FisherEM (version 1.2)

fem: The Fisher-EM algorithm

Description

Fem is a subspace clustering method. 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,init='random',maxit=100,eps=1e-6,Tinit=c(),model='AkjBk',
      kernel='',graph=F,Hess=F,method='SVD',l1=0.3,l2=0,nbit=2)

Arguments

Y

contains the data matrix (without NAs)

K

the number of clusters

init

the kind of initialization of the Fisher-EM algorithm. There are 3 options: "random" for a randomized initialization, "kmeans" for an initialization by the traditional kmeans algorithm or "user" for a chosen initialization for which the parameter Tinit ne

maxit

the maximum number of iterations before the stop of the Fisher-EM algorithm.

eps

the threshold for the stop of the Fisher-EM algorithm.

Tinit

a n x K matrix which contains posterior probabilities: each line corresponds to an individual

model

the kind of Discriminative Latent Mixture model. 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

kernel

enables to deal with the n < p problem. By default, no kernel ' ' is used. But the user has also the choice between 3 options for the kernel: 'linear', 'sigmoid' or 'rbf'.

graph

if TRUE, the clustered data are plotted on the 2 first discriminative axes fitted by the Fisher-EM algorithm.

Hess

if TRUE, the Hessian matrix is computed.

method

corresponds to 3 different methods ('SVD', 'REG', 'GS') for the fitting of the projection matrix associated to the discriminative subspace. The 'Fisher' method is used by default. If the option method='sparse' is used, then the loadings of the projection

l1

is a l1 penalty term: the figure is comprised between 0.1 (very sparse loadings of the projection matrix) and 1 (no sparsity). This option has to be used with method='sparse'.

l2

is a l2 penalty term.

nbit

number of iterations for fitting the sparse loadings at each update of the projection matrix.

Value

• A list is returned:
• cls
  the group membership of each individual estimated by the Fisher-EM algorithm
• P
  the posterior probabilities of each individual for each group
• prms
  lists of parameters of the mixture model fitted by the Fisher-EM algorithm.
• U
  projection matrix
• aic
  Akaike criterion
• bic
  Bayesian Information criterion
• icl
  Integrated Completed Likelihood criterion
• loglik
  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
• Hess
  the Hessian matrix if Hess = TRUE
• method
  Method used

References

Charles Bouveyron and Camille Brunet, Simultaneous model-based clustering and visualization in the Fisher discriminative subspace, Statistics and Computing, 22(1), 301-324.

Charles Bouveyron, Camille Brunet (2012), "Discriminative variable selection for clustering with the sparse Fisher-EM algorithm", preprint Hal n-00685183.

See Also

plot.fem, evalEM

Examples

data(iris)
res1 = fem(iris[,-5],3,model='AkB')
res1$U # print the loadings of the projection matrix 

## For a sparse case:
res2 = fem(iris[,-5],3,model='AkB',method='sparse', l1=0.2)
res2$U #print the loadings of the projection matrix