funLBM {funLBM}

The functional latent block model

Description

The funLBM algorithm, proposed by Bouveyron et al. (2018) <doi:10.1111/rssc.12260>, allows to simultaneously cluster the rows and the columns of one or more data matrix where each entry of the matrix is a (univariate or multivariate) function or a time series.

Usage

funLBM(X, K, L, maxit = 50, burn = 25, basis.name = "fourier", nbasis = 15,
        nbinit = 1, gibbs.it = 3, display = FALSE, init = "funFEM", mc.cores = 1, ...)

Arguments

X

Univariate case: The data array (n x p x T) where each entry corresponds to the measure of one individual i, i=1,...,n, for a functional variable j, j=1,...,p, at point t, t=1,...,T. Multivariate case: a list of data array as described hereinabove with one data array by variable.

K

The number of row clusters,

L

The number of column clusters,

maxit

The maximum number of iterations of the SEM-Gibbs algorithm (default is 100),

burn

The number of of iterations of the burn-in period (default is 50),

basis.name

The name ('fourier' or 'spline') of the basis functions used for the decomposition of the functions (default is 'fourier'),

nbasis

Number of the basis functions used for the decomposition of the functions (default is 15),

nbinit

Number of initializations (default is 3),

gibbs.it

Number of Gibbs iterations (default is 3),

display

Binary value. If TRUE, information about the iterations is displayed,

init

The type of initialization: 'random', 'kmeans' or 'funFEM'. Default is 'kmeans',

mc.cores

The number of cores for parallel computing (default is 1),

...

Additional parameters to provide to sub-functions.

Value

The resulting object contains, in addition to call information:

prms

A list containing all fited parameters for the best model (according to ICL)

Z

The dummy matrix of row clustering

W

The dummy matrix of column clustering

row_clust

The group memberships of rows

col_clust

The group memberships of columns

allPrms

A list containing the fited parameters for all tested models

loglik

The log-likelihood of the best model

icl

The value of ICL for the best model

References

C. Bouveyron, L. Bozzi, J. Jacques and F.-X. Jollois, The Functional Latent Block Model for the Co-Clustering of Electricity Consumption Curves, Journal of the Royal Statistical Society, Series C, 2018 (https://doi.org/10.1111/rssc.12260).

Examples

## Univariate example: Co-clustering on simulated data
set.seed(12345)
X = simulateData(n = 30, p = 30, t = 15)
out = funLBM(X$data,K=4,L=3)

# Visualization of results
plot(out,type='blocks')
plot(out,type='proportions')
plot(out,type='means')

# Evaluating clustering results
ari(out$col_clust,X$col_clust)
ari(out$row_clust,X$row_clust)

## Multivariate example:
X = simulateData2(n = 50, p = 50, t = 15)
out = funLBM(list(X$data1,X$data2),K=4,L=3)

# Visualization of results
plot(out,type='blocks')
plot(out,type='proportions')
plot(out,type='means')

# Evaluating clustering results
ari(out$col_clust,X$col_clust)
ari(out$row_clust,X$row_clust)

## The following examples could take a few minutes to run
## and depend on the number of available CPU cores!

## Co-clustering on simulated data with parallel model selection
#X = simulateData(n = 30, p = 30, t = 15)
#out = funLBM(X$data,K=2:4,L=2:4,mc.cores = 4)

## Evaluating clustering results
#ari(out$col_clust,X$col_clust)
#ari(out$row_clust,X$row_clust)

## Co-clustering of Velib data
#data(Velib)
#out = funLBM(Velib$data,K=4,L=2)

## Visualization of results
#plot(out,type='blocks')
#plot(out,type='proportions')
#plot(out,type='means')