dNMF {dcTensor}

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)

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)