dNTD {dcTensor}

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)

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

See Also

plotTensor3D

Examples

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