NTF | R Documentation |

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).

```
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)
```

`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. |

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

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*

`plotTensor3D`

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

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