teigen: Model-Based Clustering and Classification with the Multivariate t Distribution

Description

Fits mixtures of multivariate t-distributions (with eigen-decomposed covariance structure) via the expectation conditional-maximization algorithm under a clustering or classification paradigm.

Details

Author(s)

Jeffrey L. Andrews, Jaymeson R. Wickins, Nicholas M. Boers, Paul D. McNicholas

Maintained by: Jeffrey L. Andrews <jeff.andrews@ubc.ca>

References

Andrews JL, Wickins JR, Boers NM, and McNicholas PD (2018). “teigen: An R package for model-based clustering and classification via the multivariate t distribution” Journal of Statistical Software 83(7), 1–32.

Andrews JL and McNicholas PD (2012). “Model-based clustering, classification, and discriminant analysis with the multivariate t-distribution: The tEIGEN family” Statistics and Computing 22(5), 1021–1029.

Andrews JL, McNicholas PD, and Subedi S (2011) “Model-based classification via mixtures of multivariate t-distributions” Computational Statistics and Data Analysis 55, 520–529.

See Also

teigen for main function

Indian Chronic Kidney Disease Data

Description

This is a cleaned up version of the Chronic Kidney Disease data set available from the UCI learning repository:

http://archive.ics.uci.edu/ml/datasets/Chronic_Kidney_Disease

Nominal variables have been removed and rows with missing values recorded on the remaining variables have also been removed.

Usage

data("ckd")

Format

This data frame contains 203 rows (observations) and 13 columns (variables): 1.) ckdclass: There are 2 classes, ckd or notckd 2.) age: in years 3.) blood.pressure: in mm/Hg 4.) blood.glucose.random: in mgs/dl 5.) blood.urea: in mgs/dl 6.) serum.creatinine: in mgs/dl 7.) sodium: in mEq/L 8.) potassium: in mEq/L 9.) hemoglobin: in gms 10.) packed.cell.volume 11.) white.blood.cell.count: in cells/cmm 12.) red.blood.cell.count: in cells/cmm

Source

See http://archive.ics.uci.edu/ml/datasets/Chronic_Kidney_Disease for original source.

References

Lichman, M. (2013). UCI Machine Learning Repository [http://archive.ics.uci.edu/ml]. Irvine, CA: University of California, School of Information and Computer Science.

Examples

data(ckd)
hclustres <- cutree(hclust(dist(ckd[,-1])),3)
table(ckd[,1], hclustres)

plot.teigen: Plotting Function for tEIGEN Objects

Description

For multivariate data, outputs marginal contour or uncertainty plots to the graphics device for objects of class teigen. For univariate data, plot a univariate density plot.

Usage

## S3 method for class 'teigen'
plot(x, xmarg = 1, ymarg = 2, res = 200, 
	what = c("contour", "uncertainty"),	alpha = 0.4, col = rainbow(x$G),
	pch = 21, cex = NULL, bg = NULL, lty = 1, uncmult = 0,
	levels = c(seq(0.01, 1, by = 0.025), 0.001), 
	main=NULL, xlab=NULL, draw.legend=TRUE, ...) 

Arguments

Details

"contour" plots the marginal distribution of the mixture distribution. For univariate data, or if ymarg is NULL, a univariate marginal is provided that includes the kernel density estimate from density(), the mixture distribution, and colour-coded component densities.

"uncertainty" plots the uncertainty of each observation's classification - the larger the point, the more uncertainty associated with that observation. Uncertainty in this context refers to the probability that the observation arose from the mixture component specified by the colour in the plot rather than the other components.

The default behavior of the function is to specify both plot types. This opens up an interactive menu from which the user may switch back and forth between both graphs. On exiting the menu, the graph that was plotted last will remain in the open device.

Author(s)

Jeffrey L. Andrews, Jaymeson R. Wickins, Nicholas M. Boers

See Also

teigen

Examples

set.seed(2521)
tfaith <- teigen(faithful, models = "CCCC", Gs = 1:4, verbose = FALSE)

plot(tfaith, what = "uncertainty", cex = 1.5, uncmult = 1.5)
plot(tfaith, what = "contour")
plot(tfaith, ymarg = NULL, lwd = 2)

predict.teigen: Predicting Function for tEIGEN Objects

Description

Provides the fuzzy probability matrix and classification vector for inputted observations assuming the model provided by the teigen object.

Usage

## S3 method for class 'teigen'
predict(object, newdata=NULL, modelselect="BIC", ...) 

Arguments

Details

Note that the scale argument from the teigen object is passed along to the predictfunction. See examples below for plotting.

Value

Author(s)

Jeffrey L. Andrews

See Also

teigen

Examples

set.seed(2521)
ind <- sample(1:nrow(faithful), 20)
set.seed(256)
tfaith_unscaled <- teigen(faithful[-ind,], models = "UUUU", Gs = 2, verbose = FALSE, scale=FALSE)
pred_unscaled <- predict(tfaith_unscaled, faithful[ind,])
set.seed(256)
tfaith_scaled <- teigen(faithful[-ind,], models = "UUUU", Gs = 2, verbose = FALSE, scale=TRUE)
pred_scaled <- predict(tfaith_scaled, faithful[ind,])
identical(pred_unscaled$classification, pred_scaled$classification)

##Plotting UNSCALED
plot(tfaith_unscaled, what="contour")
points(faithful[ind,1], faithful[ind,2], pch=15)
plotcolours <- rainbow(tfaith_unscaled$G)
points(faithful[ind,1], faithful[ind,2], pch=20, col=plotcolours[pred_unscaled$classification])

##Plotting SCALED
plot(tfaith_scaled, what="contour")
points((faithful[ind,1]-tfaith_scaled$info$scalemeans[1])/tfaith_scaled$info$scalesd[1],
       (faithful[ind,2]-tfaith_scaled$info$scalemeans[2])/tfaith_scaled$info$scalesd[2],
       pch=15)
plotcolours <- rainbow(tfaith_scaled$G)
points((faithful[ind,1]-tfaith_scaled$info$scalemeans[1])/tfaith_scaled$info$scalesd[1],
       (faithful[ind,2]-tfaith_scaled$info$scalemeans[2])/tfaith_scaled$info$scalesd[2],
       pch=20, col=plotcolours[pred_scaled$classification])

print.teigen: Print Function for tEIGEN Objects

Description

Outputs short, concise information on the teigen object: BIC value, best model, and best group. Same info for ICL is output if it disagrees with the BIC value.

Usage

## S3 method for class 'teigen'
print(x, ...)

Arguments

Author(s)

Jaymeson R. Wickins, Nicholas M. Boers, Jeffrey L. Andrews

See Also

teigen

summary.teigen: Summary Function for tEIGEN Objects

Description

Summary method for class "teigen". Gives summary information.

Usage

## S3 method for class 'teigen'
summary(object, ...)
## S3 method for class 'summary.teigen'
print(x, ...)

Arguments

Value

An object of class "summary.teigen" that has a specialized print method. The object is a list containing the BIC and ICL values, as well as loglik value, model number and group number for the BIC. These values are also stored for ICL if it disagrees with the BIC value.

Author(s)

Jaymeson R. Wickins, Nicholas M. Boers, Jeffrey L. Andrews

See Also

teigen

teigen: Function for Model-Based Clustering and Classification with the Multivariate t Distribution

Description

Fits multivariate t-distribution mixture models (with eigen-decomposed covariance structure) to the given data within a clustering paradigm (default) or classification paradigm (by giving either training index or percentage of data taken to be known). Can be run in parallel.

Usage

teigen(x, Gs = 1:9, models = "all", init = "kmeans", scale = TRUE, dfstart = 50, 
	known = NULL, training = NULL, gauss = FALSE, dfupdate = "approx", 
	eps = c(0.001, 0.1), verbose = TRUE, maxit = c(Inf,Inf), 
	convstyle = "aitkens", parallel.cores = FALSE, 
	ememargs = list(25, 5, "UUUU", "hard"))

Arguments

Details

Model specification (via the models argument) follows either the nomenclature discussed in Andrews and McNicholas (2012), or via the nomenclature popularized in other packages. In both cases, the nomenclature refers to the decomposition and constraints on the covariance matrix:

\Sigma_g = \lambda_g D_g A_g D_g'

The nomenclature from Andrews and McNicholas (2012) gives four letters, each letter referring to (in order) \lambda, D, A, and the degrees of freedom. Possible letters are "U" for unconstrained, "C" for constrained (across groups), and "I" for when the parameter is replaced by the appropriately sized identity matrix (where applicable). As an example, the string "UICC" would refer to the model where \Sigma_g = \lambda_g A with degrees of freedom held equal across groups.

The alternative nomenclature describes (in order) the volume (\lambda), shape (A), orientation (D), and degrees of freedom in terms of "V"ariable, "E"qual, or the "I"dentity matrix. The example model discussed in the previous paragraph would then be called by "VEIE".

Possible univariate models are c("univUU", "univUC", "univCU", "univCC") where the first capital letter describes "U"nconstrained or "C"onstrained variance and the second capital letter refers to the degrees of freedom. Once again, "V"ariable or "E"qual can replace U and C, but this time the orders match between the nomenclatures.

As many models as desired can be selected and ran via the vector supplied to models. More commonly, subsets can be called by the following character strings: "all" runs all 28 tEIGEN models (default), "dfunconstrained" runs the 14 unconstrained degrees of freedom models, "dfconstrained" runs the 14 constrained degrees of freedom models, "mclust" runs the 10 MCLUST models using the multivariate Gaussian distribution rather than the multivariate t, "gaussian" is similar but includes four further mixture models than MCLUST, "univariate" runs the univariate models - will automatically be called if one of the previous shortcuts is used on univariate data.

Note that adding "alt" to the beginning of those previously mentioned characters strings will run the same models, but return results with the V-E-I nomenclature.

Also note that for G=1, several models are equivalent (for example, UUUU and CCCC). Thus, for G=1 only one model from each set of equivalent models will be run.

Value

Author(s)

Jeffrey L. Andrews, Jaymeson R. Wickins, Nicholas M. Boers, Paul D. McNicholas

References

Andrews JL and McNicholas PD. “Model-based clustering, classification, and discriminant analysis with the multivariate t-distribution: The tEIGEN family” Statistics and Computing 22(5), 1021–1029.

Andrews JL, McNicholas PD, and Subedi S (2011) “Model-based classification via mixtures of multivariate t-distributions” Computational Statistics and Data Analysis 55, 520–529.

See Also

See package manual tEIGEN

Examples

###Note that only one model is run for each example
###in order to reduce computation time

#Clustering old faithful data with hard random start
tfaith <- teigen(faithful, models="UUUU", Gs=1:3, init="hard")
plot(tfaith, what = "uncertainty")
summary(tfaith)

#Clustering old faithful with hierarchical starting values
initial_list <- list()
clustree <- hclust(dist(faithful))
for(i in 1:3){
	initial_list[[i]] <- cutree(clustree,i)
}
tfaith <- teigen(faithful, models="CUCU", Gs=1:3, init=initial_list)
print(tfaith)

#Classification with the iris data set
#Introducing NAs is not required; this is to illustrate a `true' classification scenario
irisknown <- iris[,5]
irisknown[134:150] <- NA
triris <- teigen(iris[,-5], models="CUUU", init="uniform", known=irisknown)

##Parallel examples:
###Note: parallel.cores set to 2 in order to comply
###with CRAN submission policies (set to higher
###number or TRUE to automatically use all available cores)

#Clustering old faithful data with tEIGEN
tfaith <- teigen(faithful, models="UUUU",
parallel.cores=2, Gs=1:3, init="hard")
plot(tfaith, what = "contour")

#Classification with the iris data set 
irisknown <- iris[,5]
irisknown[sample(1:nrow(iris),50)] <- NA
tiris <- teigen(iris[,-5], parallel.cores=2, models="CUUU",
init="uniform", known=irisknown)
tiris$tab