R/archetypoids_funct.R

In adamethods: Archetypoid Algorithms and Anomaly Detection

#' Archetypoid algorithm with the functional Frobenius norm
#' 
#' @aliases archetypoids_funct
#'
#' @description 
#' Archetypoid algorithm with the functional Frobenius norm 
#' to be used with functional data. 
#' 
#' @usage 
#' archetypoids_funct(numArchoid, data, huge = 200, ArchObj, PM)
#' 
#' @param numArchoid Number of archetypoids.
#' @param data Data matrix. Each row corresponds to an observation and each column 
#' corresponds to a variable. All variables are numeric.
#' @param huge Penalization added to solve the convex least squares problems.
#' @param ArchObj The list object returned by the 
#' \code{\link{stepArchetypesRawData_funct}} function.
#' @param PM Penalty matrix obtained with \code{\link[fda]{eval.penalty}}.
#'
#' @return 
#' A list with the following elements:
#' \itemize{
#' \item cases: Final vector of archetypoids.
#' \item rss: Residual sum of squares corresponding to the final vector of archetypoids.
#' \item archet_ini: Vector of initial archetypoids.
#' \item alphas: Alpha coefficients for the final vector of archetypoids.
#' \item resid: Matrix with the residuals.
#' }
#' 
#' @author 
#' Irene Epifanio
#' 
#' @seealso 
#' \code{\link[Anthropometry]{archetypoids}}
#' 
#' @references 
#' Epifanio, I., Functional archetype and archetypoid analysis, 2016. 
#' \emph{Computational Statistics and Data Analysis} \bold{104}, 24-34, 
#' \url{https://doi.org/10.1016/j.csda.2016.06.007}
#' 
#' @examples 
#' \dontrun{
#' library(fda)
#' ?growth
#' str(growth)
#' hgtm <- t(growth$hgtm)
#' # Create basis:
#' basis_fd <- create.bspline.basis(c(1,ncol(hgtm)), 10)
#' PM <- eval.penalty(basis_fd)
#' # Make fd object:
#' temp_points <- 1:ncol(hgtm)
#' temp_fd <- Data2fd(argvals = temp_points, y = growth$hgtm, basisobj = basis_fd)
#' data_archs <- t(temp_fd$coefs)
#' 
#' lass <- stepArchetypesRawData_funct(data = data_archs, numArch = 3, 
#'                                     numRep = 5, verbose = FALSE, 
#'                                     saveHistory = FALSE, PM)
#'
#' af <- archetypoids_funct(3, data_archs, huge = 200, ArchObj = lass, PM) 
#' str(af)                                
#' }                                                          
#'                                                      
#' @export

archetypoids_funct <- function(numArchoid, data, huge = 200, ArchObj, PM){
  
  N = dim(data)[1]
  
  ai <- archetypes::bestModel(ArchObj[[1]])
  
  if (is.null(archetypes::parameters(ai))) {
    stop("No archetypes computed")  
  }else{
    ras <- rbind(archetypes::parameters(ai),data)
    dras <- dist(ras, method = "euclidean", diag = FALSE, upper = TRUE, p = 2)
    mdras <- as.matrix(dras)
    diag(mdras) = 1e+11
  }
  
  ini_arch <- sapply(seq(length = numArchoid), nearestToArchetypes, numArchoid, mdras) 
  
  if (all(ini_arch > numArchoid) == FALSE) {
    k = 1
    neig <- knn(data, archetypes::parameters(ai), 1:N, k = k)
    indices1 <- attr(neig, "nn.index")
    ini_arch <- indices1[,k]
    
    while (any(duplicated(ini_arch))) {
      k = k + 1  
      neig <- knn(data, archetypes::parameters(ai), 1:N, k = k)
      indicesk <- attr(neig, "nn.index")
      
      dupl <- anyDuplicated(indices1[,1])
      ini_arch <- c(indices1[-dupl,1],indicesk[dupl,k])
    }
  }
  
  n <- ncol(t(data))
  x_gvv <- rbind(t(data), rep(huge, n))
  
  zs <- x_gvv[,ini_arch] 
  zs <- as.matrix(zs)
  
  alphas <- matrix(0, nrow = numArchoid, ncol = n)
  for (j in 1:n) {
    alphas[, j] = coef(nnls(zs, x_gvv[,j]))
  }
  
  resid <- zs[1:(nrow(zs) - 1),] %*% alphas - x_gvv[1:(nrow(x_gvv) - 1),]
  rss_ini <- frobenius_norm_funct(resid, PM) / n
  
  res_def <- swap_funct(ini_arch, rss_ini, huge, numArchoid, x_gvv, n, PM)
  
  return(res_def)
}