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.
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)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.
K-order input tensor which has I_1, I_2, ..., and I_K dimensions.
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).
The pseudo count to avoid zero division, when the element is zero (Default: Machine Epsilon).
The initial values of core tensor which has I_1, I_2, ..., and I_K dimensions (Default: NULL).
A list containing the initial values of K factor matrices (A_k, <Ik*Jk>, k=1..K, Default: NULL).
Whether the core tensor S is updated in each iteration step (Default: FALSE).
Whether the factor matrices Ak are updated in each iteration step (Default: FALSE).
A K-length vector containing the paramters for binary (0,1) regularitation (Default: rep(1e-10, length=length(dim(X)))).
A K-length vector containing the paramters for terary (0,1,2) regularitation (Default: rep(1e-10, length=length(dim(X)))).
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.
A K-length vector containing the paramters for L2 regularitation (Default: rep(1e-10, length=length(dim(X)))).
The number of low-dimension in each mode (Default: 3 for each mode).
The vector of the modes on which to perform the decomposition (Default: 1:K <all modes>).
dNTD algorithms. "Frobenius", "KL", "IS", and "Beta" are available (Default: "Frobenius").
The initialization algorithms. "NMF", "ALS", and "Random" are available (Default: "NMF").
The parameter of Beta-divergence.
When error change rate is lower than thr1, the iteration is terminated (Default: 1E-10).
The number of interation step (Default: 100).
If viz == TRUE, internal reconstructed tensor can be visualized.
the directory for saving the figure, when viz == TRUE (Default: NULL).
If verbose == TRUE, Error change rate is generated in console windos.
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
plotTensor3D
tensordata <- toyModel(model = "dNTD")
out <- dNTD(tensordata, rank=c(2,2,2), algorithm="Frobenius",
init="Random", num.iter=2)
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