SparseFunClust {SparseFunClust}

Compute Sparse Functional Clustering & Alignment

Description

Compute Sparse Functional Clustering & Alignment

Usage

SparseFunClust(
  data,
  x,
  K,
  do.alignment,
  funct.measure = "L2",
  clust.method = "kmea",
  m.prop = 0.3,
  tuning.m = FALSE,
  tuning.par = list(mbound = NULL, nperm = 20),
  perc = 0.03,
  tol = 0.01,
  template.est = "raw",
  n.out = 500,
  iter.max = 50,
  vignette = TRUE
)

Arguments

data

matrix representing the functions (n x p)

x

matrix giving the domain of each function (n x p), or a p-dimensional vector giving the common domain

K

number of clusters

do.alignment

boolean (should alignment be performed?)

funct.measure

the functional measure to be used to compare the functions in both the clustering and alignment procedures; can be 'L2' or 'H1' (default 'L2'); see Vitelli (2019) for details

clust.method

the clustering method to be used; can be: 'kmea' for k-means clustering,'pam','hier' for hierarchical clustering

m.prop

the sparsity parameter (proportion of unrelevant domain where w(x) = 0); default 30%

tuning.m

boolean (should the sparsity parameter be tuned via a permutation-based approach?)

tuning.par

list of settings for the tuning of the sparsity parameter (defaults to list(mbound = NULL, nperm = 20): mbound = max value of the sparsity parameter to be tested, default 60%; nperm = number of permutations to be performed in the tuning, default 20

perc

alignment parameter (max proportion of shift / dilation at each iter of the warping procedure) –> (default 3%)

tol

tolerance criterion on the weighting function to exit the loop (default 1%)

template.est

text string giving choices for the template estimation method

n.out

number of abscissa points on which w(x) is estimated (default 500)

iter.max

maximum number of iterations of the clustering loop (default 50)

vignette

boolean (should the algorithm progress be reported?)

Value

A list, with elements:

template

matrix (dim=K x n.out) with the final cluster templates

temp.abscissa

vector (length=n.out) of the abscissa values on which the template is defined

labels

vector (length=n) of the cluster assignments

warping

matrix (dim=n x 2) with the intercept (1st column) and slope (2nd column) of the estimated warping function for each of the n curves

reg.abscissa

matrix (dim=n x n.out) of each of the n curves registered abscissa

distance

vector (length=n) of each curve's final distance to the assigned cluster template

w

vector (length=n.out) of the estimated weighting function w(x)

x.bcss

vector (length=n.out) of the final point-wise between-cluster sum-of-squares

Note

data:

1. assumed to be a vectorized version of the functional data AFTER smoothing

2. when using the H1 functional measure, assumed to include the functions FIRST DERIVATIVES

3. when using the H1 functional measure, it supports multidimensional functions R -> R^d, then data can be an array (n x p x d)]

funct.measure: 'H1' only supported with alignment

clust.method: 'pam' and 'hier' only supported for the case of NO ALIGNMENT

m.prop: needs to be a proportion for compatibility with alignment, values > 1 not supported

tuning.m: tuning only supported for the case of NO ALIGNMENT

tuning.par:

• mbound must be lower than 1; the minimal value tested is 0

• nperm > 50 is unadvisable for computational reasons

perc: 5% is already extreme; don't set this above 8-10%

template.est:

1. only supported with H1 measure + ALIGNMENT

2. currently 2 choices are supported:'raw' or 'loess'. 'raw' just computes the vector means across functions (default choice); 'loess' estimates the template via the R loess function

Examples

set.seed(8988327)
x <- seq(0, 1, len = 500)
out <- generate.data.FV17(50, x)
result <- SparseFunClust(out$data, x, K = 2, do.alignment = FALSE)
str(result)