dSVD | R Documentation |

This function is the discretized version of SVD. The input data X is decomposed to a matrix product U V'. Unlike regular SVD, in dSVD, U and V are estimated by adding binary regularization so that the values are 0 or 1 as much as possible. Likewise, U and V are estimated by adding ternary regularization so that the values are -1, 0, or 1 as much as possible.

```
dSVD(X, M=NULL, pseudocount=.Machine$double.eps,
initU=NULL, initV=NULL, fixU=FALSE, fixV=FALSE,
Ter_U=1e-10, L1_U=1e-10, L2_U=1e-10, eta=1e+10, J = 3,
thr = 1e-10, num.iter = 100,
viz = FALSE, figdir = NULL, verbose = FALSE)
```

`X` |
The input matrix which has N-rows and M-columns. |

`M` |
The mask matrix which has N-rows and M-columns. If the input matrix 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). |

`initU` |
The initial values of factor matrix U, which has N-rows and J-columns (Default: NULL). |

`initV` |
The initial values of factor matrix V, which has M-rows and J-columns (Default: NULL). |

`fixU` |
Whether the factor matrix U is updated in each iteration step (Default: FALSE). |

`fixV` |
Whether the factor matrix V is updated in each iteration step (Default: FALSE). |

`Ter_U` |
Paramter for terary (-1,0,1) regularitation (Default: 1e-10). |

`L1_U` |
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_U` |
Paramter for L2 regularitation (Default: 1e-10). |

`eta` |
Stepsize of gradient descent algorithm (Default: 1e+10). |

`J` |
The number of low-dimension (J < {N, M}, Default: 3) |

`thr` |
When error change rate is lower than thr, the iteration is terminated (Default: 1E-10). |

`num.iter` |
The number of interation step (Default: 100). |

`viz` |
If viz == TRUE, internal reconstructed matrix can be visualized. |

`figdir` |
The directory for saving the figure, when viz == TRUE. |

`verbose` |
If verbose == TRUE, Error change rate is generated in console window. |

U : A matrix which has N-rows and J-columns (J < {N, M}). V : A matrix which has M-rows and J-columns (J < {N, M}). RecError : The reconstruction error between data tensor and reconstructed tensor from U and V. 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

```
# Test data
matdata <- toyModel(model = "dSVD")
# Simple usage
out <- dSVD(matdata, J=2, num.iter=2)
```

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