Package 'SparseFunClust'

CER function

Description

Given two partitions P and Q, cer(P, Q) measures how well they agree, the lower the better. It is rigorously defined as the proportion of pairwise disagreements in the two partitions (i.e., how many, out of all the possible couples of elements in the sample, are localized in the same cluster in one partition and in a different one in the other partition).

Usage

cer(P, Q)

Arguments

P	first vector of cluster assignments (length n)
Q	second vector of cluster assignments (length n)

Value

The CER index, which is a number between 0 and 1, and also equal to 1 - Rand index (Rand, 1971), a popular measure of the goodness of a clustering.

References

Rand, W. M. (1971). Objective criteria for the evaluation of clustering methods. Journal of the American Statistical association, 66(336), 846-850.

Examples

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

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Data generation: no-misalignment case

Description

this function generates a set of simulated functional data in 2 clusters that reproduce the examples in Simulations 2A and 2B in Floriello & Vitelli (2017).

Usage

generate.data.FV17(n, x, paramC = 0.5, plots = FALSE)

Arguments

n	number of curves
x	curves' domain
paramC	proportion of cluster overlap (default 0.5, as in Simulation 2A)
plots	boolean; should plots be drawn (FALSE default)

Value

a list including:

• $data matrix (n x length(x)) with the simulated data

• $true.partition vector (length = n) with the true cluster assignments

Examples

generate.data.FV17(5, seq(0, 1, len = 3))

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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)

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