gmfd_diss: Dissimilarity matrix function
In martinoandrea92/dpdistance: Inference and Clustering of Functional Data

Description Usage Arguments Value References Examples

This function returns the dissimilarity matrix computed by using the specified distance to compute the distances between the curves of the functional dataset.

1	gmfd_diss(FD, metric, p = NULL)

`FD`	a functional data object of type `funData`
`metric`	the chosen distance to be used. Choose `"L2"` for the classical L2-distance, `"trunc"` for the truncated Mahalanobis semi-distance, `"mahalanobis"` for the generalized Mahalanobis distance.
`p`	a positive numeric value containing the parameter of the regularizing function for the generalized Mahalanobis distance.

The function returns a matrix of numeric values containing the distances between the curves.

Ghiglietti A., Ieva F., Paganoni A. M. (2017). Statistical inference for stochastic processes: Two-sample hypothesis tests, Journal of Statistical Planning and Inference, 180:49-68.

Ghiglietti A., Paganoni A. M. (2017). Exact tests for the means of gaussian stochastic processes. Statics & Probability Letters, 131:102–107.

# Define parameters
n <- 50
P <- 100
K <- 150

# Grid of the functional dataset
t <- seq( 0, 1, length.out = P )

# Define the means and the parameters to use in the simulation
# with the Karhunen - LoÃ¨ve expansion
m1 <- t^2 * ( 1 - t )

lambda <- rep( 0, K )
theta <- matrix( 0, K, P )
for ( k in 1:K ) {
  lambda[k] <- 1 / ( k + 1 )^2
  if ( k%%2 == 0 )
    theta[k, ] <- sqrt( 2 ) * sin( k * pi * t )
  else if ( k%%2 != 0 && k != 1 )
    theta[k, ] <- sqrt( 2 ) * cos( ( k - 1 ) * pi * t )
  else
    theta[k, ] <- rep( 1, P )
}

# Simulate the functional data
FD <- simulate_KL( t, n, m1, rho = lambda, theta = theta )

D <- gmfd_diss(FD, metric = "L2")