Rob_TPM: Robust Power Tensor Method for Decomposition of A Symmetric...

In junruidi/cdHOTS: Construct and Decomposes Higher Order Tensorian Statistics

Description

Decomposes a higher order symmetric tensors (e.g. higher order centered and standardized tensorian moments) using Robut Power Tensor Method (RPTM) based on the vectorization provided by Di et al.

Usage

Rob_TPM(Y, center = TRUE, standardize = TRUE, L = 10, N = 10,
  order = c(3, 4), rank = ncol(Y), tol = 1e-06)

Arguments

Y	the symmetric tensorian stored as an array
center	column-center the data first, default is TRUE.
standardize	standardize the multivariate data, i.e. convert it to the left singular matrix
L	number of outloop, i.e. number of power tensor iterations
N	number of inner loop, i.e. steps for each power tensor iteration to converge
order	order of the decomposition, 3 or 4
rank	rank of the decomposition
tol	tolerance for the inner loop, i.e power tensor iteration, default to be 1e-06

Details

See Di et al. 2018. This function does not contruct tensor first. It can only be used directly to the data matrix, and it produces decomposition of the (standardized) moment tensors

Value

A list with eliments

eigenv	Estimated eigen vectors, sorted by based on eigenl
eigenl	Estimated eigen values, sorted from largest to smallest
w	The whitening matrix w if standardize = TRUE

References

Di et al.

A Anandkumar et al. Tensor decompositions for learning latent variable models, 2012.

Examples

data(dat)
rob_3 = Rob_TPM(Y = dat, order = 3, rank = 10, tol = 1e-6)

junruidi/cdHOTS documentation built on Aug. 29, 2021, 10:57 a.m.