Cross-Validation for Elastic Alignment Regularization Parameter

Select the optimal regularization parameter (lambda) for elastic alignment using K-fold cross-validation. The CV error measures how well the aligned curves generalize to held-out folds.

Usage

elastic.lambda.cv(
  fdataobj,
  lambdas = 10^seq(-4, 2, length.out = 20),
  n.folds = 5,
  max.iter = 15,
  tol = 0.001,
  seed = 42
)

Arguments

fdataobj

An object of class fdata.

lambdas

Numeric vector of candidate lambda values. Default is 10^seq(-4, 2, length.out = 20).

n.folds

Number of cross-validation folds (default 5).

max.iter

Maximum iterations for Karcher mean per fold (default 15).

tol

Convergence tolerance (default 1e-3).

seed

Random seed for fold assignment (default 42).

Value

An object of class lambda.cv with components:

best.lambda

The lambda value with the lowest CV error

cv.scores

Numeric vector of CV scores for each lambda

lambdas

The candidate lambda values tested

call

The matched call

References

Tucker, J.D., Wu, W., and Srivastava, A. (2013). Generative models for functional data using phase and amplitude separation. Computational Statistics & Data Analysis, 61:50–66.

See also

karcher.mean, elastic.align

Examples

# \donttest{
set.seed(1)
t <- seq(0, 1, length.out = 50)
X <- matrix(0, 15, 50)
for (i in 1:15) X[i, ] <- sin(2 * pi * (t - i / 60))
fd <- fdata(X, argvals = t)
cv <- elastic.lambda.cv(fd, lambdas = 10^seq(-2, 1, length.out = 10))
cv
#> Lambda Cross-Validation
#>   Candidates tested: 10 
#>   Best lambda: 0.01 
#>   Best CV score: 0.3533 
# }