| Title: | EM Algorithm for Model-Based Clustering of Finite Mixture Gaussian Distribution |
|---|---|
| Description: | 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 learning. |
| Authors: | Wei-Chen Chen [aut, cre], Ranjan Maitra [aut], Volodymyr Melnykov [ctb], Dan Nettleton [ctb], David Faden [ctb], Rouben Rostamian [ctb], R Core team [ctb] (some functions are modified from the R source code) |
| Maintainer: | Wei-Chen Chen <[email protected]> |
| License: | Mozilla Public License 2.0 |
| Version: | 0.2-16 |
| Built: | 2024-11-08 06:43:34 UTC |
| Source: | CRAN |
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.
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.
Wei-Chen Chen [email protected] and Ranjan Maitra.
https://www.stat.iastate.edu/people/ranjan-maitra
## Not run: demo(allinit, 'EMCluster', ask = F, echo = F) demo(allinit_ss, 'EMCluster', ask = F, echo = F) ## End(Not run)## Not run: demo(allinit, 'EMCluster', ask = F, echo = F) demo(allinit_ss, 'EMCluster', ask = F, echo = F) ## End(Not run)
This function assigns cluster id to each observation in x
according to the desired model emobj or specified
parameters pi, Mu, and LTSigma.
assign.class(x, emobj = NULL, pi = NULL, Mu = NULL, LTSigma = NULL, lab = NULL, return.all = TRUE)assign.class(x, emobj = NULL, pi = NULL, Mu = NULL, LTSigma = NULL, lab = NULL, return.all = TRUE)
x |
the data matrix, dimension |
emobj |
the desired model which is a list mainly contains |
pi |
the mixing proportion, length |
Mu |
the centers of clusters, dimension |
LTSigma |
the lower triangular matrices of dispersion, dimension
|
lab |
labeled data for semi-supervised clustering,
length |
return.all |
if returning with a whole |
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.
This function returns a list containing mainly two new variables:
nc (length numbers of observations in each class) and
class (length class id).
Wei-Chen Chen [email protected] and Ranjan Maitra.
https://www.stat.iastate.edu/people/ranjan-maitra
library(EMCluster, quietly = TRUE) set.seed(1234) x2 <- da2$da ret <- init.EM(x2, nclass = 2) ret.new <- assign.class(x2, ret, return.all = FALSE) str(ret.new)library(EMCluster, quietly = TRUE) set.seed(1234) x2 <- da2$da ret <- init.EM(x2, nclass = 2) ret.new <- assign.class(x2, ret, return.all = FALSE) str(ret.new)
These utility functions are to convert matrices in different formats.
LTSigma2variance(x) variance2LTSigma(x) LTsigma2var(x1, p = NULL) var2LTsigma(x1) class2Gamma(class) Gamma2class(Gamma)LTSigma2variance(x) variance2LTSigma(x) LTsigma2var(x1, p = NULL) var2LTsigma(x1) class2Gamma(class) Gamma2class(Gamma)
x |
a matrix/array to be converted, the dimension could be
|
x1 |
a vector/matrix to be converted, the length and dimension could be
|
p |
dimension of matrix. |
class |
id of clusters for each observation, length |
Gamma |
containing posterior probabilities if normalized,
otherwise containing component densities weighted by
mixing proportion, dimension |
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.
A vector/matrix/array is returned.
Wei-Chen Chen [email protected] and Ranjan Maitra
https://www.stat.iastate.edu/people/ranjan-maitra
## 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)## 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)
There are four small datasets to test and demonstrate EMCluster.
da1 da2 da3da1 da2 da3
da1, da2, da3 are in list.
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.
Wei-Chen Chen [email protected] and Ranjan Maitra.
https://www.stat.iastate.edu/people/ranjan-maitra
These are core functions of EMCluster performing EM algorithm for model-based clustering of finite mixture multivariate Gaussian distribution with unstructured dispersion.
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)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)
x |
the data matrix, dimension |
emobj |
the desired model which is a list mainly contains |
pi |
the mixing proportion, length |
Mu |
the centers of clusters, dimension |
LTSigma |
the lower triangular matrices of dispersion,
|
lab |
labeled data for semi-supervised clustering,
length |
EMC |
the control for the EM iterations. |
assign.class |
if assigning class id. |
maxiter |
maximum number of iterations. |
eps |
convergent tolerance. |
nclass |
the desired number of clusters, |
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.
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.
Wei-Chen Chen [email protected] and Ranjan Maitra.
https://www.stat.iastate.edu/people/ranjan-maitra
init.EM, e.step, m.step,
.EMControl.
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)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)
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.
.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.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
alpha |
only used in |
short.iter |
number of short-EM steps, default = 200. |
short.eps |
tolerance of short-EM steps, default = 1e-2. |
fixed.iter |
fixed iterations of EM for "RndEM" initialization, default = 1. |
n.candidate |
reserved for other initialization methods (unimplemented). |
em.iter |
maximum number of long-EM steps, default = 1000. |
em.eps |
tolerance of long-EM steps, default = 1e-6. |
exhaust.iter |
number of iterations for "exhaustEM" initialization, default = 5. |
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.
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.
Wei-Chen Chen [email protected] and Ranjan Maitra.
https://www.stat.iastate.edu/people/ranjan-maitra
library(EMCluster, quietly = TRUE) .EMC <- .EMControl() .EMC.Rnd <- .EMControl(short.eps = Inf) .EMC.Rndp <- .EMControl(fixed.iter = 5)library(EMCluster, quietly = TRUE) .EMC <- .EMControl() .EMC.Rnd <- .EMControl(short.eps = Inf) .EMC.Rndp <- .EMControl(fixed.iter = 5)
These functions are tools for compute information criteria for the fitted models.
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)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)
x |
the data matrix, dimension |
emobj |
the desired model which is a list mainly contains |
pi |
the mixing proportion, length |
Mu |
the centers of clusters, dimension |
LTSigma |
the lower triangular matrices of dispersion,
|
llhdval |
the total log likelihood value of |
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.
em.ic returns a list containing all other information criteria
for given the data x and the desired model emobj.
Wei-Chen Chen [email protected] and Ranjan Maitra
https://www.stat.iastate.edu/people/ranjan-maitra
library(EMCluster, quietly = TRUE) x2 <- da2$da emobj <- list(pi = da2$pi, Mu = da2$Mu, LTSigma = da2$LTSigma) em.ic(x2, emobj = emobj)library(EMCluster, quietly = TRUE) x2 <- da2$da emobj <- list(pi = da2$pi, Mu = da2$Mu, LTSigma = da2$LTSigma) em.ic(x2, emobj = emobj)
These functions perform initializations (including em.EM and RndEM) followed by the EM iterations for model-based clustering of finite mixture multivariate Gaussian distribution with unstructured dispersion in both of unsupervised and semi-supervised clusterings.
init.EM(x, nclass = 1, lab = NULL, EMC = .EMC, stable.solution = TRUE, min.n = NULL, min.n.iter = 10, method = c("em.EM", "Rnd.EM")) em.EM(x, nclass = 1, lab = NULL, EMC = .EMC, stable.solution = TRUE, min.n = NULL, min.n.iter = 10) rand.EM(x, nclass = 1, lab = NULL, EMC = .EMC.Rnd, stable.solution = TRUE, min.n = NULL, min.n.iter = 10) exhaust.EM(x, nclass = 1, lab = NULL, EMC = .EMControl(short.iter = 1, short.eps = Inf), method = c("em.EM", "Rnd.EM"), stable.solution = TRUE, min.n = NULL, min.n.iter = 10);init.EM(x, nclass = 1, lab = NULL, EMC = .EMC, stable.solution = TRUE, min.n = NULL, min.n.iter = 10, method = c("em.EM", "Rnd.EM")) em.EM(x, nclass = 1, lab = NULL, EMC = .EMC, stable.solution = TRUE, min.n = NULL, min.n.iter = 10) rand.EM(x, nclass = 1, lab = NULL, EMC = .EMC.Rnd, stable.solution = TRUE, min.n = NULL, min.n.iter = 10) exhaust.EM(x, nclass = 1, lab = NULL, EMC = .EMControl(short.iter = 1, short.eps = Inf), method = c("em.EM", "Rnd.EM"), stable.solution = TRUE, min.n = NULL, min.n.iter = 10);
x |
the data matrix, dimension |
nclass |
the desired number of clusters, |
lab |
labeled data for semi-supervised clustering,
length |
EMC |
the control for the EM iterations. |
stable.solution |
if returning a stable solution. |
min.n |
restriction for a stable solution, the minimum number of observations for every final clusters. |
min.n.iter |
restriction for a stable solution, the minimum number of iterations for trying a stable solution. |
method |
an initialization method. |
The init.EM calls either em.EM if method="em.EM" or
rand.EM if method="Rnd.EM".
The em.EM has two steps: short-EM has loose convergent
tolerance controlled by .EMC$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$short.iter, and
second starts from the best of the random result
(in terms of log likelihood) and run to convergence.
The lab is only for the semi-supervised clustering, and it contains
pre-labeled indices between 1 and for labeled observations.
Observations with index 0 is non-labeled and has to be clustered by
the EM algorithm. Indices will be assigned by the results of the EM
algorithm. See demo(allinit_ss,'EMCluster') for details.
The exhaust.EM also calls the init.EM with different
EMC and perform exhaust.iter times of EM algorithm
with different initials. The best result is returned.
These functions return an object emobj with class emret
which can be used in post-process or other functions such as
e.step, m.step, assign.class, em.ic,
and dmixmvn.
Wei-Chen Chen [email protected] and Ranjan Maitra.
https://www.stat.iastate.edu/people/ranjan-maitra
## Not run: library(EMCluster, quietly = TRUE) set.seed(1234) x <- da1$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)## 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)
This function returns the Jaccard index for binary ids.
Jaccard.Index(x, y)Jaccard.Index(x, y)
x |
true binary ids, 0 or 1. |
y |
predicted binary ids, 0 or 1. |
All ids, x and y, should be either 0 (not active) or 1 (active).
Any value other than 1 will be converted to 0.
Return the value of Jaccard index.
Wei-Chen Chen [email protected] and Ranjan Maitra.
https://www.stat.iastate.edu/people/ranjan-maitra
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)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)
This function test two mixture Gaussian models with unstructured covariance matrix and different numbers of clusters.
lmt(emobj.0, emobj.a, x, tau = 0.5, n.mc.E.delta = 1000, n.mc.E.chi2, verbose = FALSE)lmt(emobj.0, emobj.a, x, tau = 0.5, n.mc.E.delta = 1000, n.mc.E.chi2, verbose = FALSE)
emobj.0 |
a |
emobj.a |
a |
x |
the data matrix, dimension |
tau |
proportion of null and alternative hypotheses. |
n.mc.E.delta |
number of Monte Carlo simulations for expectation of delta (difference of logL). |
n.mc.E.chi2 |
number of Monte Carlo simulations for expectation of chisquare statistics. |
verbose |
if verbose. |
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.
A list of class lmt are returned.
Wei-Chen Chen [email protected] and Ranjan Maitra.
https://www.stat.iastate.edu/people/ranjan-maitra
## 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)## 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)
All likelihood mixture test (LMT) functions are for testing and can be utilized by advanced developers with caution.
Currently, these are only for workflows.
Wei-Chen Chen [email protected] and Ranjan Maitra.
https://www.stat.iastate.edu/people/ranjan-maitra
These functions are tools for compute density of (mixture) multivariate Gaussian distribution with unstructured dispersion.
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)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)
x |
the data matrix, dimension |
mu |
the centers of clusters, length |
LTsigma |
the lower triangular matrices of dispersion, length
|
log |
if logarithm returned. |
emobj |
the desired model which is a list mainly contains |
pi |
the mixing proportion, length |
Mu |
the centers of clusters, dimension |
LTSigma |
the lower triangular matrices of dispersion,
|
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.
A density value is returned.
Wei-Chen Chen [email protected] and Ranjan Maitra.
https://www.stat.iastate.edu/people/ranjan-maitra
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$LTSigma[1,]))library(EMCluster, quietly = TRUE) x2 <- da2$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$LTSigma[1,]))
Two more functions with different initialization method.
starts.via.svd(x, nclass = 1, method = c("em", "kmeans"), EMC = .EMC) emgroup(x, nclass = 1, EMC = .EMC)starts.via.svd(x, nclass = 1, method = c("em", "kmeans"), EMC = .EMC) emgroup(x, nclass = 1, EMC = .EMC)
x |
the data matrix, dimension |
nclass |
the desired number of clusters, |
method |
method with the svd initializations. |
EMC |
the control for the EM iterations. |
The starts.via.svd utilizes SVD to initial parameters,
and the emgroup runs the EM algorithm starting from the
initial.
The starts.via.svd returns an object with class svd,
and the emgroup returns and object emobj with class
emret.
Wei-Chen Chen [email protected] and Ranjan Maitra.
https://www.stat.iastate.edu/people/ranjan-maitra
library(EMCluster, quietly = TRUE) set.seed(1234) x1 <- da1$da emobj <- emgroup(x1, nclass = 10) summary(emobj) ret.0 <- starts.via.svd(x1, nclass = 10, method = "kmeans") summary(ret.0)library(EMCluster, quietly = TRUE) set.seed(1234) x1 <- da1$da emobj <- emgroup(x1, nclass = 10) summary(emobj) ret.0 <- starts.via.svd(x1, nclass = 10, method = "kmeans") summary(ret.0)
The functions plot two dimensional data for clusters.
plotem(emobj, x, main = NULL, xlab = NULL, ylab = NULL, ...) plot2d(x, emobj = NULL, k = NULL, color.pch = 1, append.BN = TRUE, ...)plotem(emobj, x, main = NULL, xlab = NULL, ylab = NULL, ...) plot2d(x, emobj = NULL, k = NULL, color.pch = 1, append.BN = TRUE, ...)
emobj |
the desired model which is a list mainly contains |
x |
the data matrix, dimension |
main |
title of plot. |
xlab |
label of x-axis. |
ylab |
label of y-axis. |
... |
other parameters to the plot. |
k |
index for symbols. |
color.pch |
color and style for symbols. |
append.BN |
if appending bivariate normal ellipsoid. |
This a simple x-y lot.
A plot is returned.
Wei-Chen Chen [email protected] and Ranjan Maitra.
https://www.stat.iastate.edu/people/ranjan-maitra
## Not run: library(EMCluster, quietly = TRUE) x1 <- da1$da ret.1 <- starts.via.svd(x1, nclass = 10, method = "em") summary(ret.1) plotem(ret.1, x1) ## End(Not run)## Not run: library(EMCluster, quietly = TRUE) x1 <- da1$da ret.1 <- starts.via.svd(x1, nclass = 10, method = "em") summary(ret.1) plotem(ret.1, x1) ## End(Not run)
The function plots multivariate data for clusters as the parallel coordinates plot.
plotmd(x, class = NULL, xlab = "Variables", ylab = "Data", ...)plotmd(x, class = NULL, xlab = "Variables", ylab = "Data", ...)
x |
the data matrix, dimension |
class |
class id for all observations. |
xlab |
label of x-axis. |
ylab |
label of y-axis. |
... |
other parameters to the plot. |
This a simplified parallel coordinate plot.
A plot is returned.
Wei-Chen Chen [email protected] and Ranjan Maitra.
https://www.stat.iastate.edu/people/ranjan-maitra
## Not run: library(EMCluster, quietly = TRUE) set.seed(1234) x <- as.matrix(iris[, 1:4], ncol = 4) ret <- em.EM(x, nclass = 5) plotmd(x, ret$class) ## End(Not run)## 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$class) ## End(Not run)
The function plots multivariate data on 2D plane with contour.
Typically, the contour is built via projection pursuit or SVD
algorithms, such as project.on.2d().
plotppcontour(da, Pi, Mu, S, class, class.true = NULL, n.grid = 128, angle = 0, xlab = "", ylab = "", main = "")plotppcontour(da, Pi, Mu, S, class, class.true = NULL, n.grid = 128, angle = 0, xlab = "", ylab = "", main = "")
da |
a projected data matrix, dimension |
Pi |
proportion, length |
Mu |
the projected centers of cluster, dimension |
S |
projected matrices of dispersion, dimension
|
class |
id of classifications, length |
class.true |
ture id of classifications if available, length |
n.grid |
number of grid points. |
angle |
a rotation angle ( |
xlab |
an option for |
ylab |
an option for |
main |
an option for |
This function plots projection output of project.on.2d().
da, Mu, and S are projected by some projection matrices
obtained via SVD or projection pursuit algorithms. The projection is made
on a 2D plane in the direction in which clusters of data x
are most distinguishable to visualize.
A 2D projection plot is returned.
Only distinguishable for up to 7 clusters due to the limited color schemes.
Wei-Chen Chen [email protected] and Ranjan Maitra.
https://www.stat.iastate.edu/people/ranjan-maitra
## Not run: library(EMCluster, quietly = TRUE) library(MASS, quietly = TRUE) set.seed(1234) ### Crabs. x <- as.matrix(crabs[, 4:8]) ret <- init.EM(x, nclass = 4, min.n = 20) ret.proj <- project.on.2d(x, ret) ### Plot. pdf("crabs_ppcontour.pdf", height = 5, width = 5) plotppcontour(ret.proj$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)## 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$class, angle = pi/6, main = "Crabs K = 4") dev.off() ## End(Not run)
All post I information functions are for computing relative quantities and can be utilized by advanced developers with caution.
Currently, these are only for workflows.
Wei-Chen Chen [email protected] and Ranjan Maitra.
https://www.stat.iastate.edu/people/ranjan-maitra
Several classes are declared in EMCluster, and these are functions to print and summary objects.
## S3 method for class 'emret' print(x, digits = max(4, getOption("digits") - 3), ...) ## S3 method for class 'emret' summary(object, ...) ## S3 method for class 'svd' summary(object, ...)## S3 method for class 'emret' print(x, digits = max(4, getOption("digits") - 3), ...) ## S3 method for class 'emret' summary(object, ...) ## S3 method for class 'svd' summary(object, ...)
x |
an object with the class attributes. |
digits |
for printing out numbers. |
object |
an object with the class attributes. |
... |
other possible options. |
These are useful functions for summarizing and debugging.
The results will cat or print on the STDOUT by default.
Wei-Chen Chen [email protected] and Ranjan Maitra.
https://www.stat.iastate.edu/people/ranjan-maitra
init.EM, emcluster, starts.via.svd.
## Not run: library(EMCluster, quietly = TRUE) x2 <- da2$da emobj <- list(pi = da2$pi, Mu = da2$Mu, LTSigma = da2$LTSigma) eobj <- e.step(x2, emobj = emobj) emobj <- m.step(x2, emobj = eobj) summary(emobj) ret <- starts.via.svd(x2, nclass = 10, method = "kmeans") summary(ret) ## End(Not run)## Not run: library(EMCluster, quietly = TRUE) x2 <- da2$da emobj <- list(pi = da2$pi, Mu = da2$Mu, LTSigma = da2$LTSigma) eobj <- e.step(x2, emobj = emobj) emobj <- m.step(x2, emobj = eobj) summary(emobj) ret <- starts.via.svd(x2, nclass = 10, method = "kmeans") summary(ret) ## End(Not run)
The function projects multivariate data on 2D plane which can be displayed
by plotppcontour() later.
project.on.2d(x, emobj = NULL, pi = NULL, Mu = NULL, LTSigma = NULL, class = NULL, method = c("PP", "SVD"))project.on.2d(x, emobj = NULL, pi = NULL, Mu = NULL, LTSigma = NULL, class = NULL, method = c("PP", "SVD"))
x |
the data matrix, dimension |
emobj |
the desired model which is a list mainly contains |
pi |
the mixing proportion, length |
Mu |
the centers of clusters, dimension |
LTSigma |
the lower triangular matrices of dispersion,
|
class |
id of classifications, length |
method |
either projection pursuit or singular value decomposition. |
This function produces projection outputs of x and emobj.
A projection is returned which is a list contains
da is a projected matrix of x.
Pi is the original proportion emobj$pi of
length .
Mu is a projected matrix of
emboj$Mu.
S is a projected array of
emboj$LTSigma.
class is the original class id emobj$class.
proj.mat is the projection matrix of dimension
.
Wei-Chen Chen [email protected] and Ranjan Maitra.
https://www.stat.iastate.edu/people/ranjan-maitra
## Not run: library(EMCluster, quietly = TRUE) set.seed(1234) ### Iris. x <- as.matrix(iris[, 1:4]) ret <- init.EM(x, nclass = 3, min.n = 30) ret.proj <- project.on.2d(x, ret) ### Plot. pdf("iris_ppcontour.pdf", height = 5, width = 5) plotppcontour(ret.proj$da, ret.proj$Pi, ret.proj$Mu, ret.proj$S, ret.proj$class, main = "Iris K = 3") dev.off() ## End(Not run)## 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)
This function returns the Rand index and the adjusted Rand index for given true class ids and predicted class ids.
RRand(trcl, prcl, lab = NULL)RRand(trcl, prcl, lab = NULL)
trcl |
true class ids. |
prcl |
predicted class ids. |
lab |
known ids for semi-supervised clustering. |
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.
Return a Class RRand contains Rand index and adjusted
Rand index.
Wei-Chen Chen [email protected] and Ranjan Maitra.
https://www.stat.iastate.edu/people/ranjan-maitra
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)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)
These functions return new classification IDs.
recolor(id.target, id.class, scatter.class = NULL, scatter.target = NULL) rematch(tg.id, cl.id) recode(id)recolor(id.target, id.class, scatter.class = NULL, scatter.target = NULL) rematch(tg.id, cl.id) recode(id)
id.target |
target class ids. |
id.class |
original class ids. |
scatter.class |
scatter class ids. |
scatter.target |
scatter target class ids. |
id |
class ids. |
tg.id |
target class ids. |
cl.id |
class ids. |
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.
See Details.
Ranjan Maitra.
https://www.stat.iastate.edu/people/ranjan-maitra
## 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)## 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)
These functions are single E- and M-step of EM algorithm for model-based clustering of finite mixture multivariate Gaussian distribution with unstructured dispersion.
e.step(x, emobj = NULL, pi = NULL, Mu = NULL, LTSigma = NULL, norm = TRUE) m.step(x, emobj = NULL, Gamma = NULL, assign.class = FALSE)e.step(x, emobj = NULL, pi = NULL, Mu = NULL, LTSigma = NULL, norm = TRUE) m.step(x, emobj = NULL, Gamma = NULL, assign.class = FALSE)
x |
the data matrix, dimension |
emobj |
the desired model which is a list mainly contains |
pi |
the mixing proportion, length |
Mu |
the centers of clusters, dimension |
LTSigma |
the lower triangular matrices of dispersion,
|
norm |
if returning normalized |
Gamma |
containing posterior probabilities if normalized,
otherwise containing component densities weighted by
mixing proportion, dimension |
assign.class |
if assigning class id. |
These two functions are mainly used in debugging for development and post process after model fitting.
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.
Wei-Chen Chen [email protected] and Ranjan Maitra.
https://www.stat.iastate.edu/people/ranjan-maitra
library(EMCluster, quietly = TRUE) x2 <- da2$da emobj <- list(pi = da2$pi, Mu = da2$Mu, LTSigma = da2$LTSigma) eobj <- e.step(x2, emobj = emobj) emobj <- m.step(x2, emobj = eobj) emobjlibrary(EMCluster, quietly = TRUE) x2 <- da2$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