EM Algorithm for Model-Based Clustering of Finite Mixture Gaussian Distribution

Description

EMCluster provides EM algorithms and several efficient initialization methods for model-based clustering of finite mixture Gaussian distribution with unstructured dispersion in both of unsupervised and semi-supervised clustering.

Details

The install command is simply as

> R CMD INSTALL EMCluster_0.2-0.tar.gz

from a command mode or

R> install.packages("EMCluster")

inside an R session.

Author(s)

Wei-Chen Chen wccsnow@gmail.com and Ranjan Maitra.

References

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

See Also

init.EM, emcluster.

Examples

## Not run: 
demo(allinit, 'EMCluster', ask = F, echo = F)
demo(allinit_ss, 'EMCluster', ask = F, echo = F)

## End(Not run)

All Internal Functions of EMCluster

Description

All internal functions are for testing and can be utilized by advanced developers with caution.

Author(s)

Wei-Chen Chen wccsnow@gmail.com and Ranjan Maitra.

References

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

Assign Class Id

Description

This function assigns cluster id to each observation in x according to the desired model emobj or specified parameters pi, Mu, and LTSigma.

Usage

  assign.class(x, emobj = NULL, pi = NULL, Mu = NULL, LTSigma = NULL,
               lab = NULL, return.all = TRUE)

Arguments

Details

This function are based either an input emobj or inputs pi, Mu, and LTSigma to assign class id to each observation of x.

If lab is submitted, then the observation with label id greater 0 will not be assigned new class.

Value

This function returns a list containing mainly two new variables: nc (length K numbers of observations in each class) and class (length n class id).

Author(s)

Wei-Chen Chen wccsnow@gmail.com and Ranjan Maitra.

References

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

See Also

init.EM, emcluster.

Examples

library(EMCluster, quietly = TRUE)
set.seed(1234)
x2 <- da2$da

ret <- init.EM(x2, nclass = 2)
ret.new <- assign.class(x2, ret, return.all = FALSE)
str(ret.new)

Convert Matrices in Different Format

Description

These utility functions are to convert matrices in different formats.

Usage

LTSigma2variance(x)
variance2LTSigma(x)
LTsigma2var(x1, p = NULL)
var2LTsigma(x1)
class2Gamma(class)
Gamma2class(Gamma)

Arguments

Details

LTSigma2variance converts LTSigma format to 3D array, and variance2LTSigma is the inversion function.

LTsigma2var converts LTsigma format to a matrix, and var2LTsigma is the inversion function. Note that LTsigma is one component of LTSigma.

class2Gamma converts id to a Gamma matrix where with probability 1 for the cluster where the observation belongs to, and Gamma2class converts posterior to cluster id where largest posterior is picked for each observation.

Value

A vector/matrix/array is returned.

Author(s)

Wei-Chen Chen wccsnow@gmail.com and Ranjan Maitra

References

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

See Also

init.EM, emcluster.

Examples

## Not run: 
library(EMCluster, quietly = TRUE)
x <- da2$LTSigma
class <- da2$class

y <- LTSigma2variance(x)
str(y)
y <- variance2LTSigma(y)
str(y)
sum(x != y)

Gamma <- class2Gamma(class)
class.new <- Gamma2class(Gamma)
sum(class != class.new)

## End(Not run)

Dataset for demonstrations

Description

There are four small datasets to test and demonstrate EMCluster.

Usage

da1
da2
da3

Format

da1, da2, da3 are in list.

Details

da1 has 500 observations in two dimensions da1$da$x and da1$da$y, and they are in 10 clusters given in da1$class.

da2 has 2,500 observations in two dimensions, too. The true parameters are given in da1$pi, da1$Mu, and da1$LTSigma. There are 40 clusters given in da1$class for this dataset.

da3 is similar to da2, but with lower overlaps between clusters.

Author(s)

Wei-Chen Chen wccsnow@gmail.com and Ranjan Maitra.

References

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

EM Algorithm for model-based clustering

Description

These are core functions of EMCluster performing EM algorithm for model-based clustering of finite mixture multivariate Gaussian distribution with unstructured dispersion.

Usage

emcluster(x, emobj = NULL, pi = NULL, Mu = NULL, LTSigma = NULL,
          lab = NULL, EMC = .EMC, assign.class = FALSE)
shortemcluster(x, emobj = NULL, pi = NULL, Mu = NULL,
               LTSigma = NULL, maxiter = 100, eps = 1e-2)
simple.init(x, nclass = 1)

Arguments

Details

The emcluster mainly performs EM iterations starting from the given parameters emobj without other initializations.

The shortemcluster performs short-EM iterations as described in init.EM.

Value

The emcluster returns 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.

The shortemcluster also returns an object emobj with class emret which is the best of several random initializations.

The simple.init utilizes rand.EM to obtain a simple initial.

Author(s)

Wei-Chen Chen wccsnow@gmail.com and Ranjan Maitra.

References

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

See Also

init.EM, e.step, m.step, .EMControl.

Examples

library(EMCluster, quietly = TRUE)
set.seed(1234)
x1 <- da1$da

emobj <- simple.init(x1, nclass = 10)
emobj <- shortemcluster(x1, emobj)
summary(emobj)

ret <- emcluster(x1, emobj, assign.class = TRUE)
summary(ret)

EM Control Generator and Controller

Description

The .EMControl generates an EM control (.EMC) controlling the options and conditions of EM algorithms, i.e. this function generate a default template. One can either modify .EMC or employ this function to control EM algorithms. By default, .EMC, .EMC.Rnd, and .EC.Rndp are three native controllers as the EMCluster is loaded.

Usage

.EMControl(alpha = 0.99, short.iter = 200, short.eps = 1e-2,
    fixed.iter = 1, n.candidate = 3,
    em.iter = 1000, em.eps = 1e-6, exhaust.iter = 5)
.EMC
.EMC.Rnd
.EMC.Rndp

Arguments

Details

exhaust.iter and fixed.iter are used to control the iterations of initialization procedures.

short.iter and short.eps are used to control the short-EM iterations.

em.iter and em.eps are used to control the long-EM iterations.

Moeover, short.eps and em.eps are for checking convergence of the iterations.

Value

This function returns a list as .EMC by default.

The .EMC.Rnd is equal to .EMControl(short.eps = Inf) and usually used by the rand.EM method.

The .EMC.Rndp is equal to .EMControl(fixed.iter = 5) where each random initials run 5 EM iterations in the rand.EM method.

Author(s)

Wei-Chen Chen wccsnow@gmail.com and Ranjan Maitra.

References

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

See Also

init.EM, emcluster.

Examples

library(EMCluster, quietly = TRUE)

.EMC <- .EMControl()
.EMC.Rnd <- .EMControl(short.eps = Inf)
.EMC.Rndp <- .EMControl(fixed.iter = 5)

Information Criteria for Model-Based Clustering

Description

These functions are tools for compute information criteria for the fitted models.

Usage

em.ic(x, emobj = NULL, pi = NULL, Mu = NULL, LTSigma = NULL,
      llhdval = NULL)
em.aic(x, emobj = NULL, pi = NULL, Mu = NULL, LTSigma = NULL)
em.bic(x, emobj = NULL, pi = NULL, Mu = NULL, LTSigma = NULL)
em.clc(x, emobj = NULL, pi = NULL, Mu = NULL, LTSigma = NULL)
em.icl(x, emobj = NULL, pi = NULL, Mu = NULL, LTSigma = NULL)
em.icl.bic(x, emobj = NULL, pi = NULL, Mu = NULL, LTSigma = NULL)

Arguments

Details

The em.ic calls all other functions to compute AIC (em.aic), BIC (em.bic), CLC (em.clc), ICL (em.icl), and ICL.BIC (em.icl.bic). All are useful information criteria for model selections, mainly choosing number of cluster.

Value

em.ic returns a list containing all other information criteria for given the data x and the desired model emobj.

Author(s)

Wei-Chen Chen wccsnow@gmail.com and Ranjan Maitra

References

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

See Also

init.EM.

Examples

library(EMCluster, quietly = TRUE)
x2 <- da2$da

emobj <- list(pi = da2$pi, Mu = da2$Mu, LTSigma = da2$LTSigma)
em.ic(x2, emobj = emobj)

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);

Arguments

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.

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.

Author(s)

Wei-Chen Chen wccsnow@gmail.com and Ranjan Maitra.

References

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

See Also

emcluster, .EMControl.

Examples

## Not run: 
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)

## End(Not run)

Jaccard Index

Description

This function returns the Jaccard index for binary ids.

Usage

Jaccard.Index(x, y)

Arguments

Details

All ids, x and y, should be either 0 (not active) or 1 (active). Any value other than 1 will be converted to 0.

Value

Return the value of Jaccard index.

Author(s)

Wei-Chen Chen wccsnow@gmail.com and Ranjan Maitra.

References

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

Examples

library(EMCluster, quietly = TRUE)

x.id <- c(1, 1, 1, 0, 0, 0, 3, 3, 3)
y.id <- c(0, 1, 0, 1, 1, 1, 0, 1, 1)

Jaccard.Index(x.id, y.id)

Likelihood Mixture Test (LMT) Functions of EMCluster

Description

All likelihood mixture test (LMT) functions are for testing and can be utilized by advanced developers with caution.

Currently, these are only for workflows.

Author(s)

Wei-Chen Chen wccsnow@gmail.com and Ranjan Maitra.

References

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

Likelihood Mixture Tests

Description

This function test two mixture Gaussian models with unstructured covariance matrix and different numbers of clusters.

Usage

lmt(emobj.0, emobj.a, x, tau = 0.5, n.mc.E.delta = 1000,
    n.mc.E.chi2, verbose = FALSE)

Arguments

Details

This function calls several subroutines to compute information, likelihood ratio statistics, degrees of freedom, non-centrality of chi-squared distributions ... etc. Based on Monte Carlo methods to estimate parameters of likelihood mixture tests, this function return a p-value for testing H0: emobj.0 v.s. Ha: emobj.a.

Value

A list of class lmt are returned.

Author(s)

Wei-Chen Chen wccsnow@gmail.com and Ranjan Maitra.

References

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

See Also

init.EM.

Examples

## Not run: 
library(EMCluster, quietly = TRUE)
set.seed(1234)

x <- as.matrix(iris[, 1:4])
p <- ncol(x)
min.n <- p * (p + 1) / 2
.EMC$short.iter <- 200

ret.2 <- init.EM(x, nclass = 2, min.n = min.n, method = "Rnd.EM")
ret.3 <- init.EM(x, nclass = 3, min.n = min.n, method = "Rnd.EM")
ret.4 <- init.EM(x, nclass = 4, min.n = min.n, method = "Rnd.EM")

(lmt.23 <- lmt(ret.2, ret.3, x))
(lmt.34 <- lmt(ret.3, ret.4, x))
(lmt.24 <- lmt(ret.2, ret.4, x))

## End(Not run)

Density of (Mixture) Multivariate Normal Distribution

Description

These functions are tools for compute density of (mixture) multivariate Gaussian distribution with unstructured dispersion.

Usage

dmvn(x, mu, LTsigma, log = FALSE)
dlmvn(x, mu, LTsigma, log = TRUE)
dmixmvn(x, emobj = NULL, pi = NULL, Mu = NULL, LTSigma = NULL, log = FALSE)
logL(x, emobj = NULL, pi = NULL, Mu = NULL, LTSigma = NULL)

Arguments

Details

The dmvn and dlmvn compute density and log density of multivariate distribution.

The dmixmvn computes density of mixture multivariate distribution and is based either an input emobj or inputs pi, Mu, and LTSigma to assign class id to each observation of x.

The logL returns the value of the observed log likelihood function of the parameters at the current values of the parameters pi, Mu, and LTSigma, with the suplied data matrix x.

Value

A density value is returned.

Author(s)

Wei-Chen Chen wccsnow@gmail.com and Ranjan Maitra.

References

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

See Also

init.EM, emcluster.

Examples

library(EMCluster, quietly = TRUE)
x2 <- da2$da
x3 <- da3$da

emobj2 <- list(pi = da2$pi, Mu = da2$Mu, LTSigma = da2$LTSigma)
emobj3 <- list(pi = da3$pi, Mu = da3$Mu, LTSigma = da3$LTSigma)

logL(x2, emobj = emobj2)
logL(x3, emobj = emobj3)

dmixmvn2 <- dmixmvn(x2, emobj2)
dmixmvn3 <- dmixmvn(x3, emobj3)

dlmvn(da2$da[1,], da2$Mu[1,], da2$LTSigma[1,])
log(dmvn(da2$da[1,], da2$Mu[1,], da2$LTSigma[1,]))

Other Initializations

Description

Two more functions with different initialization method.

Usage

starts.via.svd(x, nclass = 1, method = c("em", "kmeans"),
               EMC = .EMC)
emgroup(x, nclass = 1, EMC = .EMC)

Arguments

Details

The starts.via.svd utilizes SVD to initial parameters, and the emgroup runs the EM algorithm starting from the initial.

Value

The starts.via.svd returns an object with class svd, and the emgroup returns and object emobj with class emret.

Author(s)

Wei-Chen Chen wccsnow@gmail.com and Ranjan Maitra.

References

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

See Also

init.EM, .EMControl.

Examples

library(EMCluster, quietly = TRUE)
set.seed(1234)
x1 <- da1$da

emobj <- emgroup(x1, nclass = 10)
summary(emobj)

ret.0 <- starts.via.svd(x1, nclass = 10, method = "kmeans")
summary(ret.0)

Plot Two Dimensional Data with clusters

Description

The functions plot two dimensional data for clusters.

Usage

plotem(emobj, x, main = NULL, xlab = NULL, ylab = NULL,
       ...)
plot2d(x, emobj = NULL, k = NULL, color.pch = 1,
       append.BN = TRUE, ...)

Arguments

Details

This a simple x-y lot.

Value

A plot is returned.

Author(s)

Wei-Chen Chen wccsnow@gmail.com and Ranjan Maitra.

References

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

See Also

init.EM, emcluster.

Examples

## Not run: 
library(EMCluster, quietly = TRUE)
x1 <- da1$da

ret.1 <- starts.via.svd(x1, nclass = 10, method = "em")
summary(ret.1)

plotem(ret.1, x1)

## End(Not run)

Plot Multivariate Data

Description

The function plots multivariate data for clusters as the parallel coordinates plot.

Usage

plotmd(x, class = NULL, xlab = "Variables", ylab = "Data", ...)

Arguments

Details

This a simplified parallel coordinate plot.

Value

A plot is returned.

Author(s)

Wei-Chen Chen wccsnow@gmail.com and Ranjan Maitra.

References

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

See Also

init.EM, emcluster.

Examples

## Not run: 
library(EMCluster, quietly = TRUE)
set.seed(1234)

x <- as.matrix(iris[, 1:4], ncol = 4)
ret <- em.EM(x, nclass = 5)
plotmd(x, ret$class)

## End(Not run)

Plot Contour

Description

The function plots multivariate data on 2D plane with contour. Typically, the contour is built via projection pursuit or SVD algorithms, such as project.on.2d().

Usage

plotppcontour(da, Pi, Mu, S, class, class.true = NULL, n.grid = 128,
    angle = 0, xlab = "", ylab = "", main = "")

Arguments

Details

This function plots projection output of project.on.2d().

da, Mu, and S are projected by some projection matrices obtained via SVD or projection pursuit algorithms. The projection is made on a 2D plane in the direction in which clusters of data x are most distinguishable to visualize.

Value

A 2D projection plot is returned.

Note

Only distinguishable for up to 7 clusters due to the limited color schemes.

Author(s)

Wei-Chen Chen wccsnow@gmail.com and Ranjan Maitra.

References

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

See Also

project.on.2d().

Examples

## Not run: 
library(EMCluster, quietly = TRUE)
library(MASS, quietly = TRUE)
set.seed(1234)

### Crabs.
x <- as.matrix(crabs[, 4:8])
ret <- init.EM(x, nclass = 4, min.n = 20)
ret.proj <- project.on.2d(x, ret)

### Plot.
pdf("crabs_ppcontour.pdf", height = 5, width = 5)
plotppcontour(ret.proj$da, ret.proj$Pi, ret.proj$Mu, ret.proj$S,
              ret.proj$class, angle = pi/6, main = "Crabs K = 4")
dev.off()

## End(Not run)

Post I Information Functions of EMCluster

Description

All post I information functions are for computing relative quantities and can be utilized by advanced developers with caution.

Currently, these are only for workflows.

Author(s)

Wei-Chen Chen wccsnow@gmail.com and Ranjan Maitra.

References

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

Functions for Printing or Summarizing Objects According to Classes

Description

Several classes are declared in EMCluster, and these are functions to print and summary objects.

Usage

## S3 method for class 'emret'
print(x, digits = max(4, getOption("digits") - 3), ...)
## S3 method for class 'emret'
summary(object, ...)
## S3 method for class 'svd'
summary(object, ...)

Arguments

Details

These are useful functions for summarizing and debugging.

Value

The results will cat or print on the STDOUT by default.

Author(s)

Wei-Chen Chen wccsnow@gmail.com and Ranjan Maitra.

References

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

See Also

init.EM, emcluster, starts.via.svd.

Examples

## Not run: 
library(EMCluster, quietly = TRUE)
x2 <- da2$da

emobj <- list(pi = da2$pi, Mu = da2$Mu, LTSigma = da2$LTSigma)
eobj <- e.step(x2, emobj = emobj)
emobj <- m.step(x2, emobj = eobj)
summary(emobj)

ret <- starts.via.svd(x2, nclass = 10, method = "kmeans")
summary(ret)

## End(Not run)

Produce Projection on 2D

Description

The function projects multivariate data on 2D plane which can be displayed by plotppcontour() later.

Usage

project.on.2d(x, emobj = NULL, pi = NULL, Mu = NULL,
    LTSigma = NULL, class = NULL, method = c("PP", "SVD"))

Arguments

Details

This function produces projection outputs of x and emobj.

Value

A projection is returned which is a list contains

• da is a n \times 2 projected matrix of x.

• Pi is the original proportion emobj$pi of length K.

• Mu is a K \times 2 projected matrix of emboj$Mu.

• S is a 2 \times 2 \times K projected array of emboj$LTSigma.

• class is the original class id emobj$class.

• proj.mat is the projection matrix of dimension p \times 2.

Author(s)

Wei-Chen Chen wccsnow@gmail.com and Ranjan Maitra.

References

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

See Also

project.on.2d().

Examples

## Not run: 
library(EMCluster, quietly = TRUE)
set.seed(1234)

### Iris.
x <- as.matrix(iris[, 1:4])
ret <- init.EM(x, nclass = 3, min.n = 30)
ret.proj <- project.on.2d(x, ret)

### Plot.
pdf("iris_ppcontour.pdf", height = 5, width = 5)
plotppcontour(ret.proj$da, ret.proj$Pi, ret.proj$Mu, ret.proj$S,
              ret.proj$class, main = "Iris K = 3")
dev.off()

## End(Not run)

Rand Index and Adjusted Rand Index

Description

This function returns the Rand index and the adjusted Rand index for given true class ids and predicted class ids.

Usage

RRand(trcl, prcl, lab = NULL)

Arguments

Details

All ids, trcl and prcl, should be positive integers and started from 1 to K, and the maximums are allowed to be different.

lab used in semi-supervised clustering contains the labels which are known before clustering. It should be positive integer and started from 1 for labeled data and 0 for unlabeled data.

Value

Return a Class RRand contains Rand index and adjusted Rand index.

Author(s)

Wei-Chen Chen wccsnow@gmail.com and Ranjan Maitra.

References

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

Examples

library(EMCluster, quietly = TRUE)

true.id <- c(1, 1, 1, 2, 2, 2, 3, 3, 3)
pred.id <- c(2, 1, 2, 1, 1, 1, 2, 1, 1)
label   <- c(0, 0, 0, 0, 1, 0, 2, 0, 0)

RRand(true.id, pred.id)
RRand(true.id, pred.id, lab = label)

Recolor Classification IDs

Description

These functions return new classification IDs.

Usage

recolor(id.target, id.class, scatter.class = NULL, scatter.target = NULL)
rematch(tg.id, cl.id)
recode(id)

Arguments

Details

The function recolor colors id.target in accordance with the most likely candidate in id.class. Note that if scatter is present, then the class given by 0 is represented as scatter and it is assumed to be the same for both classifications.

The function rematch returns a list as id.trcl and id.prcl. It is the heart of the recolor function and is usually called from recolor.

The function recode reoders classes to eliminate group ids without any members. It is assumed that the group ids are integers.

Value

See Details.

Author(s)

Ranjan Maitra.

References

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

Examples

## Not run: 
library(EMCluster, quietly = TRUE)

true.id <- c(1, 1, 1, 2, 2, 2, 3, 3, 3)
pred.id <- c(2, 1, 2, 1, 1, 1, 2, 1, 1)

recolor(pred.id, true.id)

## End(Not run)

Single E- and M-step

Description

These functions are single E- and M-step of EM algorithm for model-based clustering of finite mixture multivariate Gaussian distribution with unstructured dispersion.

Usage

e.step(x, emobj = NULL, pi = NULL, Mu = NULL, LTSigma = NULL,
          norm = TRUE)
m.step(x, emobj = NULL, Gamma = NULL, assign.class = FALSE)

Arguments

Details

These two functions are mainly used in debugging for development and post process after model fitting.

Value

The e.step returns a list contains Gamma, the posterior probabilities if norm=TRUE, otherwise it contains component densities. This is one E-step and Gamma is used to update emobj in the M-step next.

The m.step returns a new emobj according to the Gamma from the E-step above.

Author(s)

Wei-Chen Chen wccsnow@gmail.com and Ranjan Maitra.

References

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

See Also

init.EM.

Examples

library(EMCluster, quietly = TRUE)
x2 <- da2$da

emobj <- list(pi = da2$pi, Mu = da2$Mu, LTSigma = da2$LTSigma)
eobj <- e.step(x2, emobj = emobj)
emobj <- m.step(x2, emobj = eobj)
emobj