LSE {SmoothTensor}

The least squares estimation for nonparametric tensor estimation with unknown permutation.

Description

Estimate a permuted signal tensor from a noisy data tensor based on the least squares estimation with constant block approximation.

Usage

LSE(A, kvec, sym = FALSE, mode = 3)

Arguments

A

A given noisy data tensor.

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.

mode

An integer from 1 to 3 representing a type of methods for estimating the clustering functions. Higher-order spectral clustering method is default.
mode = 1: k-means algorithm applied on unfolded matrices.
mode = 2: k-means algorithm for community detection in stocahstic block model (only availble on binary observation).
mode = 3: higher-order spectral clustering algorithm.

Value

An estimated permuted signal tensor based on the least squares estimation.

References

C. Gao, Y. Lu, and H. H. Zhou. Rate-optimal graphon estimation. The Annals of Statistics, 2015.
K. Balasubramanian. Nonparametric modeling of higher-order interactions via hypergraphons. Journal of Machine Learning Research, 2021.
R. Han, Y. Luo, M. Wang, and A. R. Zhang. Exact clustering in tensor block model: Statistical optimality and computational limit. arXiv:2012.09996, 2020.

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
kvec = c(10,10,10)
hatpTheta = LSE(observe_T,kvec,sym = TRUE)

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