fdakma (version 1.1.1)

kma.compare: kma.compare runs kma with different numbers of clusters and different warping methods.

Description

In kma.compare the user can specify multiple values for n.clust and warping.method. kma.compare runs the K-Mean Alignment algorithm (kma function) for all couples of specified values of n.clust and warping.method.

Usage

kma.compare(x, y0 = NULL, y1 = NULL, n.clust = c(1, 2),warping.method = c("NOalignment", "shift", "dilation", "affine"),similarity.method = "d1.pearson", center.method = "k-means", seeds = NULL,optim.method = "L-BFGS-B", span = 0.15, t.max = 0.1, m.max = 0.1, n.out = NULL,tol = 0.01, fence = TRUE, iter.max = 100, show.iter = 0, plot.graph = 0,nstart = 1, return.all = FALSE)

Arguments

x

matrix n.func X grid.size or vector grid.size: the abscissa values where each function is evaluated. n.func: number of functions in the dataset. grid.size: maximal number of abscissa values where each functi

y0

matrix n.func X grid.size or array n.func X grid.size X d: evaluations of the set of original functions on the abscissa grid x. n.func: number of functions in the dataset. grid.size

y1

matrix n.func X grid.size or array n.func X grid.size X d: evaluations of the set of original functions first derivatives on the abscissa grid x. Default value of y1 is NULL

n.clust

vector: n.clust contains the numbers of clusters with which kma.compare runs kma function. Default value is c(1,2). See details.

warping.method

vector: warping.method contains the types of alignment with which kma.compare runs kma function. See details.

similarity.method

character: required similarity measure. Possible choices are: 'd0.pearson', 'd1.pearson', 'd0.L2', 'd1.L2', 'd0.L2.centered', 'd1.L2.centered'. Default value is 'd1.pearso

center.method

character: type of clustering method to be used. Possible choices are: 'k-means' and 'k-medoids'. Default value is 'k-means'.

seeds

vector max(n.clust) or matrix nstart X n.clust: indexes of the functions to be used as initial centers. If it is a matrix, each row contains the indexes of the initial centers of one of the nstart initializations; i

optim.method

character: optimization method chosen to find the best warping functions at each iteration. Possible choices are: 'L-BFGS-B' and 'SANN'. See optim function for details. Default method is 'L

span

scalar: the span to be used for the loess procedure in the center estimation step when center.method='k-means'. Default value is 0.15. If center.method='k-medoids' value of span is i

t.max

scalar: t.max controls the maximal allowed shift, at each iteration, in the alignment procedure with respect to the range of curve domains. t.max must be such that 0 (e.g., t.max=0.1 means that shift

m.max

scalar: m.max controls the maximal allowed dilation, at each iteration, in the alignment procedure. m.max must be such that 0 (e.g., m.max=0.1 means that dilation is bounded, at each iteration, betwe

n.out

scalar: the desired length of the abscissa for computation of the similarity indexes and the centers. Default value is round(1.1*grid.size).

tol

scalar: the algorithm stops when the increment of similarity of each function with respect to the corrispondent center is lower than tol. Default value is 0.01.

fence

boolean: if fence=TRUE a control is activated at the end of each iteration. The aim of the control is to avoid shift/dilation outlighers with respect to their computed distributions. If fence=TRUE the running time can increase co

iter.max

scalar: maximum number of iterations in the k-mean alignment cycle. Default value is 100.

show.iter

boolean: if show.iter=TRUE kma shows the current iteration of the algorithm. Default value is FALSE.

plot.graph

boolean: if plot.graph=TRUE, kma.compare plots a graphic with the means of similarity indexes as ordinate and the number of clusters as abscissa. Default value is FALSE.

nstart

scalar: number of initializations with different seeds. Default value is 1.

return.all

boolean: if return.all=TRUE the results of all the nstart initializations are return; the output is a list of length nstart. If return.all=FALSE only the best result is provided (the one with higher mean

Value

• The function output is a list containing the following elements:
• Result.NOalignment
  list of outputs of kma function with warping.type='NOalignment'. The sublist Result.NOalignment[[k]] corresponds to the results when number of clusters is n.clust[k]. Note that if 'NOalignment' is not chosen as warping.type, then Result.NOalignment will be NULL.
• Result.shift
  list of outputs of kma function with warping.type='shift'. The sublist Result.shift[[k]] corresponds to the results when number of clusters is n.clust[k]. Note that if 'shift' is not chosen as warping.type, then Result.shift will be NULL.
• Result.dilation
  list of outputs of kma function with warping.type='dilation'. The sublist Result.dilation[[k]] corresponds to the results when number of clusters is n.clust[k]. Note that if 'dilation' is not chosen as warping.type, then Result.dilation will be NULL.
• Result.affine
  list of outputs of kma function with warping.type='affine'. The sublist Result.affine[[k]] corresponds to the results when number of clusters is n.clust[k]. Note that if 'affine' is not chosen as warping.type, then Result.affine will be NULL.
• n.clust
  as input.
• mean.similarity.NOalignment
  vector: mean similarity indexes of functions after running kma function with all elements of n.clust and warping.type='NOalignment'. mean.similarity.NOalignment contains the ordinates of the black curve ("without alignment" in the legend) of the output graphic of the kma.compare function (if plot.graph=1).
• mean.similarity.shift
  vector: mean similarity indexes of curves after running kma function with all elements of n.clust and warping.type='shift'. mean.similarity.shift contains the ordinates of the blue curve ("shift" in the legend) of the output graphic of the kma.compare function (if plot.graph=1).
• mean.similarity.dilation
  vector: mean similarity indexes of curves after running kma function with all elements of n.clust and warping.type='dilation'. mean.similarity.dilation contains the ordinates of the green curve ("dilation" in the legend) of the output graphic of the kma.compare function (if plot.graph=1).
• mean.similarity.affine
  vector: mean similarity indexes of curves after running kma function with all elements of n.clust and warping.type='affine'. mean.similarity.affine contains the ordinates of the orange curve ("affine" in the legend) of the output graphic of the kma.compare function (if plot.graph=1).

Details

Example of use: if n.clust=c(1,2,3) and warping.method=c('shift','affine'), kma.compare runs kma function with number of clusters equal to 1, 2 and 3 using warping.method='shift' and warping.method='affine'.

References

Sangalli, L.M., Secchi, P., Vantini, S., Vitelli, V., 2010. "K-mean alignment for curve clustering". Computational Statistics and Data Analysis, 54, 1219-1233.

See Also

kma, kma.similarity, fdakma, kma.data, kma.show.results

Examples

data(kma.data)

x <- kma.data$x # abscissas
y0 <- kma.data$y0 # evaluations of original functions
y1 <- kma.data$y1 # evaluations of original function first derivatives

# Plot of original functions
matplot(t(x),t(y0), type='l', xlab='x', ylab='orig.func')
title ('Original functions')

# Plot of original function first derivatives
matplot(t(x),t(y1), type='l', xlab='x', ylab='orig.deriv')
title ('Original function first derivatives')


# Example: results of kma function with 3 different 
# numbers of clusters (1,2,3) combined with four alignment
# methods ('NOalignment' by default, 'shift', 'dilation',
# 'affine') and considering 'd1.pearson' as similarity.method.
kma.compare_example <- kma.compare (
  x=x, y0=y0, y1=y1, n.clust = 1:3, 
  warping.method = c('affine'), 
  similarity.method = 'd1.pearson',
  center.method = 'k-means', 
  seeds = c(1,21,30),
  plot.graph=1)

names (kma.compare_example)

# To see results for kma function with n.clust=2 
# and warping.method='affine'.
kma.show.results (kma.compare_example$Result.affine[[2]])


# Labels assigned to each function for the 
# kma function with n.clust=2 and warping.method='affine'.
kma.compare_example$Result.affine[[2]]$labels