fem: The Fisher-EM algorithm

In FisherEM: The FisherEM Algorithm to Simultaneously Cluster and Visualize High-Dimensional Data

Description

The Fisher-EM algorithm is a subspace clustering method for high-dimensional data. It is based on the Gaussian Mixture Model and on the idea that the data lives in a common and low dimensional subspace. An EM-like algorithm estimates both the discriminative subspace and the parameters of the mixture model.

Usage

fem(Y,K=2:6,model='AkjBk',method='gs',crit='icl',maxit=50,eps=1e-4,init='kmeans',
                nstart=5,Tinit=c(),kernel='',disp=FALSE,mc.cores=(detectCores()-1),
                subset=NULL)

Arguments

Y	The data matrix. Categorical variables and missing values are not allowed.
K	An integer vector specifying the numbers of mixture components (clusters) among which the model selection criterion will choose the most appropriate number of groups. Default is 2:6.
model	A vector of discriminative latent mixture (DLM) models to fit. There are 12 different models: "DkBk", "DkB", "DBk", "DB", "AkjBk", "AkjB", "AkBk", "AkBk", "AjBk", "AjB", "ABk", "AB". The option "all" executes the Fisher-EM algorithm on the 12 DLM models and select the best model according to the maximum value obtained by model selection criterion.
method	The method used for the fitting of the projection matrix associated to the discriminative subspace. Three methods are available: 'gs' (Gram-Schmidt, the original proposition), 'svd' (based on SVD, fastest approach, it should be preferred on large data sets) and 'reg' (the Fisher criterion is rewritten as a regression problem). The 'gs' method is the default method since it is the most efficient one on most data sets.
crit	The model selection criterion to use for selecting the most appropriate model for the data. There are 3 possibilities: "bic", "aic" or "icl". Default is "icl".
maxit	The maximum number of iterations before the stop of the Fisher-EM algorithm.
eps	The threshold value for the likelihood differences to stop the Fisher-EM algorithm.
init	The initialization method for the Fisher-EM algorithm. There are 4 options: "random" for a randomized initialization, "kmeans" for an initialization by the kmeans algorithm, "hclust" for hierarchical clustering initialization or "user" for a specific initialization through the parameter "Tinit". Default is "kmeans". Notice that for "kmeans" and "random", several initializations are asked and the initialization associated with the highest likelihood is kept (see "nstart").
nstart	The number of restart if the initialization is "kmeans" or "random". In such a case, the initialization associated with the highest likelihood is kept.
Tinit	A n x K matrix which contains posterior probabilities for initializing the algorithm (each line corresponds to an individual).
kernel	It enables to deal with the n < p problem. By default, no kernel (" ") is used. But the user has the choice between 3 options for the kernel: "linear", "sigmoid" or "rbf".
disp	If true, some messages are printed during the clustering. Default is false.
mc.cores	The number of CPUs to use to fit in parallel the different models (only for non-Windows platforms). Default is the number of available cores minus 1.
subset	A positive integer defining the size of the subsample, default is NULL. In case of large data sets, it might be useful to fit a FisherEM model on a subsample of the data, and then use this model to predict cluster assignments for the whole data set. Notice that in, such a case, likelihood values and model selection criteria are computed for the subsample and not the whole data set.

Value

A list is returned:

K	The number of groups.
cls	the group membership of each individual estimated by the Fisher-EM algorithm.
P	the posterior probabilities of each individual for each group.
U	The loading matrix which determines the orientation of the discriminative subspace.
mean	The estimated mean in the subspace.
my	The estimated mean in the observation space.
prop	The estimated mixture proportion.
D	The covariance matrices in the subspace.
aic	The value of the Akaike information criterion.
bic	The value of the Bayesian information criterion.
icl	The value of the integrated completed likelihood criterion.
loglik	The log-likelihood values computed at each iteration of the FEM algorithm.
ll	the log-likelihood value obtained at the last iteration of the FEM algorithm.
method	The method used.
call	The call of the function.
plot	Some information to pass to the plot.fem function.
crit	The model selction criterion used.

Author(s)

Charles Bouveyron, Camille Brunet & Nicolas Jouvin.

References

Charles Bouveyron and Camille Brunet (2012), Simultaneous model-based clustering and visualization in the Fisher discriminative subspace, Statistics and Computing, 22(1), 301-324 <doi:10.1007/s11222-011-9249-9>.

Charles Bouveyron and Camille Brunet (2014), "Discriminative variable selection for clustering with the sparse Fisher-EM algorithm", Computational Statistics, vol. 29(3-4), pp. 489-513 <10.1007/s00180-013-0433-6>.

See Also

sfem, plot.fem, fem.ari, summary.fem

Examples

data(iris)
res = fem(iris[,-5],K=3,model='AkBk',method='gs')
res
plot(res)
fem.ari(res,as.numeric(iris$Species))
table(iris$Species,res$cls)


# Fit several models and numbers of groups (use by default on non-Windows
# platforms the parallel computing).
res = fem(iris[,-5],K=2:6,model='all',method='gs', mc.cores=2)
res
plot(res)
fem.ari(res,as.numeric(iris$Species))
table(iris$Species,res$cls)

FisherEM documentation built on Oct. 23, 2020, 8:08 p.m.