cp: Canonical Polyadic Decomposition

Description Usage Arguments Details Value References See Also Examples

View source: R/rTensor_Decomp.R

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 *tnsr@num_modes vectors in the output, stored in tnsr@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

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

Arguments

tnsr

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

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 tnsr after compression

fnorm_resid

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

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

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tnsr <- rand_tensor(c(6,7,8))
cpD <- cp(tnsr,num_components=5)
cpD$conv
cpD$norm_percent
plot(cpD$all_resids)

jamesyili/rTensor documentation built on May 18, 2019, 11:22 a.m.