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Symmetric CP Decomposition via Direct Optimization

Source: R/cp_sym.R
cp_sym.Rd

Fits a symmetric CP model sum_r lambda_r * u_r^(o m) to a symmetric tensor by minimizing the Frobenius residual over the weights and the shared factor matrix with L-BFGS-B, mirroring the MATLAB Tensor Toolbox cp_sym.

Usage

cp_sym(
  X,
  R,
  init = "random",
  maxiters = 500L,
  factr = 1e+07,
  symmetrize = FALSE,
  printitn = 0L
)

Arguments

X

A symmetric Tensor (all modes the same size).

R

Number of symmetric rank-one components.

init

"random" or an n x R matrix of initial factors.

maxiters

Maximum optimizer iterations (default 500).

factr

optim L-BFGS-B factr convergence parameter.

symmetrize

Logical; if TRUE, symmetrize X first instead of requiring exact symmetry.

printitn

If positive, print the optimizer trace.

Value

A SymKTensor.

Details

With t_r = <X, u_r^(o m)> and c_rs = u_r . u_s, the objective is ||X||^2 - 2 sum_r lambda_r t_r + sum_rs lambda_r lambda_s c_rs^m, whose gradients are evaluated exactly using ttsv().

Examples

set.seed(1)
u <- matrix(rnorm(6), 3, 2)
X <- as.tensor(symktensor(c(1, 2), u, m = 3))
S <- cp_sym(X, R = 2)