cp: Canonical Polyadic Decomposition
In rTensor: Tools for Tensor Analysis and Decomposition

Description Usage Arguments Details Value References See Also Examples

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).

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

`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

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

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

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

tucker

### How to retrieve faces_tnsr from figshare
# faces_tnsr <- load_orl()
# subject <- faces_tnsr[,,14,]
dummy_faces_tnsr <- rand_tensor(c(92,112,40,10))
subject <- dummy_faces_tnsr[,,14,]
cpD <- cp(subject, num_components=3)
cpD$conv
cpD$norm_percent
plot(cpD$all_resids)

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[1] TRUE
[1] 0.6586191