rrcov3way (version 0.5-0)

cp_int2: ATLD-ALS algorithm for Candecomp/Parafac (CP)

Description

Integrated algorithm combining ATLD and ALS for the minimization of the Candecomp/Parafac (CP) loss function.

Usage

cp_int2(
  X,
  n,
  m,
  p,
  ncomp,
  initconv = 0.01,
  conv = 1e-06,
  const = "none",
  start = "random",
  maxit = 5000,
  trace = FALSE
)

Value

The result of the decomposition as a list with the following elements:

• fit Value of the loss function

• fp Fit value expressed as a percentage

• ss Sum of squares

• A Component matrix for the A-mode

• B Component matrix for the B-mode

• C Component matrix for the C-mode

• iter Number of iterations

• tripcos Minimal triple cosine between two components across the three component matrices, used to inspect degeneracy

• mintripcos Minimal triple cosine during the iterative algorithm observed at every 10 iterations, used to inspect degeneracy

• ftiter Matrix containing in each row the function value and the minimal triple cosine at every 10 iterations

• const Optional constraints (same as the input parameter const)

Arguments

X

A three-way array or a matrix. If X is a matrix (matricised threeway array), n, m and p must be given and are the number of A-, B- and C-mode entities respectively

n

Number of A-mode entities

m

Number of B-mode entities

p

Number of C-mode entities

ncomp

Number of components to extract

initconv

Convergence criterion for the initialization phase (ATLD), default is conv=1e-2.

conv

Convergence criterion, default is conv=1e-6.

const

Optional constraints for each mode. Can be a three element character vector or a single character, one of "none" for no constraints (default), "orth" for orthogonality constraints or "zerocor" for zero correlation between the extracted factors. For example, const="orth" means orthogonality constraints for all modes, while const=c("orth", "none", "none") sets the orthogonality constraint only for mode A.

start

Initial values for the A, B and C components. Can be "svd" for starting point of the algorithm from SVD's, "random" for random starting point (orthonormalized component matrices or nonnegative matrices in case of nonnegativity constraint), or a list containing user specified components.

maxit

Maximum number of iterations, default is maxit=10000.

trace

Logical, provide trace output.

Author

Valentin Todorov, ; Violetta Simonacci,

References

H.-L. Wu, M. Shibukawa, K. Oguma, An alternating trilinear decomposition algorithm with application to calibration of HPLC-DAD for simultaneous determination of overlapped chlorinated aromatic hydrocarbons, Journal of Chemometrics 12 (1998) 1--26.

Simonacci, V. and Gallo, M. (2020). An ATLD--ALS method for the trilinear decomposition of large third-order tensors, Soft Computing 24 13535--13546.

Todorov, V. and Simonacci, V. and Gallo, M. and Trendafilov, N. (2023). A novel estimation procedure for robust CANDECOMP/PARAFAC model fitting. Econometrics and Statistics. In press.

Examples

if (FALSE) {
## Example with the OECD data
 data(elind)
 dim(elind)

 res <- cp_int2(elind, ncomp=3)
 res$fp
 res$fp
 res$iter

 res <- cp_int2(elind, ncomp=3, const="orth")
 res$A
}