rTensor-package {rTensor}

Tools for tensor analysis and decomposition

Description

This package is centered around the Tensor-class, which defines a S4 class for tensors of arbitrary number of modes. A vignette and/or a possible paper will be included in a future release of this package.

Details

This page will summarize the full functionality of this package. Note that since all the methods associated with S4 class Tensor-class are documented there, we will not duplicate it here.

The remaining functions can be split into two groups: the first is a set of tensor decompositions, and the second is a set of helper functions that are useful in tensor manipulation.

rTensor implements the following tensor decompositions:

cp

Canonical Polyadic (CP) decomposition

tucker

General Tucker decomposition

mpca

Multilinear Principal Component Analysis; note that for 3-Tensors this is also known as Generalized Low Rank Approximation of Matrices(GLRAM)

hosvd

(Truncated-)Higher-order singular value decomposition

t_svd

Tensor singular value decomposition; 3-Tensors only; also note that there is an asociated reconstruction function t_svd_reconstruct

pvd

Population value decomposition of images; 3-Tensors only

rTensor also provides a set functions for tensors multiplication:

ttm

Tensor times matrix, aka m-mode product

ttl

Tensor times list (of matrices)

t_mult

Tensor product based on block circulant unfolding; only implemented for a pair of 3-Tensors

...as well as for matrices:

hadamard_list

Computes the Hadamard (element-wise) product of a list of matrices

kronecker_list

Computes the Kronecker product of a list of matrices

khatri_rao

Computes the Khatri-Rao product of two matrices

khatri_rao_list

Computes the Khatri-Rao product of a list of matrices

fold

General folding of a matrix into a tensor

k_fold

Inverse operation for k_unfold

unmatvec

Inverse operation for matvec

For more information on any of the functions, please consult the individual man pages.

Author(s)

James Li [e-mail], Jacob Bien, and Martin T. Wells