", "IS", "ALS", "PG", "COD", "Beta"), Beta = 2, root = FALSE, thr = 1e-10, num.iter = 100, viz = FALSE, figdir = NULL, verbose = FALSE)NMTF(X, M=NULL, pseudocount=.Machine$double.eps, initU=NULL, initS=NULL, initV=NULL, fixU=FALSE, fixS=FALSE, fixV=FALSE, L1_U=1e-10, L1_S=1e-10, L1_V=1e-10, L2_U=1e-10, L2_S=1e-10, L2_V=1e-10, orthU=FALSE, orthV=FALSE, rank = c(3, 4), algorithm = c("Frobenius", "KL", "IS", "ALS", "PG", "COD", "Beta"), Beta = 2, root = FALSE, thr = 1e-10, num.iter = 100, viz = FALSE, figdir = NULL, verbose = FALSE)
X |
The input matrix which has N-rows and M-columns. |
M |
The mask matrix which has N-rows and M-columns. If the input matrix has missing values, specify the elements as 0 (otherwise 1). |
pseudocount |
The pseudo count to avoid zero division, when the element is zero (Default: Machine Epsilon). |
initU |
The initial values of factor matrix U, which has N-rows and J1-columns (Default: NULL). |
initS |
The initial values of factor matrix S, which has J1-rows and J2-columns (Default: NULL). |
initV |
The initial values of factor matrix V, which has M-rows and J2-columns (Default: NULL). |
fixU |
Whether the factor matrix U is updated in each iteration step (Default: FALSE). |
fixS |
Whether the factor matrix S is updated in each iteration step (Default: FALSE). |
fixV |
Whether the factor matrix V is updated in each iteration step (Default: FALSE). |
L1_U |
Paramter for L1 regularitation (Default: 1e-10). |
L1_S |
Paramter for L1 regularitation (Default: 1e-10). |
L1_V |
Paramter for L1 regularitation (Default: 1e-10). |
L2_U |
Paramter for L2 regularitation (Default: 1e-10). |
L2_S |
Paramter for L2 regularitation (Default: 1e-10). |
L2_V |
Paramter for L2 regularitation (Default: 1e-10). |
orthU |
Whether the column vectors of matrix U are orthogonalized (Default: FALSE). |
orthV |
Whether the column vectors of matrix V are orthogonalized (Default: FALSE). |
rank |
The number of low-dimension (J1 (< N) and J2 (< M)) (Default: c(3,4)). |
algorithm |
NMTF algorithms. "Frobenius", "KL", "IS", "ALS", "PG", "COD", and "Beta" are available (Default: "Frobenius"). |
Beta |
The parameter of Beta-divergence (Default: 2, which means "Frobenius"). |
root |
Whether square root is calculed in each iteration (Default: FALSE). |
thr |
When error change rate is lower than thr, the iteration is terminated (Default: 1E-10). |
num.iter |
The number of interation step (Default: 100). |
viz |
If viz == TRUE, internal reconstructed matrix can be visualized. |
figdir |
The directory for saving the figure, when viz == TRUE. |
verbose |
If verbose == TRUE, Error change rate is generated in console window. |
U : A matrix which has N-rows and J1-columns (J1 < N). S : A matrix which has J1-rows and J2-columns. V : A matrix which has M-rows and J2-columns (J2 < M). rank : The number of low-dimension (J1 (< N) and J2 (< M)). RecError : The reconstruction error between data tensor and reconstructed tensor from U and V. TrainRecError : The reconstruction error calculated by training set (observed values specified by M). TestRecError : The reconstruction error calculated by test set (missing values specified by M). RelChange : The relative change of the error. algorithm: algorithm specified.
Koki Tsuyuzaki
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
Orthogonal Nonnegative Matrix Tri-Factorizations for Clustering, Chris Ding et. al., 12th ACM SIGKDD, 2006
if(interactive()){ # Test data matdata <- toyModel(model = "NMF") # Simple usage out <- NMTF(matdata, rank=c(4,4)) }if(interactive()){ # Test data matdata <- toyModel(model = "NMF") # Simple usage out <- NMTF(matdata, rank=c(4,4)) }
The input data is assumed to be non-negative tensor. NTD decompose the tensor to the dense core tensor (S) and low-dimensional factor matices (A).
NTD(X, M=NULL, pseudocount=.Machine$double.eps, initS=NULL, initA=NULL, fixS=FALSE, fixA=FALSE, L1_A=1e-10, L2_A=1e-10, rank = rep(3, length=length(dim(X))), modes = seq_along(dim(X)), algorithm = c("Frobenius", "KL", "IS", "Pearson", "Hellinger", "Neyman", "HALS", "Alpha", "Beta", "NMF"), init = c("NMF", "ALS", "Random"), nmf.algorithm = c("Frobenius", "KL", "IS", "Pearson", "Hellinger", "Neyman", "Alpha", "Beta", "ALS", "PGD", "HALS", "GCD", "Projected", "NHR", "DTPP", "Orthogonal", "OrthReg"), Alpha = 1, Beta = 2, thr = 1e-10, num.iter = 100, num.iter2 = 10, viz = FALSE, figdir = NULL, verbose = FALSE)NTD(X, M=NULL, pseudocount=.Machine$double.eps, initS=NULL, initA=NULL, fixS=FALSE, fixA=FALSE, L1_A=1e-10, L2_A=1e-10, rank = rep(3, length=length(dim(X))), modes = seq_along(dim(X)), algorithm = c("Frobenius", "KL", "IS", "Pearson", "Hellinger", "Neyman", "HALS", "Alpha", "Beta", "NMF"), init = c("NMF", "ALS", "Random"), nmf.algorithm = c("Frobenius", "KL", "IS", "Pearson", "Hellinger", "Neyman", "Alpha", "Beta", "ALS", "PGD", "HALS", "GCD", "Projected", "NHR", "DTPP", "Orthogonal", "OrthReg"), Alpha = 1, Beta = 2, thr = 1e-10, num.iter = 100, num.iter2 = 10, viz = FALSE, figdir = NULL, verbose = FALSE)
X |
K-order input tensor which has I_1, I_2, ..., and I_K dimensions. |
M |
K-order mask tensor which has I_1, I_2, ..., and I_K dimensions. If the mask tensor has missing values, specify the element as 0 (otherwise 1). |
pseudocount |
The pseudo count to avoid zero division, when the element is zero (Default: Machine Epsilon). |
initS |
The initial values of core tensor which has I_1, I_2, ..., and I_K dimensions (Default: NULL). |
initA |
A list containing the initial values of K factor matrices (A_k, <Ik*Jk>, k=1..K, Default: NULL). |
fixS |
Whether the core tensor S is updated in each iteration step (Default: FALSE). |
fixA |
Whether the factor matrices Ak are updated in each iteration step (Default: FALSE). |
L1_A |
Paramter for L1 regularitation (Default: 1e-10). This also works as small positive constant to prevent division by zero, so should be set as 0. |
L2_A |
Paramter for L2 regularitation (Default: 1e-10). |
rank |
The number of low-dimension in each mode (Default: 3 for each mode). |
modes |
The vector of the modes on which to perform the decomposition (Default: 1:K <all modes>). |
algorithm |
NTD algorithms. "Frobenius", "KL", "IS", "Pearson", "Hellinger", "Neyman", "HALS", "Alpha", "Beta", "NMF" are available (Default: "Frobenius"). |
nmf.algorithm |
NMF algorithms, when the algorithm is "NMF". "Frobenius", "KL", "IS", "Pearson", "Hellinger", "Neyman", "Alpha", "Beta", "ALS", "PGD", "HALS", "GCD", "Projected", "NHR", "DTPP", "Orthogonal", and "OrthReg" are available (Default: "Frobenius"). |
init |
The initialization algorithms. "NMF", "ALS", and "Random" are available (Default: "NMF"). |
Alpha |
The parameter of Alpha-divergence. |
Beta |
The parameter of Beta-divergence. |
thr |
When error change rate is lower than thr1, the iteration is terminated (Default: 1E-10). |
num.iter |
The number of interation step (Default: 100). |
num.iter2 |
The number of NMF interation step, when the algorithm is "NMF" (Default: 10). |
viz |
If viz == TRUE, internal reconstructed tensor can be visualized. |
figdir |
the directory for saving the figure, when viz == TRUE (Default: NULL). |
verbose |
If verbose == TRUE, Error change rate is generated in console windos. |
S : K-order tensor object, which is defined as S4 class of rTensor package. A : A list containing K factor matrices. RecError : The reconstruction error between data tensor and reconstructed tensor from S and A. TrainRecError : The reconstruction error calculated by training set (observed values specified by M). TestRecError : The reconstruction error calculated by test set (missing values specified by M). RelChange : The relative change of the error.
Koki Tsuyuzaki
Yong-Deok Kim et. al., (2007). Nonnegative Tucker Decomposition. IEEE Conference on Computer Vision and Pattern Recognition
Yong-Deok Kim et. al., (2008). Nonneegative Tucker Decomposition With Alpha-Divergence. IEEE International Conference on Acoustics, Speech and Signal Processing
Anh Huy Phan, (2008). Fast and efficient algorithms for nonnegative Tucker decomposition. Advances in Neural Networks - ISNN2008
Anh Hyu Phan et. al. (2011). Extended HALS algorithm for nonnegative Tucker decomposition and its applications for multiway analysis and classification. Neurocomputing
tensordata <- toyModel(model = "Tucker") out <- NTD(tensordata, rank=c(2,2,2), algorithm="Frobenius", init="Random", num.iter=2)tensordata <- toyModel(model = "Tucker") out <- NTD(tensordata, rank=c(2,2,2), algorithm="Frobenius", init="Random", num.iter=2)
The input data is assumed to be non-negative tensor. NTF decompose the tensor to the diagonal core tensor (S) and low-dimensional factor matices (A).
NTF(X, M=NULL, pseudocount=.Machine$double.eps, initA=NULL, fixA=FALSE, L1_A=1e-10, L2_A=1e-10, rank = 3, algorithm = c("Frobenius", "KL", "IS", "Pearson", "Hellinger", "Neyman", "HALS", "Alpha-HALS", "Beta-HALS", "Alpha", "Beta"), init = c("NMF", "ABS-SVD", "ALS", "Random"), Alpha = 1, Beta = 2, thr = 1e-10, num.iter = 100, viz = FALSE, figdir = NULL, verbose = FALSE)NTF(X, M=NULL, pseudocount=.Machine$double.eps, initA=NULL, fixA=FALSE, L1_A=1e-10, L2_A=1e-10, rank = 3, algorithm = c("Frobenius", "KL", "IS", "Pearson", "Hellinger", "Neyman", "HALS", "Alpha-HALS", "Beta-HALS", "Alpha", "Beta"), init = c("NMF", "ABS-SVD", "ALS", "Random"), Alpha = 1, Beta = 2, thr = 1e-10, num.iter = 100, viz = FALSE, figdir = NULL, verbose = FALSE)
X |
K-order input tensor which has I_1, I_2, ..., and I_K dimensions. |
M |
K-order mask tensor which has I_1, I_2, ..., and I_K dimensions. If the mask tensor has missing values, specify the element as 0 (otherwise 1). |
pseudocount |
The pseudo count to avoid zero division, when the element is zero (Default: Machine Epsilon). |
initA |
A list containing the initial values of K factor matrices (A_k, <Ik*Jk>, k=1..K, Default: NULL). |
fixA |
Whether the factor matrices Ak are updated in each iteration step (Default: FALSE). |
L1_A |
Paramter for L1 regularitation (Default: 1e-10). This also works as small positive constant to prevent division by zero, so should be set as 0. |
L2_A |
Paramter for L2 regularitation (Default: 1e-10). |
rank |
The number of low-dimension in each mode (Default: 3). |
algorithm |
NTF algorithms. "Frobenius", "KL", "IS", "Pearson", "Hellinger", "Neyman", "HALS", "Alpha-HALS", "Beta-HALS", "Alpha", and "Beta" are available (Default: "Frobenius"). |
init |
The initialization algorithms. "NMF", "ABS-SVD", "ALS", and "Random" are available (Default: "NMF"). |
Alpha |
The parameter of Alpha-divergence. |
Beta |
The parameter of Beta-divergence. |
thr |
When error change rate is lower than thr1, the iteration is terminated (Default: 1E-10). |
num.iter |
The number of interation step (Default: 100). |
viz |
If viz == TRUE, internal reconstructed tensor can be visualized. |
figdir |
the directory for saving the figure, when viz == TRUE (Default: NULL). |
verbose |
If verbose == TRUE, Error change rate is generated in console windos. |
S : K-order tensor object, which is defined as S4 class of rTensor package. A : A list containing K factor matrices. RecError : The reconstruction error between data tensor and reconstructed tensor from S and A. TrainRecError : The reconstruction error calculated by training set (observed values specified by M). TestRecError : The reconstruction error calculated by test set (missing values specified by M). RelChange : The relative change of the error.
Koki Tsuyuzaki
Andrzej CICHOCKI et. al., (2007). Non-negative Tensor Factorization using Alpha and Beta Divergence. IEEE ICASSP 2007
Anh Huy PHAN et. al., (2008). Multi-way Nonnegative Tensor Factorization Using Fast Hierarchical Alternating Least Squares Algorithm (HALS). NOLTA2008
Andrzej CICHOCKI et. al., (2008). Fast Local Algorithms for Large Scale Nonnegative Matrix and Tensor Factorizations. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
tensordata <- toyModel(model = "CP") out <- NTF(tensordata, rank=3, algorithm="Beta-HALS", num.iter=2)tensordata <- toyModel(model = "CP") out <- NTF(tensordata, rank=3, algorithm="Beta-HALS", num.iter=2)
Only if J is specified as a vector longer than 1, this function will be active.
Koki Tsuyuzaki
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
methods(class = "NMF")methods(class = "NMF")
Combined with recTensor function and the result of NTF or NTD, the reconstructed tensor structure can be visullized.
plotTensor2D(X = NULL, method=c("sd", "mad"), sign=c("positive", "negative", "both"), thr=2)plotTensor2D(X = NULL, method=c("sd", "mad"), sign=c("positive", "negative", "both"), thr=2)
X |
Matrix object. |
method |
Cutoff method to focus on large/small value in the tensor data (Default: "sd"). |
sign |
Direction to cutoff the large/small value in the tensor data (Default: "positive"). |
thr |
Threshold of cutoff method (Default: 2). |
Koki Tsuyuzaki
tensordata <- toyModel(model = "CP") out <- NTF(tensordata, rank=3, num.iter=2) tmp <- tempdir() png(filename=paste0(tmp, "/NTF.png")) plotTensor2D(out$A[[1]]) dev.off()tensordata <- toyModel(model = "CP") out <- NTF(tensordata, rank=3, num.iter=2) tmp <- tempdir() png(filename=paste0(tmp, "/NTF.png")) plotTensor2D(out$A[[1]]) dev.off()
Combined with recTensor function and the result of NTF or NTD, the reconstructed tensor structure can be visullized.
plotTensor3D(X = NULL, method=c("sd", "mad"), sign=c("positive", "negative", "both"), thr=2)plotTensor3D(X = NULL, method=c("sd", "mad"), sign=c("positive", "negative", "both"), thr=2)
X |
Tensor object, which is defined as S4 class of rTensor package. |
method |
Cutoff method to focus on large/small value in the tensor data (Default: "sd"). |
sign |
Direction to cutoff the large/small value in the tensor data (Default: "positive"). |
thr |
Threshold of cutoff method (Default: 2). |
Koki Tsuyuzaki
tensordata <- toyModel(model = "CP") out <- NTF(tensordata, rank=3, algorithm="Beta-HALS", num.iter=2) tmp <- tempdir() png(filename=paste0(tmp, "/NTF.png")) plotTensor3D(recTensor(out$S, out$A)) dev.off()tensordata <- toyModel(model = "CP") out <- NTF(tensordata, rank=3, algorithm="Beta-HALS", num.iter=2) tmp <- tempdir() png(filename=paste0(tmp, "/NTF.png")) plotTensor3D(recTensor(out$S, out$A)) dev.off()
Combined with plotTensor3D function and the result of NTF or NTD, the reconstructed tesor structure can be visullized.
recTensor(S = NULL, A = NULL, idx = seq_along(dim(S)), reverse = FALSE)recTensor(S = NULL, A = NULL, idx = seq_along(dim(S)), reverse = FALSE)
S |
K-order tensor object, which is defined as S4 class of rTensor package. |
A |
A list containing K factor matrices. |
idx |
The direction of mode-n muliplication (Default: 1:K). For example idx=1 is defined. S x_1 A is calculated (x_1 : mode-1 multiplication). |
reverse |
If reverse = TRUE, t(A[[n]]) is multiplicated to S (Default: FALSE). |
Tensor object, which is defined as S4 class of rTensor package.
Koki Tsuyuzaki
tensordata <- toyModel(model = "CP") out <- NTF(tensordata, rank=3, algorithm="Beta-HALS", num.iter=2) rec <- recTensor(out$S, out$A)tensordata <- toyModel(model = "CP") out <- NTF(tensordata, rank=3, algorithm="Beta-HALS", num.iter=2) rec <- recTensor(out$S, out$A)
The input data objects are assumed to be non-negative matrices. siNMF decompose the matrices to two low-dimensional factor matices simultaneously.
siNMF(X, M=NULL, pseudocount=.Machine$double.eps, initW=NULL, initH=NULL, fixW=FALSE, fixH=FALSE, L1_W=1e-10, L1_H=1e-10, L2_W=1e-10, L2_H=1e-10, J = 3, w=NULL, algorithm = c("Frobenius", "KL", "IS", "PLTF"), p=1, thr = 1e-10, num.iter = 100, viz = FALSE, figdir = NULL, verbose = FALSE)siNMF(X, M=NULL, pseudocount=.Machine$double.eps, initW=NULL, initH=NULL, fixW=FALSE, fixH=FALSE, L1_W=1e-10, L1_H=1e-10, L2_W=1e-10, L2_H=1e-10, J = 3, w=NULL, algorithm = c("Frobenius", "KL", "IS", "PLTF"), p=1, thr = 1e-10, num.iter = 100, viz = FALSE, figdir = NULL, verbose = FALSE)
X |
A list containing the input matrices (X_k, <N*Mk>, k=1..K). |
M |
A list containing the mask matrices (X_k, <N*Mk>, k=1..K). If the input matrix has missing values, specify the element as 0 (otherwise 1). |
pseudocount |
The pseudo count to avoid zero division, when the element is zero (Default: Machine Epsilon). |
initW |
The initial values of factor matrix W, which has N-rows and J-columns (Default: NULL). |
initH |
A list containing the initial values of multiple factor matrices (H_k, <Mk*J>, k=1..K, Default: NULL). |
fixW |
Whether the factor matrix W is updated in each iteration step (Default: FALSE). |
fixH |
Whether the factor matrices Hk are updated in each iteration step (Default: FALSE). |
L1_W |
Paramter for L1 regularitation (Default: 1e-10). This also works as small positive constant to prevent division by zero, so should be set as 0. |
L1_H |
Paramter for L1 regularitation (Default: 1e-10). This also works as small positive constant to prevent division by zero, so should be set as 0. |
L2_W |
Paramter for L2 regularitation (Default: 1e-10). |
L2_H |
Paramter for L2 regularitation (Default: 1e-10). |
J |
Number of low-dimension (J < N, Mk). |
w |
Weight vector (Default: NULL) |
algorithm |
Divergence between X and X_bar. "Frobenius", "KL", and "IS" are available (Default: "KL"). |
p |
The parameter of Probabilistic Latent Tensor Factorization (p=0: Frobenius, p=1: KL, p=2: IS) |
thr |
When error change rate is lower than thr, the iteration is terminated (Default: 1E-10). |
num.iter |
The number of interation step (Default: 100). |
viz |
If viz == TRUE, internal reconstructed matrix can be visualized. |
figdir |
the directory for saving the figure, when viz == TRUE. |
verbose |
If verbose == TRUE, Error change rate is generated in console windos. |
W : A matrix which has N-rows and J-columns (J < N, Mk). H : A list which has multiple elements containing Mk-rows and J-columns matrix (J < N, Mk). RecError : The reconstruction error between data matrix and reconstructed matrix from W and H. TrainRecError : The reconstruction error calculated by training set (observed values specified by M). TestRecError : The reconstruction error calculated by test set (missing values specified by M). RelChange : The relative change of the error.
Koki Tsuyuzaki
Liviu Badea, (2008) Extracting Gene Expression Profiles Common to Colon and Pancreatic Adenocarcinoma using Simultaneous nonnegative matrix factorization. Pacific Symposium on Biocomputing 13:279-290
Shihua Zhang, et al. (2012) Discovery of multi-dimensional modules by integrative analysis of cancer genomic data. Nucleic Acids Research 40(19), 9379-9391
Zi Yang, et al. (2016) A non-negative matrix factorization method for detecting modules in heterogeneous omics multi-modal data, Bioinformatics 32(1), 1-8
Y. Kenan Yilmaz et al., (2010) Probabilistic Latent Tensor Factorization, International Conference on Latent Variable Analysis and Signal Separation 346-353
N. Fujita et al., (2018) Biomarker discovery by integrated joint non-negative matrix factorization and pathway signature analyses, Scientific Report
matdata <- toyModel(model = "siNMF_Easy") out <- siNMF(matdata, J=2, num.iter=2)matdata <- toyModel(model = "siNMF_Easy") out <- siNMF(matdata, J=2, num.iter=2)
The data is used for confirming the algorithm are properly working.
toyModel(model = "CP", seeds=123)toyModel(model = "CP", seeds=123)
model |
Single character string is specified. "NMF", "CP", and "Tucker" are available (Default: "CP"). |
seeds |
Random number for setting set.seeds in the function (Default: 123). |
If model is specified as "NMF", a matrix is generated. Otherwise, a tensor is generated.
Koki Tsuyuzaki
matdata <- toyModel(model = "NMF", seeds=123) tensordata1 <- toyModel(model = "CP", seeds=123) tensordata2 <- toyModel(model = "Tucker", seeds=123)matdata <- toyModel(model = "NMF", seeds=123) tensordata1 <- toyModel(model = "CP", seeds=123) tensordata2 <- toyModel(model = "Tucker", seeds=123)