EMCluster (version 0.2-16)

Initialization and EM: Initialization and EM Algorithm

Description

These functions perform initializations (including em.EM and RndEM) followed by the EM iterations for model-based clustering of finite mixture multivariate Gaussian distribution with unstructured dispersion in both of unsupervised and semi-supervised clusterings.

Usage

init.EM(x, nclass = 1, lab = NULL, EMC = .EMC,
        stable.solution = TRUE, min.n = NULL, min.n.iter = 10,
        method = c("em.EM", "Rnd.EM"))
em.EM(x, nclass = 1, lab = NULL, EMC = .EMC,
      stable.solution = TRUE, min.n = NULL, min.n.iter = 10)
rand.EM(x, nclass = 1, lab = NULL, EMC = .EMC.Rnd,
        stable.solution = TRUE, min.n = NULL, min.n.iter = 10)
exhaust.EM(x, nclass = 1, lab = NULL,
           EMC = .EMControl(short.iter = 1, short.eps = Inf),
           method = c("em.EM", "Rnd.EM"),
           stable.solution = TRUE, min.n = NULL, min.n.iter = 10);

Value

These functions return an object emobj with class emret

which can be used in post-process or other functions such as

e.step, m.step, assign.class, em.ic, and dmixmvn.

Arguments

x

the data matrix, dimension \(n\times p\).

nclass

the desired number of clusters, \(K\).

lab

labeled data for semi-supervised clustering, length \(n\).

EMC

the control for the EM iterations.

stable.solution

if returning a stable solution.

min.n

restriction for a stable solution, the minimum number of observations for every final clusters.

min.n.iter

restriction for a stable solution, the minimum number of iterations for trying a stable solution.

method

an initialization method.

Author

Wei-Chen Chen and Ranjan Maitra.

Details

The init.EM calls either em.EM if method="em.EM" or rand.EM if method="Rnd.EM".

The em.EM has two steps: short-EM has loose convergent tolerance controlled by .EMC$short.eps and try several random initializations controlled by .EMC$short.iter, while long-EM starts from the best short-EM result (in terms of log likelihood) and run to convergence with a tight tolerance controlled by .EMC$em.eps.

The rand.EM also has two steps: first randomly pick several random initializations controlled by .EMC$short.iter, and second starts from the best of the random result (in terms of log likelihood) and run to convergence.

The lab is only for the semi-supervised clustering, and it contains pre-labeled indices between 1 and \(K\) for labeled observations. Observations with index 0 is non-labeled and has to be clustered by the EM algorithm. Indices will be assigned by the results of the EM algorithm. See demo(allinit_ss,'EMCluster') for details.

The exhaust.EM also calls the init.EM with different EMC and perform exhaust.iter times of EM algorithm with different initials. The best result is returned.

References

https://www.stat.iastate.edu/people/ranjan-maitra

See Also

emcluster, .EMControl.

Examples

if (FALSE) {
library(EMCluster, quietly = TRUE)
set.seed(1234)
x <- da1$da

ret.em <- init.EM(x, nclass = 10, method = "em.EM")
ret.Rnd <- init.EM(x, nclass = 10, method = "Rnd.EM", EMC = .EMC.Rnd)

emobj <- simple.init(x, nclass = 10)
ret.init <- emcluster(x, emobj, assign.class = TRUE)

par(mfrow = c(2, 2))
plotem(ret.em, x)
plotem(ret.Rnd, x)
plotem(ret.init, x)
}