Package 'dcTensor' reference manual

Title:	Discrete Matrix/Tensor Decomposition
Description:	Semi-Binary and Semi-Ternary Matrix Decomposition are performed based on Non-negative Matrix Factorization (NMF) and Singular Value Decomposition (SVD). For the details of the methods, see the reference section of GitHub README.md <https://github.com/rikenbit/dcTensor>.
Authors:	Koki Tsuyuzaki [aut, cre]
Maintainer:	Koki Tsuyuzaki <[email protected]>
License:	MIT + file LICENSE
Version:	1.3.0
Built:	2025-02-08 02:51:48 UTC
Source:	https://github.com/rikenbit/dctensor

Discrete Matrix/Tensor Decomposition

Description

Semi-Binary and Semi-Ternary Matrix Decomposition are performed based on Non-negative Matrix Factorization (NMF) and Singular Value Decomposition (SVD). For the details of the methods, see the reference section of GitHub README.md <https://github.com/rikenbit/dcTensor>.

Details

The DESCRIPTION file:

Package:	dcTensor
Type:	Package
Title:	Discrete Matrix/Tensor Decomposition
Version:	1.3.0
Authors@R:	c(person("Koki", "Tsuyuzaki", role = c("aut", "cre"), email = "[email protected]"))
Depends:	R (>= 3.4.0)
Imports:	methods, MASS, fields, rTensor, nnTensor
Suggests:	knitr, rmarkdown, testthat
Description:	Semi-Binary and Semi-Ternary Matrix Decomposition are performed based on Non-negative Matrix Factorization (NMF) and Singular Value Decomposition (SVD). For the details of the methods, see the reference section of GitHub README.md <https://github.com/rikenbit/dcTensor>.
License:	MIT + file LICENSE
URL:	https://github.com/rikenbit/dcTensor
VignetteBuilder:	knitr
Repository:	https://rikenbit.r-universe.dev
RemoteUrl:	https://github.com/rikenbit/dctensor
RemoteRef:	HEAD
RemoteSha:	72a6c8065625d644a14f004aacbc5d745d627290
Author:	Koki Tsuyuzaki [aut, cre]
Maintainer:	Koki Tsuyuzaki <[email protected]>

Index of help topics:

dNMF                    Discretized Non-negative Matrix Factorization
                        Algorithms (dNMF)
dNMTF                   Discretized Non-negative Matrix
                        Tri-Factorization Algorithms (dNMTF)
dNTD                    Discretized Non-negative Tucker Decomposition
                        Algorithms (dNTD)
dNTF                    Discretized Non-negative CP Decomposition
                        Algorithms (dNTF)
dPLS                    Discretized Partial Least Squares (dPLS)
dSVD                    Discretized Singular Value Decomposition (dSVD)
dcTensor-package        Discrete Matrix/Tensor Decomposition
djNMF                   Discretized Joint Non-negative Matrix
                        Factorization Algorithms (djNMF)
dsiNMF                  Discretized Simultaneous Non-negative Matrix
                        Factorization Algorithms (dsiNMF)
toyModel                Toy model data for using dNMF, dSVD, dsiNMF,
                        djNMF, dPLS, dNTF, and dNTD

Author(s)

Koki Tsuyuzaki [aut, cre]

Maintainer: Koki Tsuyuzaki <[email protected]>

References

Z. Zhang, T. Li, C. Ding and X. Zhang, (2007). Binary Matrix Factorization with Applications, Seventh IEEE International Conference on Data Mining (ICDM 2007), 391-400

Examples

ls("package:dcTensor")
ls("package:dcTensor")

Discretized Joint Non-negative Matrix Factorization Algorithms (djNMF)

Description

This function is the discretized version of nnTensor::jNMF. The input data objects are assumed to be a list containing multiple non-negative matrices (X_1, X_2, ..., X_K), and decomposed to multiple matrix products ((W + V_1) H_1', (W + V_2) H_2', ..., (W + V_K) H_K'), where W is common across all the data matrices but each V_k or H_k (k=1..K) is specific in each X_k. Unlike regular jNMF, in djNMF, W, V_k, and H_k are estimated by adding binary regularization so that the values are 0 or 1 as much as possible. Likewise, W, V_k, and H_k are estimated by adding ternary regularization so that the values are 0, 1, or 2 as much as possible.

Usage

djNMF(X, M=NULL, pseudocount=.Machine$double.eps,
    initW=NULL, initV=NULL, initH=NULL,
    fixW=FALSE, fixV=FALSE, fixH=FALSE,
    Bin_W=1e-10, Bin_V=rep(1e-10, length=length(X)), Bin_H=rep(1e-10, length=length(X)),
    Ter_W=1e-10, Ter_V=rep(1e-10, length=length(X)), Ter_H=rep(1e-10, length=length(X)),
    L1_W=1e-10, L1_V=rep(1e-10, length=length(X)), L1_H=rep(1e-10, length=length(X)),
    L2_W=1e-10, L2_V=rep(1e-10, length=length(X)), L2_H=rep(1e-10, length=length(X)),
    J = 3, w=NULL, algorithm = c("Frobenius", "KL", "IS", "PLTF"), p=1,
    thr = 1e-10, num.iter = 100,
    viz = FALSE, figdir = NULL, verbose = FALSE)
djNMF(X, M=NULL, pseudocount=.Machine$double.eps,
    initW=NULL, initV=NULL, initH=NULL,
    fixW=FALSE, fixV=FALSE, fixH=FALSE,
    Bin_W=1e-10, Bin_V=rep(1e-10, length=length(X)), Bin_H=rep(1e-10, length=length(X)),
    Ter_W=1e-10, Ter_V=rep(1e-10, length=length(X)), Ter_H=rep(1e-10, length=length(X)),
    L1_W=1e-10, L1_V=rep(1e-10, length=length(X)), L1_H=rep(1e-10, length=length(X)),
    L2_W=1e-10, L2_V=rep(1e-10, length=length(X)), L2_H=rep(1e-10, length=length(X)),
    J = 3, w=NULL, algorithm = c("Frobenius", "KL", "IS", "PLTF"), p=1,
    thr = 1e-10, num.iter = 100,
    viz = FALSE, figdir = NULL, verbose = FALSE)

Arguments

`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).
`Bin_W`	Paramter for binary (0,1) regularitation (Default: 1e-10).
`Bin_V`	A K-length vector containing the paramters for binary (0,1) regularitation (Default: rep(1e-10, length=length(dim(X)))).
`Bin_H`	A K-length vector containing the paramters for binary (0,1) regularitation (Default: rep(1e-10, length=length(dim(X)))).
`Ter_W`	Paramter for terary (0,1,2) regularitation (Default: 1e-10).
`Ter_V`	A K-length vector containing the paramters for terary (0,1,2) regularitation (Default: rep(1e-10, length=length(dim(X)))).
`Ter_H`	A K-length vector containing the paramters for terary (0,1,2) regularitation (Default: rep(1e-10, length=length(dim(X)))).
`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`	A K-length vector containing the paramters for L1 regularitation (Default: rep(1e-10, length=length(dim(X)))). This also works as small positive constant to prevent division by zero, so should be set as 0.
`L1_H`	A K-length vector containing the paramters for L1 regularitation (Default: rep(1e-10, length=length(dim(X)))). 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`	A K-length vector containing the paramters for L2 regularitation (Default: rep(1e-10, length=length(dim(X)))).
`L2_H`	A K-length vector containing the paramters for L2 regularitation (Default: rep(1e-10, length=length(dim(X)))).
`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.

Value

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.

Author(s)

Koki Tsuyuzaki

References

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

Examples

matdata <- toyModel(model = "dsiNMF_Hard")
out <- djNMF(matdata, J=2, num.iter=2)
matdata <- toyModel(model = "dsiNMF_Hard")
out <- djNMF(matdata, J=2, num.iter=2)

Discretized Non-negative Matrix Factorization Algorithms (dNMF)

Description

This function is the discretized version of nnTensor::NMF. The input data X is assumed to be a non-negative matrix and decomposed to a matrix product U V'. Unlike regular NMF, in dNMF, U and V are estimated by adding binary regularization so that the values are 0 or 1 as much as possible. Likewise, U and V are estimated by adding ternary regularization so that the values are 0, 1, or 2 as much as possible.

Usage

dNMF(X, M=NULL, pseudocount=.Machine$double.eps,
    initU=NULL, initV=NULL, fixU=FALSE, fixV=FALSE,
    Bin_U=1e-10, Bin_V=1e-10, Ter_U=1e-10, Ter_V=1e-10,
    L1_U=1e-10, L1_V=1e-10, L2_U=1e-10, L2_V=1e-10, J = 3,
    algorithm = c("Frobenius", "KL", "IS", "Beta"), Beta = 2,
    thr = 1e-10, num.iter = 100,
    viz = FALSE, figdir = NULL, verbose = FALSE)
dNMF(X, M=NULL, pseudocount=.Machine$double.eps,
    initU=NULL, initV=NULL, fixU=FALSE, fixV=FALSE,
    Bin_U=1e-10, Bin_V=1e-10, Ter_U=1e-10, Ter_V=1e-10,
    L1_U=1e-10, L1_V=1e-10, L2_U=1e-10, L2_V=1e-10, J = 3,
    algorithm = c("Frobenius", "KL", "IS", "Beta"), Beta = 2,
    thr = 1e-10, num.iter = 100,
    viz = FALSE, figdir = NULL, verbose = FALSE)

Arguments

`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 element 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).
`Bin_U`	Paramter for binary (0,1) regularitation (Default: 1e-10).
`Bin_V`	Paramter for binary (0,1) regularitation (Default: 1e-10).
`Ter_U`	Paramter for terary (0,1,2) regularitation (Default: 1e-10).
`Ter_V`	Paramter for terary (0,1,2) regularitation (Default: 1e-10).
`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}, Default: 3)
`algorithm`	dNMF algorithms. "Frobenius", "KL", "IS", and "Beta" are available (Default: "Frobenius").
`Beta`	The parameter of Beta-divergence.
`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.

Value

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}). 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.

Author(s)

Koki Tsuyuzaki

References

Z. Zhang, T. Li, C. Ding and X. Zhang, (2007). Binary Matrix Factorization with Applications, Seventh IEEE International Conference on Data Mining (ICDM 2007), 391-400

Examples

# Test data
matdata <- toyModel(model = "dNMF")

# Simple usage
out <- dNMF(matdata, J=5)
# Test data
matdata <- toyModel(model = "dNMF")

# Simple usage
out <- dNMF(matdata, J=5)

Discretized Non-negative Matrix Tri-Factorization Algorithms (dNMTF)

Description

This function is the discretized version of nnTensor::NMTF. The input data is assumed to be non-negative matrix. dNMTF decompose the matrix to three low-dimensional factor matices.

Usage

dNMTF(X, M=NULL, pseudocount=.Machine$double.eps,
    initU=NULL, initS=NULL, initV=NULL,
    fixU=FALSE, fixS=FALSE, fixV=FALSE,
    Bin_U=1e-10, Bin_S=1e-10, Bin_V=1e-10,
    Ter_U=1e-10, Ter_S=1e-10, Ter_V=1e-10,
    L1_U=1e-10, L1_S=1e-10, L1_V=1e-10,
    L2_U=1e-10, L2_S=1e-10, L2_V=1e-10,
    rank = c(3, 4),
    algorithm = c("Frobenius", "KL", "IS", "Beta"),
    Beta = 2, root = FALSE, thr = 1e-10, num.iter = 100,
    viz = FALSE, figdir = NULL, verbose = FALSE)
dNMTF(X, M=NULL, pseudocount=.Machine$double.eps,
    initU=NULL, initS=NULL, initV=NULL,
    fixU=FALSE, fixS=FALSE, fixV=FALSE,
    Bin_U=1e-10, Bin_S=1e-10, Bin_V=1e-10,
    Ter_U=1e-10, Ter_S=1e-10, Ter_V=1e-10,
    L1_U=1e-10, L1_S=1e-10, L1_V=1e-10,
    L2_U=1e-10, L2_S=1e-10, L2_V=1e-10,
    rank = c(3, 4),
    algorithm = c("Frobenius", "KL", "IS", "Beta"),
    Beta = 2, root = FALSE, thr = 1e-10, num.iter = 100,
    viz = FALSE, figdir = NULL, verbose = FALSE)

Arguments

`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).
`Bin_U`	Paramter for binary (0,1) regularitation (Default: 1e-10).
`Bin_S`	Paramter for binary (0,1) regularitation (Default: 1e-10).
`Bin_V`	Paramter for binary (0,1) regularitation (Default: 1e-10).
`Ter_U`	Paramter for terary (0,1,2) regularitation (Default: 1e-10).
`Ter_S`	Paramter for terary (0,1,2) regularitation (Default: 1e-10).
`Ter_V`	Paramter for terary (0,1,2) regularitation (Default: 1e-10).
`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).
`rank`	The number of low-dimension (J1 (< N) and J2 (< M)) (Default: c(3,4)).
`algorithm`	dNMTF algorithms. "Frobenius", "KL", "IS", 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.

Value

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.

Author(s)

Koki Tsuyuzaki

References

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

Examples

  if(interactive()){
    # Test data
    matdata <- toyModel(model = "dNMF")

    # Simple usage
    out <- dNMTF(matdata, rank=c(4,4))
  }
if(interactive()){
    # Test data
    matdata <- toyModel(model = "dNMF")

    # Simple usage
    out <- dNMTF(matdata, rank=c(4,4))
  }

Discretized Non-negative Tucker Decomposition Algorithms (dNTD)

Description

This function is the discretized version of nnTensor::NTD. The input data X is assumed to be a non-negative tensor and decomposed to a product of a dense core tensor (S) and low-dimensional factor matrices (A_k, k=1..K). Unlike regular NTD, in dNTD, each A_k is estimated by adding binary regularization so that the values are 0 or 1 as much as possible. Likewise, each A_k are estimated by adding ternary regularization so that the values are 0, 1, or 2 as much as possible.

Usage

dNTD(X, M=NULL, pseudocount=.Machine$double.eps,
    initS=NULL, initA=NULL, fixS=FALSE, fixA=FALSE,
    Bin_A=rep(1e-10, length=length(dim(X))),
    Ter_A=rep(1e-10, length=length(dim(X))),
    L1_A=rep(1e-10, length=length(dim(X))),
    L2_A=rep(1e-10, length=length(dim(X))),
    rank = rep(3, length=length(dim(X))),
    modes = seq_along(dim(X)),
    algorithm = c("Frobenius", "KL", "IS", "Beta"),
    init = c("dNMF", "Random"),
    Beta = 2, thr = 1e-10, num.iter = 100,
    viz = FALSE,
    figdir = NULL, verbose = FALSE)
dNTD(X, M=NULL, pseudocount=.Machine$double.eps,
    initS=NULL, initA=NULL, fixS=FALSE, fixA=FALSE,
    Bin_A=rep(1e-10, length=length(dim(X))),
    Ter_A=rep(1e-10, length=length(dim(X))),
    L1_A=rep(1e-10, length=length(dim(X))),
    L2_A=rep(1e-10, length=length(dim(X))),
    rank = rep(3, length=length(dim(X))),
    modes = seq_along(dim(X)),
    algorithm = c("Frobenius", "KL", "IS", "Beta"),
    init = c("dNMF", "Random"),
    Beta = 2, thr = 1e-10, num.iter = 100,
    viz = FALSE,
    figdir = NULL, verbose = FALSE)

Arguments

`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).
`Bin_A`	A K-length vector containing the paramters for binary (0,1) regularitation (Default: rep(1e-10, length=length(dim(X)))).
`Ter_A`	A K-length vector containing the paramters for terary (0,1,2) regularitation (Default: rep(1e-10, length=length(dim(X)))).
`L1_A`	A K-length vector containing the paramters for L1 regularitation (Default: rep(1e-10, length=length(dim(X)))). This also works as small positive constant to prevent division by zero, so should be set as 0.
`L2_A`	A K-length vector containing the paramters for L2 regularitation (Default: rep(1e-10, length=length(dim(X)))).
`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`	dNTD algorithms. "Frobenius", "KL", "IS", and "Beta" are available (Default: "Frobenius").
`init`	The initialization algorithms. "NMF", "ALS", and "Random" are available (Default: "NMF").
`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.

Value

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.

Author(s)

Koki Tsuyuzaki

References

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

Examples

tensordata <- toyModel(model = "dNTD")
out <- dNTD(tensordata, rank=c(2,2,2), algorithm="Frobenius",
  init="Random", num.iter=2)
tensordata <- toyModel(model = "dNTD")
out <- dNTD(tensordata, rank=c(2,2,2), algorithm="Frobenius",
  init="Random", num.iter=2)

Discretized Non-negative CP Decomposition Algorithms (dNTF)

Description

This function is the discretized version of nnTensor::NTF. The input data X is assumed to be a non-negative tensor and decomposed to a product of a diagonal core tensor (S) and low-dimensional factor matrices (A_k, k=1..K). Unlike regular NTF, in dNTF, each A_k is estimated by adding binary regularization so that the values are 0 or 1 as much as possible. Likewise, each A_k are estimated by adding ternary regularization so that the values are 0, 1, or 2 as much as possible.

Usage

dNTF(X, M=NULL, pseudocount=.Machine$double.eps,
    initA=NULL, fixA=FALSE,
    Bin_A=rep(1e-10, length=length(dim(X))),
    Ter_A=rep(1e-10, length=length(dim(X))),
    L1_A=rep(1e-10, length=length(dim(X))),
    L2_A=rep(1e-10, length=length(dim(X))),
    rank = 3,
    algorithm = c("Frobenius", "KL", "IS", "Beta"),
    init = c("dNMF", "Random"),
    Beta = 2, thr = 1e-10, num.iter = 100, viz = FALSE, figdir = NULL,
    verbose = FALSE)
dNTF(X, M=NULL, pseudocount=.Machine$double.eps,
    initA=NULL, fixA=FALSE,
    Bin_A=rep(1e-10, length=length(dim(X))),
    Ter_A=rep(1e-10, length=length(dim(X))),
    L1_A=rep(1e-10, length=length(dim(X))),
    L2_A=rep(1e-10, length=length(dim(X))),
    rank = 3,
    algorithm = c("Frobenius", "KL", "IS", "Beta"),
    init = c("dNMF", "Random"),
    Beta = 2, thr = 1e-10, num.iter = 100, viz = FALSE, figdir = NULL,
    verbose = FALSE)

Arguments

`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).
`Bin_A`	A K-length vector containing the paramters for binary (0,1) regularitation (Default: rep(1e-10, length=length(dim(X)))).
`Ter_A`	A K-length vector containing the paramters for terary (0,1,2) regularitation (Default: rep(1e-10, length=length(dim(X)))).
`L1_A`	A K-length vector containing the paramters for L1 regularitation (Default: rep(1e-10, length=length(dim(X)))). This also works as small positive constant to prevent division by zero, so should be set as 0.
`L2_A`	A K-length vector containing the paramters for L2 regularitation (Default: rep(1e-10, length=length(dim(X)))).
`rank`	The number of low-dimension in each mode (Default: 3).
`algorithm`	dNTF algorithms. "Frobenius", "KL", "IS", and "Beta" are available (Default: "Frobenius").
`init`	The initialization algorithms. "dNMF", and "Random" are available (Default: "dNMF").
`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.

Value

Author(s)

Koki Tsuyuzaki

References

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

Examples

tensordata <- toyModel(model = "dNTF")
out <- dNTF(tensordata, rank=3, num.iter=2)
tensordata <- toyModel(model = "dNTF")
out <- dNTF(tensordata, rank=3, num.iter=2)

Discretized Partial Least Squares (dPLS)

Description

This function is the discretized version of PLS. The input data objects are assumed to be a list containing multiple matrices (X_1, X_2, ..., X_K), and decomposed to multiple matrix products (U_1 V_1', U_2 V_2', ..., U_K V_K'), where each U_k and V_k (k=1..K) is specific in each X_k. Unlike regular PLS, in dPLS, U_k and V_k are estimated by adding ternary regularization so that the values are -1, 0, or 1 as much as possible.

Usage

dPLS(X, M=NULL, pseudocount=.Machine$double.eps,
    initV=NULL, fixV=FALSE, Ter_V=1e-10,
    L1_V=1e-10, L2_V=1e-10, eta=1e+10, J = 3,
    thr = 1e-10, num.iter = 100,
    viz = FALSE, figdir = NULL, verbose = FALSE)
dPLS(X, M=NULL, pseudocount=.Machine$double.eps,
    initV=NULL, fixV=FALSE, Ter_V=1e-10,
    L1_V=1e-10, L2_V=1e-10, eta=1e+10, J = 3,
    thr = 1e-10, num.iter = 100,
    viz = FALSE, figdir = NULL, verbose = FALSE)

Arguments

`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 element as 0 (otherwise 1).
`pseudocount`	The pseudo count to avoid zero division, when the element is zero (Default: Machine Epsilon).
`initV`	The initial values of factor matrix V, which has M-rows and J-columns (Default: NULL).
`fixV`	Whether the factor matrix V is updated in each iteration step (Default: FALSE).
`Ter_V`	Paramter for terary (-1,0,1) regularitation (Default: 1e-10).
`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_V`	Paramter for L2 regularitation (Default: 1e-10).
`eta`	Stepsize of gradient descent algorithm (Default: 1e+10).
`J`	The number of low-dimension (J < {N, M}, Default: 3)
`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.

Value

Author(s)

Koki Tsuyuzaki

Examples

# Test data
matdata <- toyModel(model = "dPLS_Easy")

# Simple usage
out <- dPLS(matdata, J=2, num.iter=2)
# Test data
matdata <- toyModel(model = "dPLS_Easy")

# Simple usage
out <- dPLS(matdata, J=2, num.iter=2)

Discretized Simultaneous Non-negative Matrix Factorization Algorithms (dsiNMF)

Description

This function is the discretized version of nnTensor::siNMF. The input data objects are assumed to be a list containing multiple non-negative matrices (X_1, X_2, ..., X_K), and decomposed to multiple matrix products (W H_1', W H_2', ..., W H_K'), where W is common across all the data matrices but each H_k (k=1..K) is specific in each X_k. Unlike regular siNMF, in dsiNMF, W and H_k are estimated by adding binary regularization so that the values are 0 or 1 as much as possible. Likewise, W and H_k are estimated by adding ternary regularization so that the values are 0, 1, or 2 as much as possible.

Usage

dsiNMF(X, M=NULL, pseudocount=.Machine$double.eps,
    initW=NULL, initH=NULL,
    fixW=FALSE, fixH=FALSE,
    Bin_W=1e-10, Bin_H=rep(1e-10, length=length(X)),
    Ter_W=1e-10, Ter_H=rep(1e-10, length=length(X)),
    L1_W=1e-10, L1_H=rep(1e-10, length=length(X)),
    L2_W=1e-10, L2_H=rep(1e-10, length=length(X)),
    J = 3, w=NULL, algorithm = c("Frobenius", "KL", "IS", "PLTF"), p=1,
    thr = 1e-10, num.iter = 100,
    viz = FALSE, figdir = NULL, verbose = FALSE)
dsiNMF(X, M=NULL, pseudocount=.Machine$double.eps,
    initW=NULL, initH=NULL,
    fixW=FALSE, fixH=FALSE,
    Bin_W=1e-10, Bin_H=rep(1e-10, length=length(X)),
    Ter_W=1e-10, Ter_H=rep(1e-10, length=length(X)),
    L1_W=1e-10, L1_H=rep(1e-10, length=length(X)),
    L2_W=1e-10, L2_H=rep(1e-10, length=length(X)),
    J = 3, w=NULL, algorithm = c("Frobenius", "KL", "IS", "PLTF"), p=1,
    thr = 1e-10, num.iter = 100,
    viz = FALSE, figdir = NULL, verbose = FALSE)

Arguments

`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).
`Bin_W`	Paramter for binary (0,1) regularitation (Default: 1e-10).
`Bin_H`	A K-length vector containing the paramters for binary (0,1) regularitation (Default: rep(1e-10, length=length(dim(X)))).
`Ter_W`	Paramter for terary (0,1,2) regularitation (Default: 1e-10).
`Ter_H`	A K-length vector containing the paramters for terary (0,1,2) regularitation (Default: rep(1e-10, length=length(dim(X)))).
`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`	A K-length vector containing the paramters for L1 regularitation (Default: rep(1e-10, length=length(dim(X)))). 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`	A K-length vector containing the paramters for L2 regularitation (Default: rep(1e-10, length=length(dim(X)))).
`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.

Value

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.

Author(s)

Koki Tsuyuzaki

References

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

Examples

matdata <- toyModel(model = "dsiNMF_Easy")
out <- dsiNMF(matdata, J=2, num.iter=2)
matdata <- toyModel(model = "dsiNMF_Easy")
out <- dsiNMF(matdata, J=2, num.iter=2)

Discretized Singular Value Decomposition (dSVD)

Description

This function is the discretized version of SVD. The input data X is decomposed to a matrix product U V'. Unlike regular SVD, in dSVD, U and V are estimated by adding binary regularization so that the values are 0 or 1 as much as possible. Likewise, U and V are estimated by adding ternary regularization so that the values are -1, 0, or 1 as much as possible.

Usage

dSVD(X, M=NULL, pseudocount=.Machine$double.eps,
    initU=NULL, initV=NULL, fixU=FALSE, fixV=FALSE,
    Ter_U=1e-10, L1_U=1e-10, L2_U=1e-10, eta=1e+10, J = 3,
    thr = 1e-10, num.iter = 100,
    viz = FALSE, figdir = NULL, verbose = FALSE)
dSVD(X, M=NULL, pseudocount=.Machine$double.eps,
    initU=NULL, initV=NULL, fixU=FALSE, fixV=FALSE,
    Ter_U=1e-10, L1_U=1e-10, L2_U=1e-10, eta=1e+10, J = 3,
    thr = 1e-10, num.iter = 100,
    viz = FALSE, figdir = NULL, verbose = FALSE)

Arguments

`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 element 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).
`Ter_U`	Paramter for terary (-1,0,1) regularitation (Default: 1e-10).
`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.
`L2_U`	Paramter for L2 regularitation (Default: 1e-10).
`eta`	Stepsize of gradient descent algorithm (Default: 1e+10).
`J`	The number of low-dimension (J < {N, M}, Default: 3)
`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.

Value

Author(s)

Koki Tsuyuzaki

Examples

# Test data
matdata <- toyModel(model = "dSVD")

# Simple usage
out <- dSVD(matdata, J=2, num.iter=2)
# Test data
matdata <- toyModel(model = "dSVD")

# Simple usage
out <- dSVD(matdata, J=2, num.iter=2)

Toy model data for using dNMF, dSVD, dsiNMF, djNMF, dPLS, dNTF, and dNTD

Description

The data is used to confirm that the algorithm are properly working.

Usage

toyModel(model = "dNMF", seeds=123)
toyModel(model = "dNMF", seeds=123)

Arguments

`model`	Single character string is specified. "dNMF", "dSVD", "dsiNMF_Easy", "dsiNMF_Hard", "dPLS_Easy", "dPLS_Hard", "dNTF", and "dNTD" are available (Default: "dNMF").
`seeds`	Random number for setting set.seeds in the function (Default: 123).

Value

If model is specified as "dNMF" or "dSVD" a matrix is generated. If model is specified as "dsiNMF_Easy", "dsiNMF_Hard", "dPLS_Easy", or "dPLS_Hard" three matrices are generated. Otherwise, a tensor is generated.

Author(s)

Koki Tsuyuzaki

Examples

matdata <- toyModel(model = "dNMF", seeds=123)
matdata <- toyModel(model = "dNMF", seeds=123)

Package 'dcTensor'

Help Index

Discrete Matrix/Tensor Decomposition

Description

Details

Author(s)

References

See Also

Examples

Discretized Joint Non-negative Matrix Factorization Algorithms (djNMF)

Description

Usage

Arguments

Value

Author(s)

References

Examples

Discretized Non-negative Matrix Factorization Algorithms (dNMF)

Description

Usage

Arguments

Value

Author(s)

References

Examples

Discretized Non-negative Matrix Tri-Factorization Algorithms (dNMTF)

Description

Usage

Arguments

Value

Author(s)

References

Examples

Discretized Non-negative Tucker Decomposition Algorithms (dNTD)

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

Discretized Non-negative CP Decomposition Algorithms (dNTF)

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

Discretized Partial Least Squares (dPLS)

Description

Usage

Arguments

Value

Author(s)

Examples

Discretized Simultaneous Non-negative Matrix Factorization Algorithms (dsiNMF)

Description

Usage

Arguments

Value

Author(s)

References

Examples

Discretized Singular Value Decomposition (dSVD)

Description

Usage

Arguments

Value

Author(s)

Examples

Toy model data for using dNMF, dSVD, dsiNMF, djNMF, dPLS, dNTF, and dNTD

Description

Usage

Arguments

Value

Author(s)

See Also