Borda_count {SmoothTensor}

Borda count algorithm for nonparametric tensor estimation with unknown permutation.

Description

Estimate a signal tensor and permutation from a noisy and incomplete data tensor using Borda count estimation method.

Usage

Borda_count(A, l, kvec, sym = FALSE)

Arguments

A

A given (possibly noisy and incomplete) data tensor. Missing value should be encoded as NA.

l

Degree of polynomial approximation.

kvec

A vector of the number of groups for each mode.

sym

Boolean variables representing symmetricity of the signal tensor. Non-symmetric tensor (sym = FALSE) is default.

Value

The returned object is a list of components.

Theta - An estimated signal tensor based on Borda count estimation.

permutation - An estimated permutation based on Borda count estimation.

References

C. Lee and M. Wang. Smooth tensor estimation with unknown permutations. arXiv:2111.04681, 2021.

Examples

# Generate the noisy observation from smooth tensor and permutation
d = 20
sim1 = simulation(d,mode = 1)
signal_T = sim1$signal
observe_T = sim1$observe
permutation = sim1$permutation

# Estimate signal tensor and permutation
kvec = c(3,3,3)
result = Borda_count(observe_T,2,kvec,sym = TRUE)

# Calculate MSE
hatTheta = result$Theta
mean((hatTheta-signal_T)^2)