# fit_ordinal: Main function for parametric tensor estimation and completion... In TensorComplete: Tensor Noise Reduction and Completion Methods

## Description

Estimate a signal tensor from a noisy and incomplete ordinal-valued tensor using the cumulative logistic model.

## Usage

 `1` ```fit_ordinal(ttnsr,r,omega=TRUE,alpha = TRUE) ```

## Arguments

 `ttnsr` A given (possibly noisy and incomplete) data tensor. The function allows binary- and ordinal-valued tensors. Missing value should be encoded as `NA`. `r` A rank to be fitted (Tucker rank). `omega` The cut-off points if known, `omega = TRUE` if unknown. `alpha` A signal level `alpha = TRUE` if the signal level is unknown.

## Value

A list containing the following:

`C` - An estimated core tensor.

`A` - Estimated factor matrices.

`theta` - An estimated latent parameter tensor.

`iteration` - The number of iterations.

`cost` - Log-likelihood value at each iteration.

`omega` - Estimated cut-off points.

## References

C. Lee and M. Wang. Tensor denoising and completion based on ordinal observations. International Conference on Machine Learning (ICML), 2020.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18``` ```# Latent parameters library(tensorregress) alpha = 10 A_1 = matrix(runif(15*2,min=-1,max=1),nrow = 15) A_2 = matrix(runif(15*2,min=-1,max=1),nrow = 15) A_3 = matrix(runif(15*2,min=-1,max=1),nrow = 15) C = as.tensor(array(runif(2^3,min=-1,max=1),dim = c(2,2,2))) theta = ttm(ttm(ttm(C,A_1,1),A_2,2),A_3,3)@data theta = alpha*theta/max(abs(theta)) adj = mean(theta) theta = theta-adj omega = c(-0.2,0.2)+adj # Observed tensor ttnsr <- realization(theta,omega)@data # Estimation of parameters ordinal_est = fit_ordinal(ttnsr,c(2,2,2),omega = TRUE,alpha = 10) ```

TensorComplete documentation built on May 11, 2021, 5:08 p.m.