NTF: Non-negative CP Decomposition Algorithms (NTF)

In nnTensor: Non-Negative Tensor Decomposition

Non-negative CP Decomposition Algorithms (NTF)

Description

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

Usage

NTF(X, M=NULL, pseudocount=.Machine$double.eps, initA=NULL,
  fixA=FALSE, L1_A=1e-10, L2_A=1e-10, rank = 3,
  algorithm = c("Frobenius", "KL", "IS", "Pearson", "Hellinger", "Neyman",
    "HALS", "Alpha-HALS", "Beta-HALS", "Alpha", "Beta"),
  init = c("NMF", "ABS-SVD", "ALS", "Random"), Alpha = 1,
  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).
initA	A list containing the initial values of K factor matrices (A_k, <Ik*Jk>, k=1..K, Default: NULL).
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).
algorithm	NTF algorithms. "Frobenius", "KL", "IS", "Pearson", "Hellinger", "Neyman", "HALS", "Alpha-HALS", "Beta-HALS", "Alpha", and "Beta" are available (Default: "Frobenius").
init	The initialization algorithms. "NMF", "ABS-SVD", "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).
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

Andrzej CICHOCKI et. al., (2007). Non-negative Tensor Factorization using Alpha and Beta Divergence. IEEE ICASSP 2007

Anh Huy PHAN et. al., (2008). Multi-way Nonnegative Tensor Factorization Using Fast Hierarchical Alternating Least Squares Algorithm (HALS). NOLTA2008

Andrzej CICHOCKI et. al., (2008). Fast Local Algorithms for Large Scale Nonnegative Matrix and Tensor Factorizations. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

See Also

plotTensor3D

Examples

tensordata <- toyModel(model = "CP")
out <- NTF(tensordata, rank=3, algorithm="Beta-HALS", num.iter=2)

nnTensor documentation built on July 9, 2023, 7:37 p.m.