Canonical Polyadic Decomposition
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).
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 |
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
lambdasa vector of normalizing constants, one for each component
Ua list of matrices - one for each mode - each matrix with num_components columns
convwhether or not resid < tol by the last iteration
norm_percentthe percent of Frobenius norm explained by the approximation
estestimate of tnsr after compression
fnorm_residthe Frobenius norm of the error fnorm(est-tnsr)
all_residsvector containing the Frobenius norm of error for all the iterations
T. Kolda, B. Bader, "Tensor decomposition and applications". SIAM Applied Mathematics and Applications 2009.
### 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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