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#' Symbolic interval principal curves limits
#' @name sym.interval.pc.limits
#' @aliases sym.interval.pc.limits
#' @author Jorge Arce.
#' @description Symbolic interval principal curves limits.
#' @usage sym.interval.pc.limits(sym.data, prin.curve, num.vertex, lambda, var.ord)
#' @param sym.data Symbolic interval data table.
#' @param prin.curve Principal curves.
#' @param num.vertex Number of vertices of the hipercube.
#' @param lambda Lambda.
#' @param var.ord Order of the variables.
#' @references
#' Arce J. and Rodriguez O. (2015) 'Principal Curves and Surfaces
#' to Interval Valued Variables'. The 5th Workshop on Symbolic
#' Data Analysis, SDA2015, Orleans, France, November.
#'
#' Hastie,T. (1984).
#' Principal Curves and Surface. Ph.D Thesis Stanford University.
#'
#' Hastie,T. & Weingessel,A. (2014).
#' princurve - Fits a Principal Curve in Arbitrary Dimension.R package version 1.1--12
#' http://cran.r-project.org/web/packages/princurve/index.html.
#'
#' Hastie,T. & Stuetzle, W. (1989). Principal Curves.
#' Journal of the American Statistical Association, Vol. 84-406, 502--516.
#'
#' Hastie, T., Tibshirani, R. & Friedman, J. (2008).
#' The Elements of Statistical Learning; Data Mining, Inference and Prediction. Springer, New York.
#' @seealso sym.interval.pc
#' @keywords Principal Curve
#' @import princurve
#' @export
#'
#'
sym.interval.pc.limits <- function(sym.data, prin.curve, num.vertex, lambda, var.ord) {
num.vars <- sym.data$M
num.ind <- sym.data$N
res <- as.data.frame(prin.curve)
res$lambda <- lambda
sym.indiv <- rep("X", sum(num.vertex))
start <- 1
finish <- num.vertex[1]
sym.indiv[start:finish] <- sym.data$sym.obj.names[1]
for (i in 2:num.ind) {
previous <- num.vertex[i - 1]
start <- start + previous
finish <- num.vertex[i] + finish
sym.indiv[start:finish] <- sym.data$sym.obj.names[i]
}
res$symindiv <- sym.indiv
var.type <- rep("$I", num.vars + 1)
variables <- rep("X", num.vars)
for (i in 1:num.vars) {
variables[var.ord[i]] <- paste0("prin_surface_", as.character(i))
}
colnames(res)[1:num.vars] <- variables
variables <- c(variables[var.ord], "lambda")
sym.res <- classic.to.sym(x = res, concept = symindiv)
return(sym.res)
}
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