dNMTF {dcTensor}

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)

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))
  }