# NTD: Non-negative Tucker Decomposition Algorithms (NTD) In nnTensor: Non-Negative Tensor Decomposition

 NTD R Documentation

## Non-negative Tucker Decomposition Algorithms (NTD)

### Description

The input data is assumed to be non-negative tensor. NTD decompose the tensor to the dense core tensor (S) and low-dimensional factor matices (A).

### Usage

``````NTD(X, M=NULL, pseudocount=.Machine\$double.eps, initS=NULL, initA=NULL,
fixS=FALSE, fixA=FALSE, L1_A=1e-10, L2_A=1e-10,
rank = rep(3, length=length(dim(X))),
modes = seq_along(dim(X)),
algorithm = c("Frobenius", "KL", "IS", "Pearson", "Hellinger", "Neyman",
"HALS", "Alpha", "Beta", "NMF"), init = c("NMF", "ALS", "Random"),
nmf.algorithm = c("Frobenius", "KL", "IS", "Pearson", "Hellinger", "Neyman",
"Alpha", "Beta", "ALS", "PGD", "HALS", "GCD", "Projected", "NHR", "DTPP",
"Orthogonal", "OrthReg"),
Alpha = 1,
Beta = 2, thr = 1e-10, num.iter = 100, num.iter2 = 10, 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, , 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). `L1_A` 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_A` Paramter for L2 regularitation (Default: 1e-10). `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 ). `algorithm` NTD algorithms. "Frobenius", "KL", "IS", "Pearson", "Hellinger", "Neyman", "HALS", "Alpha", "Beta", "NMF" are available (Default: "Frobenius"). `nmf.algorithm` NMF algorithms, when the algorithm is "NMF". "Frobenius", "KL", "IS", "Pearson", "Hellinger", "Neyman", "Alpha", "Beta", "ALS", "PGD", "HALS", "GCD", "Projected", "NHR", "DTPP", "Orthogonal", and "OrthReg" are available (Default: "Frobenius"). `init` The initialization algorithms. "NMF", "ALS", and "Random" are available (Default: "NMF"). `Alpha` The parameter of Alpha-divergence. `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). `num.iter2` The number of NMF interation step, when the algorithm is "NMF" (Default: 10). `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.

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

`plotTensor3D`
``````tensordata <- toyModel(model = "Tucker")