Time-varying (convolutive) muscle synergies

Extracts shift-invariant spatiotemporal muscle synergies by convolutive NMF. Each of the n_synergies components is a muscle x L template that the model can place at any time with any amplitude, so a synergy captures a fixed spatiotemporal pattern of muscle activation (d'Avella time-varying synergies), not just a spatial weighting.

Usage

convolutiveSynergy(
  emg,
  n_synergies,
  L,
  max_iter = 300,
  tol = 1e-06,
  restarts = 3,
  seed = NULL
)

Arguments

emg

A non-negative muscle x time matrix (rows = muscles).

n_synergies

Number of synergies.

L

Temporal length of each synergy (samples).

max_iter

Maximum multiplicative-update iterations (default 300).

tol

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

restarts

Random restarts; the best is kept (default 3).

seed

Optional integer seed.

Value

An object of class "convolutive_synergy": a list with synergies (a muscle x synergy x L array), activations (synergy x time), vaf, iterations, n_synergies, and L.

References

d'Avella A, Saltiel P, Bizzi E (2003). Combinations of muscle synergies in the construction of a natural motor behavior. Nat Neurosci 6:300-308. Smaragdis P (2004). Non-negative matrix factor deconvolution. ICA.

Examples

set.seed(1)
M <- 5; Tt <- 200; N <- 2; L <- 15
W0 <- array(0, c(M, N, L))
for (nn in 1:N) W0[, nn, ] <- outer(runif(M), dnorm(1:L, L / 2, 3))
H0 <- matrix(0, N, Tt); H0[1, c(30, 120)] <- 1; H0[2, c(70, 160)] <- 1
V <- matrix(0, M, Tt)
for (tau in 0:(L - 1)) V <- V +
  W0[, , tau + 1] %*% cbind(matrix(0, N, tau), H0[, 1:(Tt - tau), drop = FALSE])
fit <- convolutiveSynergy(V, n_synergies = 2, L = 15, seed = 1)
fit$vaf
#> [1] 0.9996941