Spectral {SmoothTensor}

Spectral method for nonparametric tensor estimation with unknown permutation.

Description

Estimate a permuted signal tensor from a noisy data tensor using spectral method, which performs universal singualr value thresholding on the unfolded tensor.

Usage

Spectral(A, row_idx, col_idx, threshold = NULL)

Arguments

A

A given noisy data tensor.

row_idx

The indices of the modes that map onto the row space

col_idx

The indices of the modes that map onto the column space

threshold

A threshold to disregard singular values. Default value is the square root of unfolded matrix dimension.

Value

An estimated permuted signal tensor based on Spectral method.

References

J. Xu. Rates of convergence of spectral methods for graphon estimation. International Conference on Machine Learning, 2018.
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
psignal_T = signal_T[permutation,permutation,permutation]

# Estimate permuted signal tensor
hatpTheta = Spectral(observe_T,1,c(2,3))

# Calculate MSE
mean((hatpTheta-psignal_T)^2)