Partitioning Using Local Subregions (PULS)

PULS function for functional data (only used when you know that the data shouldn't be converted into functional because it's already smooth, e.g. your data are step function)

PULS(
  toclust.fd,
  method = c("pam", "ward"),
  intervals = c(0, 1),
  spliton = NULL,
  distmethod = c("usc", "manual"),
  labels = toclust.fd$fdnames[2]$reps,
  nclusters = length(toclust.fd$fdnames[2]$reps),
  minbucket = 2,
  minsplit = 4
)

Arguments

toclust.fd	A functional data object (i.e., having class fd) created from fda package. See fda::fd().
method	The clustering method you want to run in each subregion. Can be chosen between pam and ward.
intervals	A data set (or matrix) with rows are intervals and columns are the beginning and ending indexes of of the interval.
spliton	Restrict the partitioning on a specific set of subregions.
distmethod	The method for calculating the distance matrix. Choose between "usc" and "manual". "usc" uses fda.usc::metric.lp() function while "manual" uses squared distance between functions. See Details.
labels	The name of entities.
nclusters	The number of clusters.
minbucket	The minimum number of data points in one cluster allowed.
minsplit	The minimum size of a cluster that can still be considered to be a split candidate.

Value

A PULS object. See PULS.object for details.

Details

If choosing distmethod = "manual", the L2 distance between all pairs of functions \(y_i(t)\) and \(y_j(t)\) is given by: $$d_R(y_i, y_j) = \sqrt{\int_{a_r}^{b_r} [y_i(t) - y_j(t)]^2 dt}.$$

See also

fda::is.fd()

Examples

# \donttest{
library(fda)
#> Loading required package: splines
#> Loading required package: Matrix
#> Loading required package: fds
#> Loading required package: rainbow
#> Loading required package: MASS
#> Loading required package: pcaPP
#> Loading required package: RCurl
#> 
#> Attaching package: ‘fda’
#> The following object is masked from ‘package:graphics’:
#> 
#>     matplot

# Build a simple fd object from already smoothed smoothed_arctic
data(smoothed_arctic)
NBASIS <- 300
NORDER <- 4
y <- t(as.matrix(smoothed_arctic[, -1]))
splinebasis <- create.bspline.basis(rangeval = c(1, 365),
                                    nbasis = NBASIS,
                                    norder = NORDER)
fdParobj <- fdPar(fdobj = splinebasis,
                  Lfdobj = 2,
                  # No need for any more smoothing
                  lambda = .000001)
yfd <- smooth.basis(argvals = 1:365, y = y, fdParobj = fdParobj)

Jan <- c(1, 31); Feb <- c(31, 59); Mar <- c(59, 90)
Apr <- c(90, 120); May <- c(120, 151); Jun <- c(151, 181)
Jul <- c(181, 212); Aug <- c(212, 243); Sep <- c(243, 273)
Oct <- c(273, 304); Nov <- c(304, 334); Dec <- c(334, 365)

intervals <-
  rbind(Jan, Feb, Mar, Apr, May, Jun, Jul, Aug, Sep, Oct, Nov, Dec)

PULS4_pam <- PULS(toclust.fd = yfd$fd, intervals = intervals,
                  nclusters = 4, method = "pam")
PULS4_pam
#> n = 39 
#> 
#> Node) Split, N, Cluster Inertia, Proportion Inertia Explained,  
#>       * denotes terminal node
#> 
#> 1) root 39 8453.2190 0.7072663   
#>   2) Jul 15  885.3640 0.8431711   
#>     4) Aug 8  311.7792   *
#>     5) Aug 7  178.8687   *
#>   3) Jul 24 1589.1780 0.7964770   
#>     6) Jul 13  463.8466   *
#>     7) Jul 11  371.2143   *
#> 
#> Note: One or more of the splits chosen had an alternative split that reduced inertia by the same amount. See "alt" column of "frame" object for details.
# }