mclust (version 4.1)

MclustDA: MclustDA discriminant analysis

Description

Discriminant analysis based on Gaussian finite mixture modeling.

Usage

MclustDA(data, class, G = NULL, modelNames = NULL, 
         modelType = c("MclustDA", "EDDA"), 
         prior = NULL, control = emControl(), 
         initialization = NULL, warn = FALSE, ...)

Arguments

data

A data frame or matrix giving the training data.

class

A vector giving the class labels for the observations in the training data.

G

An integer vector specifying the numbers of mixture components (clusters) for which the BIC is to be calculated within each class. The default is G = 1:5. A different set of mixture components for each class can be specified by p

modelNames

A vector of character strings indicating the models to be fitted by EM within each class (see the description in mclustModelNames). A different set of mixture models for each class ca

modelType

A character string specifying whether the models given in modelNames should fit a different number of mixture components and covariance structures for each class ("MclustDA", the default) or should be constrained

prior

The default assumes no prior, but this argument allows specification of a conjugate prior on the means and variances through the function priorControl.

control

A list of control parameters for EM. The defaults are set by the call emControl().

initialization

A list containing zero or more of the following components: [object Object],[object Object]

warn

A logical value indicating whether or not certain warnings (usually related to singularity) should be issued when estimation fails. The default is to suppress these warnings.

...

Further arguments passed to or from other methods.

Value

• An object of class "MclustDA" providing the optimal (according to BIC) mixture model. The details of the output components are as follows:
• call
  The matched call
• models
  A list of Mclust objects containing information on fitted model for each class.
• n
  The total number of observations in the data.
• d
  The dimension of the data.
• BIC
  All BIC values.
• bic
  Optimal BIC value.
• loglik
  Log-likelihood for the selected model.
• df
  Number of estimated parameters.

References

Bensmail, H., and Celeux, G. (1996) Regularized Gaussian Discriminant Analysis Through Eigenvalue Decomposition. Journal of the American Statistical Association, 91, 1743-1748. C. Fraley and A. E. Raftery (2002). Model-based clustering, discriminant analysis, and density estimation. Journal of the American Statistical Association, 97, 611-631.

C. Fraley, A. E. Raftery, T. B. Murphy and L. Scrucca (2012). mclust Version 4 for R: Normal Mixture Modeling for Model-Based Clustering, Classification, and Density Estimation. Technical Report No. 597, Department of Statistics, University of Washington.

Details

The "EDDA" method for discriminant analysis is described in Bensmail and Celeux (1996), while "MclustDA" in Fraley and Raftery (2002).

See Also

summary.MclustDA, plot.MclustDA, predict.MclustDA, classError

Examples

odd <- seq(from = 1, to = nrow(iris), by = 2)
even <- odd + 1
X.train <- iris[odd,-5]
Class.train <- iris[odd,5]
X.test <- iris[even,-5]
Class.test <- iris[even,5]

# common EEE covariance structure (which is essentially equivalent to linear discriminant analysis)
irisMclustDA <- MclustDA(X.train, Class.train, modelType = "EDDA", modelNames = "EEE")
summary(irisMclustDA, parameters = TRUE)
summary(irisMclustDA, newdata = X.test, newclass = Class.test)

# common covariance structure selected by BIC
irisMclustDA <- MclustDA(X.train, Class.train, modelType = "EDDA")
summary(irisMclustDA, parameters = TRUE)
summary(irisMclustDA, newdata = X.test, newclass = Class.test)

# general covariance structure selected by BIC
irisMclustDA <- MclustDA(X.train, Class.train)
summary(irisMclustDA, parameters = TRUE)
summary(irisMclustDA, newdata = X.test, newclass = Class.test)

plot(irisMclustDA)
plot(irisMclustDA, dimens = 3:4)
plot(irisMclustDA, dimens = 4)

plot(irisMclustDA, what = "classification")
plot(irisMclustDA, what = "classification", newdata = X.test)
plot(irisMclustDA, what = "classification", dimens = 3:4)
plot(irisMclustDA, what = "classification", newdata = X.test, dimens = 3:4)
plot(irisMclustDA, what = "classification", dimens = 4)
plot(irisMclustDA, what = "classification", dimens = 4, newdata = X.test)

plot(irisMclustDA, what = "train&test", newdata = X.test)
plot(irisMclustDA, what = "train&test", newdata = X.test, dimens = 3:4)
plot(irisMclustDA, what = "train&test", newdata = X.test, dimens = 4)

plot(irisMclustDA, what = "error")
plot(irisMclustDA, what = "error", dimens = 3:4)
plot(irisMclustDA, what = "error", dimens = 4)
plot(irisMclustDA, what = "error", newdata = X.test, newclass = Class.test)
plot(irisMclustDA, what = "error", newdata = X.test, newclass = Class.test, dimens = 3:4)
plot(irisMclustDA, what = "error", newdata = X.test, newclass = Class.test, dimens = 4)

# simulated 1D data
n <- 250 
set.seed(1)
triModal <- c(rnorm(n,-5), rnorm(n,0), rnorm(n,5))
triClass <- c(rep(1,n), rep(2,n), rep(3,n))
odd <- seq(from = 1, to = length(triModal), by = 2)
even <- odd + 1
triMclustDA <- MclustDA(triModal[odd], triClass[odd])
summary(triMclustDA, parameters = TRUE)
summary(triMclustDA, newdata = triModal[even], newclass = triClass[even])
plot(triMclustDA)
plot(triMclustDA, what = "classification")
plot(triMclustDA, what = "classification", newdata = triModal[even])
plot(triMclustDA, what = "train&test", newdata = triModal[even])
plot(triMclustDA, what = "error")
plot(triMclustDA, what = "error", newdata = triModal[even], newclass = triClass[even])

# simulated 2D cross data
data(cross)
odd <- seq(from = 1, to = nrow(cross), by = 2)
even <- odd + 1
crossMclustDA <- MclustDA(cross[odd,-1], cross[odd,1])
summary(crossMclustDA, parameters = TRUE)
summary(crossMclustDA, newdata = cross[even,-1], newclass = cross[even,1])
plot(crossMclustDA)
plot(crossMclustDA, what = "classification")
plot(crossMclustDA, what = "classification", newdata = cross[even,-1])
plot(crossMclustDA, what = "train&test", newdata = cross[even,-1])
plot(crossMclustDA, what = "error")
plot(crossMclustDA, what = "error", newdata =cross[even,-1], newclass = cross[even,1])