cp: Canonical Polyadic Decomposition

In rikenbit/DelayedTensor: R package for sparse and out-of-core arithmetic and decomposition of Tensor

Canonical Polyadic Decomposition

Description

Canonical Polyadic (CP) decomposition of a tensor, aka CANDECOMP/PARAFRAC. Approximate a K-Tensor using a sum of num_components rank-1 K-Tensors. A rank-1 K-Tensor can be written as an outer product of K vectors. There are a total of num_compoents *darr@num_modes vectors in the output, stored in darr@num_modes matrices, each with num_components columns. This is an iterative algorithm, with two possible stopping conditions: either relative error in Frobenius norm has gotten below tol, or the max_iter number of iterations has been reached. For more details on CP decomposition, consult Kolda and Bader (2009).

Usage

cp(darr, num_components=NULL, max_iter=25, tol=1e-05)

## S4 method for signature 'DelayedArray'
cp(darr, num_components, max_iter, tol)

Arguments

darr	Tensor with K modes
num_components	the number of rank-1 K-Tensors to use in approximation
max_iter	maximum number of iterations if error stays above tol
tol	relative Frobenius norm error tolerance

Details

This function is an extension of the cp by DelayedArray.

Uses the Alternating Least Squares (ALS) estimation procedure. A progress bar is included to help monitor operations on large tensors.

Value

a list containing the following

lambdas

a vector of normalizing constants, one for each component

U

a list of matrices - one for each mode - each matrix with num_components columns

conv

whether or not resid < tol by the last iteration

norm_percent

the percent of Frobenius norm explained by the approximation

est

estimate of darr after compression

fnorm_resid

the Frobenius norm of the error fnorm(est-darr)

all_resids

vector containing the Frobenius norm of error for all the iterations

References

T. Kolda, B. Bader, "Tensor decomposition and applications". SIAM Applied Mathematics and Applications 2009.

See Also

tucker

Examples

library("DelayedRandomArray")
darr <- RandomUnifArray(c(3,4,5))
cp(darr, num_components=2)

rikenbit/DelayedTensor documentation built on Sept. 28, 2024, 5:43 a.m.