Muscle-synergy tensor decomposition (non-negative PARAFAC)

Non-negative CANDECOMP/PARAFAC of a three-way EMG tensor muscle x time x trial. Each of the n_synergies components is a rank-one term with a muscle weight vector, a temporal activation profile, and a per-trial loading — the multiway analogue of a muscle synergy that captures how the same spatial/temporal modules are reused and rescaled across trials or conditions.

Usage

muscleSynergyTensor(
  tensor,
  n_synergies,
  max_iter = 500,
  tol = 1e-06,
  restarts = 5,
  seed = NULL
)

Arguments

tensor

A non-negative numeric array with dimensions muscle x time x trial.

n_synergies

Number of synergies (rank) to extract.

max_iter

Maximum multiplicative-update iterations (default 500).

tol

Relative reconstruction-error tolerance for convergence (default 1e-6).

restarts

Random restarts; the best (lowest error) is kept (default 5).

seed

Optional integer seed for reproducibility.

Value

An object of class "synergy_tensor": a list with muscle_weights (muscle x synergy), temporal (time x synergy), trial_loadings (trial x synergy), vaf (variance accounted for), iterations, and n_synergies.

References

Cichocki A, Zdunek R, Phan AH, Amari S (2009). Nonnegative Matrix and Tensor Factorizations. Wiley.

Examples

set.seed(1)
M <- 6; Tt <- 50; K <- 8; R <- 2
A0 <- matrix(runif(M * R), M, R); B0 <- matrix(runif(Tt * R), Tt, R)
C0 <- matrix(runif(K * R), K, R)
X <- array(0, c(M, Tt, K))
for (r in 1:R) for (k in 1:K) X[, , k] <- X[, , k] +
  (A0[, r] %o% B0[, r]) * C0[k, r]
fit <- muscleSynergyTensor(X, n_synergies = 2, restarts = 3, seed = 1)
fit$vaf
#> [1] 0.9999953