Density of a Multivariate Normal Distribution

Description

Intended for internal use only.

Usage

.dmvnorm(x, mu = NA, inv.sigma = NA, logDetCov = NA)

Arguments

Calculation of beta scaling parameters

Description

Calculates the scaling parameter for betascale.

Usage

b.scal(member, grouping, dis = FALSE, eps = 1e-04)

Arguments

Details

With betascale and b.scal, membership values of an argmax classifier are scaled in such a way, that the mean membership value of those values which are assigned to each class reflect the mean correctness rate of that values. This is done via qbeta and pbeta with the appropriate shape parameters. If dis is TRUE, it is tried that the variation of membership values is optimal for the accuracy relative to the correctness rate. If the variation of the membership values is less than eps, they are treated as one point and shifted towards the correctness rate.

Value

A list containing

Author(s)

Karsten Luebke (karsten.luebke@fom.de), Uwe Ligges

References

Garczarek, Ursula Maria (2002): Classification rules in standardized partition spaces. Dissertation, University of Dortmund. URL http://hdl.handle.net/2003/2789

See Also

betascale, e.scal

Examples

library(MASS)
data(B3)
pB3 <- predict(lda(PHASEN ~ ., data = B3))$posterior
pbB3 <- b.scal(pB3, B3$PHASEN, dis = TRUE)
ucpm(pB3, B3$PHASEN)
ucpm(pbB3$member, B3$PHASEN)

West German Business Cycles 1955-1994

Description

West German Business Cycles 1955-1994

Usage

data(B3)

Format

A data frame with 157 observations on the following 14 variables.

PHASEN

a factor with levels 1 (upswing), 2 (upper turning points), 3 (downswing), and 4 (lower turning points).

BSP91JW

GNP (y)

CP91JW

Private Consumption (y)

DEFRATE

Government deficit (percent of GNP)

EWAJW

Wage and salary earners (y)

EXIMRATE

Net exports as (percent of GNP)

GM1JW

Money supply M1 (y)

IAU91JW

Investment in equipment (y)

IB91JW

Investment in construction (y)

LSTKJW

Unit labor cost (y)

PBSPJW

GNP price deflator (y)

PCPJW

Consumer price index (y)

ZINSK

Short term interest rate (nominal)

ZINSLR

Long term interest rate (real)

where (y) stands for “yearly growth rates”.

Note that years and corresponding year quarters are given in the row names of the data frame, e.g. “1988,3” for the third quarter in 1988.

Details

The West German Business Cycles data (1955-1994) is analyzed by the project B3 of the SFB475 (Collaborative Research Centre “Reduction of Complexity for Multivariate Data Structures”), supported by the Deutsche Forschungsgemeinschaft.

Source

RWI (Rheinisch Westfälisches Institut für Wirtschaftsforschung), Essen, Germany.

References

Heilemann, U. and Münch, H.J. (1996): West German Business Cycles 1963-1994: A Multivariate Discriminant Analysis. CIRET–Conference in Singapore, CIRET–Studien 50.

See Also

For benchmarking on this data see also benchB3

Examples

data(B3)
summary(B3)

Benchmarking on B3 data

Description

Evaluates the performance of a classification method on the B3 data.

Usage

benchB3(method, prior = rep(1/4, 4), sv = "4", scale = FALSE, ...)

Arguments

Details

The performance of classification methods on cyclic data can be measured by a special form of cross-validation: Leave-One-Cycle-Out. That means that a complete cycle is used as test data and the others are used as training data. This is repeated for all complete cycles in the data.

Value

A list with elements

Author(s)

Karsten Luebke, karsten.luebke@fom.de

See Also

B3

Examples

perLDA <- benchB3("lda")
## Not run: 
## due to parameter optimization rda takes a while 
perRDA <- benchB3("rda")
library(rpart)
## rpart will not work with prior argument:
perRpart <- benchB3("rpart", prior = NULL)

## End(Not run)

Scale membership values according to a beta scaling

Description

Performs the scaling for beta scaling learned by b.scal.

Usage

betascale(betaobj, member)

Arguments

Details

See b.scal.

Value

A matrix with the scaled membership values.

See Also

b.scal, e.scal

Examples

library(MASS)
data(B3)
pB3 <- predict(lda(PHASEN ~ ., data = B3))$posterior
pbB3 <- b.scal(pB3, B3$PHASEN)
betascale(pbB3)

Calculation of transition probabilities

Description

Function to estimate the probabilities of a time series to stay or change the state.

Usage

calc.trans(x)

Arguments

Details

To estimate the transition probabilities the empirical frequencies are counted.

Value

The transition probabilities matrix. x[i,j] is the probability to change from state i to state j.

Author(s)

Karsten Luebke, karsten.luebke@fom.de

Examples

data(B3)
calc.trans(B3$PHASEN)

Lines from classborders to the center

Description

Function which constructs the lines from the borders between two classes to the center. To be used in connection with triplot and quadplot.

Usage

centerlines(n)

Arguments

Value

a matrix with n-columns.

Author(s)

Karsten Luebke, karsten.luebke@fom.de

See Also

triplot, quadplot

Examples

centerlines(3)
centerlines(4)

Classification scatterplot matrix

Description

Function to plot a scatterplot matrix with a classification result.

Usage

classscatter(formula, data, method, col.correct = "black", 
    col.wrong = "red", gs = NULL, ...)

Arguments

Value

The actual error rate.

Author(s)

Karsten Luebke, karsten.luebke@fom.de

See Also

plot

Examples

data(B3)
library(MASS)
classscatter(PHASEN ~ BSP91JW + EWAJW + LSTKJW, 
    data = B3, method = "lda")

Calculation of Condition Indices for Linear Regression

Description

Diagnosis of collinearity in X

Usage

cond.index(formula, data, ...)

Arguments

Details

Collinearities can inflate the variance of the estimated regression coefficients and numerical stability. The condition indices are calculated by the eigenvalues of the crossproduct matrix of the scaled but uncentered explanatory variables. Indices > 30 may indicate collinearity.

Value

A vector of the condition indices.

Author(s)

Andrea Preusser, Karsten Luebke (karsten.luebke@fom.de)

References

Belsley, D. , Kuh, E. and Welsch, R. E. (1979), Regression Diagnostics: Identifying Influential Data and Sources of Collinearity, John Wiley (New York)

See Also

stepclass, manova

Examples

data(Boston)
condition_medv <- cond.index(medv ~ ., data = Boston)
condition_medv

Function to identify groups of highly correlated variables for removing correlated features from the data for further analysis.

Description

A hierarchical clustering of variables using hclust is performed using 1 - the absolute correlation as a distance measure between tow variables.

Usage

corclust(x, cl = NULL, method = "complete")
## S3 method for class 'corclust'
plot(x, selection = "both", mincor = NULL, ...)

Arguments

Details

Each cluster consists of a set of correlated variables according to the chosen clustering criterion. The default criterion is ‘complete’. This choice is meaningful as it represents the minimum absolute correlation between all variables of a cluster.
The data set is split into numerics and factors two separate clustering models are built, depending on the variable type. For factors distances are computed based on 1-Cramer's V statistic using chisq.test. For a large number of factor variables this might take some time. The resulting trees can be plotted using plot.
Further proceeding would consist in chosing one variable of each cluster to obtain a subset of rather uncorrelated variables for further analysis. An automatic variable selection can be done using cvtree and xtractvars.
If an additional class vector cl is given to the function for any two variables their minimum correlation over all classes is used.

Value

Object of class corclust.

Author(s)

Gero Szepannek

References

Roever, C. and Szepannek, G. (2005): Application of a genetic algorithm to variable selection in fuzzy clustering. In C. Weihs and W. Gaul (eds), Classification - The Ubiquitous Challenge, 674-681, Springer.

See Also

plot.corclust and hclust for details on the clustering algorithm, and cvtree, xtractvars for postprocessing.

Examples

    data(iris)
    classes <- iris$Species
    variables <- iris[,1:4]
    ccres <- corclust(variables, classes)
    plot(ccres, mincor = 0.6)

Socioeconomic data for the most populous countries.

Description

Socioeconomic data for the most populous countries.

Usage

data(countries)

Format

A data frame with 42 observations on the following 7 variables.

Country

name of the country.

Popul

population.

PopDens

population density.

GDPpp

GDP per inhabitant.

LifeEx

mean life expectation

InfMor

infant mortality

Illit

illiteracy rate

Source

CIA World Factbook https://www.cia.gov/the-world-factbook/

Examples

data(countries)
summary(countries)

Extracts variable cluster IDs

Description

Extracts cluster IDs for variables according to a dendrogram from object of class cvtree.

Usage

cvtree(object, k = 2, mincor = NULL, ...)

Arguments

Details

Like in corclust for correlation comparison numerics and factors are considered separately. For factors Cramer's V statistic is used.

Value

Object of class cvtree with elements:

Author(s)

Gero Szepannek

References

Roever, C. and Szepannek, G. (2005): Application of a genetic algorithm to variable selection in fuzzy clustering. In C. Weihs and W. Gaul (eds), Classification - The Ubiquitous Challenge, 674-681, Springer.

See Also

See also corclust, plot.corclust and hclust for details on the clustering algorithm.

Examples

    data(B3)
    ccres <- corclust(B3)
    plot(ccres)
    cvtree(ccres, k = 3)

Internal function to convert a distance structure to a matrix

Description

For internal use only.

Usage

distmirr(dis)

Arguments

Value

A symmetric distance matrix is returned.

See Also

dist

Estimate density of a given kernel

Description

Given an estimated kernel density this function estimates the density of a new vector.

Usage

dkernel(x, kernel = density(x), interpolate = FALSE, ...)

Arguments

Value

Denstiy of x in kernel.

Author(s)

Karsten Luebke, karsten.luebke@fom.de

See Also

density, NaiveBayes

Examples

kern <- density(rnorm(50))
x <- seq(-3, 3, len = 100)
y <- dkernel(x, kern)
plot(x, y, type = "l")

Plotting the 2-d partitions of classification methods

Description

Plot showing the classification of observations based on classification methods (e.g. lda, qda) for two variables. Moreover, the classification borders are displayed and the apparent error rates are given in each title.

Usage

drawparti(grouping, x, y, method = "lda", prec = 100, xlab = NULL, 
    ylab = NULL, col.correct = "black", col.wrong = "red", 
    col.mean = "black", col.contour = "darkgrey", 
    gs = as.character(grouping), pch.mean = 19, cex.mean = 1.3, 
    print.err = 0.7, legend.err = FALSE, legend.bg = "white",
    imageplot = TRUE, image.colors = cm.colors(nc), 
    plot.control = list(), ...)        

Arguments

.

Author(s)

Karsten Luebke, karsten.luebke@fom.de, Uwe Ligges, Irina Czogiel

See Also

partimat

Function to calculate e- or softmax scaled membership values

Description

Calculates the e- or softmax scaled membership values of an argmax based classification rule.

Usage

e.scal(x, k = 1, tc = NULL)

Arguments

Details

For any membership vector y \exp(y\cdot k) / \sum\exp(y\cdot k) is calculated. If k=1, the classical softmax scaling is used. If the true classes are given, k is optimized so that the apparent error rate is minimized.

Value

A list containing elements

Author(s)

Karsten Luebke, karsten.luebke@fom.de

References

Garczarek, Ursula Maria (2002): Classification rules in standardized partition spaces. Dissertation, University of Dortmund. URL http://hdl.handle.net/2003/2789

Examples

library(MASS)
data(iris)
ldaobj <- lda(Species ~ ., data = iris)
ldapred <- predict(ldaobj)$posterior
e.scal(ldapred)
e.scal(ldapred, tc = iris$Species)

Computation of an Eight Direction Arranged Map

Description

Produces an object of class EDAM which is a two dimensional representation of data in a rectangular, equally spaced grid as known from Self-Organizing Maps.

Usage

EDAM(EV0, nzx = 0, iter.max = 10, random = TRUE, standardize = FALSE, 
    wghts = 0, classes = 0, sa = TRUE, temp.in = 0.5, temp.fin = 1e-07, 
    temp.gamma = 0)

Arguments

Details

The data given by EV0 is visualized by the EDAM-algorithm. This method approximates the best visualization where goodness is measured by S, a transformation of the criterion stress as i.e. known from sammon. The target space of the visualization is restricted to a grid so the problem has a discrete solution space. Originally this restriction was made to make the results comparable to those of Kohonen Self-Organizing Maps. But it turns out that also for reasons of a clear arrangement the representation in a grid can be more favorable than in the hole plane.

During the computation of EDAM 3 values indicating its progress are given online. The first is the number of the actual iteration, the second the maximum number of overall performed iterations. The latter may reduce during computation, since the neighborhood reduces in case of convergence before the last iteration. The last number gives the actual criterion S. The default plot method plot.edam for objects of class EDAM is shardsplot.

Value

EDAM returns an object of class EDAM, which is a list containing the following components:

Author(s)

Nils Raabe

References

Raabe, N. (2003). Vergleich von Kohonen Self-Organizing-Maps mit einem nichtsimultanen Klassifikations- und Visualisierungsverfahren. Diploma Thesis, Department of Statistics, University of Dortmund.

See Also

shardsplot, TopoS

Examples

# Compute an Eight Directions Arranged Map for a random sample 
# of the iris data.
data(iris)
set.seed(1234)
iris.sample <- sample(150, 42)
irisEDAM <- EDAM(iris[iris.sample, 1:4], classes = iris[iris.sample, 5], 
    standardize = TRUE, iter.max = 3)
plot(irisEDAM, vertices = FALSE)
legend(3, 5, col = rainbow(3), legend = levels(iris[,5]), pch = 16)
print(irisEDAM)

# Construct clusters within the phases of the german business data 
# and visualize the centroids by EDAM.
data(B3)
phasemat <- lapply(1:4, function(x) B3[B3[,1] == x, 2:14])
subclasses <- lapply(phasemat, 
    function(x) cutree(hclust(dist(x)), k = round(nrow(x) / 4.47)))
centroids <- lapply(1:4, 
    function(y) apply(phasemat[[y]], 2, 
        function(x) by(x, subclasses[[y]], mean)))
centmat <- matrix(unlist(sapply(centroids, t)), ncol = 13, 
    byrow = TRUE, dimnames = list(NULL, colnames(centroids[[1]])))
centclasses <- unlist(lapply(1:4, 
    function(x) rep(x, unlist(lapply(centroids, nrow))[x])))
B3EDAM <- EDAM(centmat, classes = centclasses, standardize = TRUE, 
    iter.max = 6, rand = FALSE)
plot(B3EDAM, standardize = TRUE)
opar <- par(xpd = NA)
legend(4, 5.1, col = rainbow(4), pch = 16, xjust = 0.5, yjust = 0,
    ncol = 2, legend = c("upswing", "upper turning point", 
                         "downswing", "lower turning point"))
print(B3EDAM)
par(opar)

Tabulation of prediction errors by classes

Description

Cross-tabulates true and predicted classes with the option to show relative frequencies.

Usage

errormatrix(true, predicted, relative = FALSE)

Arguments

Details

Given vectors of true and predicted classes, a (symmetric) table of misclassifications is constructed.

Element [i,j] shows the number of objects of class i that were classified as class j; so the main diagonal shows the correct classifications. The last row and column show the corresponding sums of misclassifications, the lower right element is the total sum of misclassifications.

If ‘relative’ is TRUE, the rows are normalized so they show relative frequencies instead. The lower right element now shows the total error rate, and the remaining last row sums up to one, so it shows “where the misclassifications went”.

Value

A (named) matrix.

Note

Concerning the case that ‘relative’ is TRUE:

If a prior distribution over the classes is given, the misclassification rate that is returned as the lower right element (which is only the fraction of misclassified data) is not an estimator for the expected misclassification rate.

In that case you have to multiply the individual error rates for each class (returned in the last column) with the corresponding prior probabilities and sum these up (see example below).

Both error rate estimates are equal, if the fractions of classes in the data are equal to the prior probabilities.

Author(s)

Christian Röver, roever@statistik.tu-dortmund.de

See Also

table

Examples

data(iris)
library(MASS)
x <- lda(Species ~ Sepal.Length + Sepal.Width, data=iris)
y <- predict(x, iris)

# absolute numbers: 
errormatrix(iris$Species, y$class)

# relative frequencies: 
errormatrix(iris$Species, y$class, relative = TRUE)

# percentages: 
round(100 * errormatrix(iris$Species, y$class, relative = TRUE), 0)

# expected error rate in case of class prior: 
indiv.rates <- errormatrix(iris$Species, y$class, relative = TRUE)[1:3, 4]
prior <- c("setosa" = 0.2, "versicolor" = 0.3, "virginica" = 0.5)
total.rate <- t(indiv.rates) %*% prior
total.rate

Friedman's classification benchmark data

Description

Function to generate 3-class classification benchmarking data as introduced by J.H. Friedman (1989)

Usage

friedman.data(setting = 1, p = 6, samplesize = 40, asmatrix = FALSE)

Arguments

Details

When J.H. Friedman introduced the Regularized Discriminant Analysis (rda) in 1989, he used artificially generated data to test the procedure and to examine its performance in comparison to Linear and Quadratic Discriminant Analysis (see also lda and qda).

6 different settings were considered to demonstrate potential strengths and weaknesses of the new method:

1. equal spherical covariance matrices,

2. unequal spherical covariance matrices,

3. equal, highly ellipsoidal covariance matrices with mean differences in low-variance subspace,

4. equal, highly ellipsoidal covariance matrices with mean differences in high-variance subspace,

5. unequal, highly ellipsoidal covariance matrices with zero mean differences and

6. unequal, highly ellipsoidal covariance matrices with nonzero mean differences.

For each of the 6 settings data was generated with 6, 10, 20 and 40 variables.

Classification performance was then measured by repeatedly creating training-datasets of 40 observations and estimating the misclassification rates by test sets of 100 observations.

The number of classes is always 3, class labels are assigned randomly (with equal probabilities) to observations, so the contributions of classes to the data differs from dataset to dataset. To make sure covariances can be estimated at all, there are always at least two observations from each class in a dataset.

Value

Depending on asmatrix either a data frame or a matrix with samplesize rows and p+1 columns, the first column containing the class labels, the remaining columns being the variables.

Author(s)

Christian Röver, roever@statistik.tu-dortmund.de

References

Friedman, J.H. (1989): Regularized Discriminant Analysis. In: Journal of the American Statistical Association 84, 165-175.

See Also

rda

Examples

# Reproduce the 1st setting with 6 variables.
# Error rate should be somewhat near 9 percent.
training <- friedman.data(1, 6, 40)
x <- rda(class ~ ., data = training, gamma = 0.74, lambda = 0.77)
test <- friedman.data(1, 6, 100)
y <- predict(x, test[,-1])
errormatrix(test[,1], y$class)

Statlog German Credit

Description

The dataset contains data of past credit applicants. The applicants are rated as good or bad. Models of this data can be used to determine if new applicants present a good or bad credit risk.

Usage

data("GermanCredit")

Format

A data frame containing 1,000 observations on 21 variables.

status

factor variable indicating the status of the existing checking account, with levels ... < 100 DM, 0 <= ... < 200 DM, ... >= 200 DM/salary for at least 1 year and no checking account.

duration

duration in months.

credit_history

factor variable indicating credit history, with levels no credits taken/all credits paid back duly, all credits at this bank paid back duly, existing credits paid back duly till now, delay in paying off in the past and critical account/other credits existing.

purpose

factor variable indicating the credit's purpose, with levels car (new), car (used), furniture/equipment, radio/television, domestic appliances, repairs, education, retraining, business and others.

amount

credit amount.

savings

factor. savings account/bonds, with levels ... < 100 DM, 100 <= ... < 500 DM, 500 <= ... < 1000 DM, ... >= 1000 DM and unknown/no savings account.

employment_duration

ordered factor indicating the duration of the current employment, with levels unemployed, ... < 1 year, 1 <= ... < 4 years, 4 <= ... < 7 years and ... >= 7 years.

installment_rate

installment rate in percentage of disposable income.

personal_status_sex

factor variable indicating personal status and sex, with levels male:divorced/separated, female:divorced/separated/married, male:single, male:married/widowed and female:single.

other_debtors

factor. Other debtors, with levels none, co-applicant and guarantor.

present_residence

present residence since?

property

factor variable indicating the client's highest valued property, with levels real estate, building society savings agreement/life insurance, car or other and unknown/no property.

age

client's age.

other_installment_plans

factor variable indicating other installment plans, with levels bank, stores and none.

housing

factor variable indicating housing, with levels rent, own and for free.

number_credits

number of existing credits at this bank.

job

factor indicating employment status, with levels unemployed/unskilled - non-resident, unskilled - resident, skilled employee/official and management/self-employed/highly qualified employee/officer.

people_liable

Number of people being liable to provide maintenance.

telephone

binary variable indicating if the customer has a registered telephone number.

foreign_worker

binary variable indicating if the customer is a foreign worker.

credit_risk

binary variable indicating credit risk, with levels good and bad.

Source

The original data was provided by:

Professor Dr. Hans Hofmann, Institut fuer Statistik und Oekonometrie, Universitaet Hamburg, FB Wirtschaftswissenschaften, Von-Melle-Park 5, 2000 Hamburg 13

The dataset has been taken from the UCI Repository Of Machine Learning Databases at http://archive.ics.uci.edu/ml/.

It was published this way in CRAN package evtree (maintainer: Thomas Grubinger) that has been archived from CRAN on May 31, 2014. Afterwards the exactly same data object has been copied from the evtree package to klaR.

Stepwise forward variable selection for classification

Description

Performs a stepwise forward variable/model selection using the Wilk's Lambda criterion.

Usage

greedy.wilks(X, ...)
## Default S3 method:
greedy.wilks(X, grouping, niveau = 0.2, ...)
## S3 method for class 'formula'
greedy.wilks(formula, data = NULL, ...) 

Arguments

Details

A stepwise forward variable selection is performed. The initial model is defined by starting with the variable which separates the groups most. The model is then extended by including further variables depending on the Wilk's lambda criterion: Select the one which minimizes the Wilk's lambda of the model including the variable if its p-value still shows statistical significance.

Value

A list of two components, a formula of the form ‘response ~ list + of + selected + variables’, and a data.frame results containing the following variables:

Author(s)

Andrea Preusser, Karsten Luebke (karsten.luebke@fom.de)

References

Mardia, K. V. , Kent, J. T. and Bibby, J. M. (1979), Multivariate analysis, Academic Press (New York; London)

See Also

stepclass, manova

Examples

data(B3)
gw_obj <- greedy.wilks(PHASEN ~ ., data = B3, niveau = 0.1)
gw_obj
## now you can say stuff like
## lda(gw_obj$formula, data = B3)

Calculation of HMM Sum of Path

Description

A Hidden Markov Model for the classification of states in a time series. Based on the transition probabilities and the so called emission probabilities (p(class|x)) the ‘prior probablilities’ of states (classes) in time period t given all past information in time period t are calculated.

Usage

hmm.sop(sv, trans.matrix, prob.matrix)

Arguments

Value

Returns the ‘prior probablilities’ of states.

Author(s)

Daniel Fischer, Reinald Oetsch

References

Garczarek, Ursula Maria (2002): Classification rules in standardized partition spaces. Dissertation, University of Dortmund. URL http://hdl.handle.net/2003/2789

See Also

calc.trans

Examples

library(MASS)
data(B3)
trans.matrix <- calc.trans(B3$PHASEN)

# Calculate posterior prob. for the classes via lda
prob.matrix <- predict(lda(PHASEN ~ ., data = B3))$post
errormatrix(B3$PHASEN, apply(prob.matrix, 1, which.max))
prior.prob <- hmm.sop("2", trans.matrix, prob.matrix)
errormatrix(B3$PHASEN, apply(prior.prob, 1, which.max))

K-Modes Clustering

Description

Perform k-modes clustering on categorical data.

Usage

kmodes(data, modes, iter.max = 10, weighted = FALSE, fast = TRUE)

Arguments

Details

The k-modes algorithm (Huang, 1997) an extension of the k-means algorithm by MacQueen (1967).

The data given by data is clustered by the k-modes method (Huang, 1997) which aims to partition the objects into k groups such that the distance from objects to the assigned cluster modes is minimized.

By default simple-matching distance is used to determine the dissimilarity of two objects. It is computed by counting the number of mismatches in all variables. Alternative this distance is weighted by the frequencies of the categories in data (see Huang, 1997, for details).

If an initial matrix of modes is supplied, it is possible that no object will be closest to one or more modes. In this case less cluster than supplied modes will be returned and a warning is given.

If called using fast = TRUE the reassignment of the data to clusters is done for the entire data set before recomputation of the modes is done. For computational reasons this option should be chosen unless moderate data sizes.

For clustering mixed type data it is referred to kproto.

Value

An object of class "kmodes" which is a list with components:

Author(s)

Christian Neumann, christian2.neumann@tu-dortmund.de, Gero Szepannek, gero.szepannek@web.de

References

Huang, Z. (1997) A Fast Clustering Algorithm to Cluster Very Large Categorical Data Sets in Data Mining. in KDD: Techniques and Applications (H. Lu, H. Motoda and H. Luu, Eds.), pp. 21-34, World Scientific, Singapore.

MacQueen, J. (1967) Some methods for classification and analysis of multivariate observations. In Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, eds L. M. Le Cam & J. Neyman, 1, pp. 281-297. Berkeley, CA: University of California Press.

Examples

### a 5-dimensional toy-example:

## generate data set with two groups of data:
set.seed(1)
x <- rbind(matrix(rbinom(250, 2, 0.25), ncol = 5),
           matrix(rbinom(250, 2, 0.75), ncol = 5))
colnames(x) <- c("a", "b", "c", "d", "e")

## run algorithm on x:
(cl <- kmodes(x, 2))

## and visualize with some jitter:
plot(jitter(x), col = cl$cluster)
points(cl$modes, col = 1:5, pch = 8)

Localized Linear Discriminant Analysis (LocLDA)

Description

A localized version of Linear Discriminant Analysis.

Usage

loclda(x, ...)

## S3 method for class 'formula'
loclda(formula, data, ..., subset, na.action)

## Default S3 method:
loclda(x, grouping, weight.func = function(x) 1/exp(x), 
    k = nrow(x), weighted.apriori = TRUE, ...)

## S3 method for class 'data.frame'
 loclda(x, ...)

## S3 method for class 'matrix'
loclda(x, grouping, ..., subset, na.action)

Arguments

Details

This is an approach to apply the concept of localization described by Tutz and Binder (2005) to Linear Discriminant Analysis. The function loclda generates an object of class loclda (see Value below). As localization makes it necessary to build an individual decision rule for each test observation, this rule construction has to be handled by predict.loclda. For convenience, the rule building procedure is still described here.

To classify a test observation x_s, only the k nearest neighbours of x_s within the train data are used. Each of these k train observations x_i, i = 1,\dots,k, is assigned a weight w_i according to

w_i = K\left(\frac{||x_i-x_s||}{d_k}\right), i=1,\dots,k

where K is the weighting function given by weight.func, ||x_i-x_s|| is the euclidian distance of x_i and x_s and d_k is the euclidian distance of x_s to its k-th nearest neighbour. With these weights for each class A_g, g=1,\dots,G, its weighted empirical mean \hat{\mu}_g and weighted empirical covariance matrix are computed. The estimated pooled (weighted) covariance matrix \hat{\Sigma} is then calculated from the individual weighted empirical class covariance matrices. If weighted.apriori is TRUE (the default), prior class probabilities are estimated according to:

prior_g := \frac{\sum_{i=1}^k \left(w_i \cdot I (x_i \in A_g)\right)}{\sum_{i=1}^k \left( w_i \right)}

where I is the indicator function. If FALSE, equal priors for all classes are used. In analogy to Linear Discriminant Analysis, the decision rule for x_s is

\hat{A} := argmax_{g \in 1,\dots,G} (posterior_g)

where

posterior_g := prior_g \cdot \exp{\left( (-\frac{1}{2}) t(x_s-\hat{\mu}_g)\hat{\Sigma}^{-1}(x_s-\hat{\mu}_g)\right)}

If posterior_g < 10^{(-150)} \forall g \in \{1,\dots,G\}, posterior_g is set to \frac{1}{G} for all g \in 1,\dots,G and the test observation x_s is simply assigned to the class whose weighted mean has the lowest euclidian distance to x_s.

Value

A list of class loclda containing the following components:

Author(s)

Marc Zentgraf (marc-zentgraf@gmx.de) and Karsten Luebke (karsten.luebke@fom.de)

References

Tutz, G. and Binder, H. (2005): Localized classification. Statistics and Computing 15, 155-166.

See Also

predict.loclda, lda

Examples

benchB3("lda")$l1co.error
benchB3("loclda")$l1co.error

Pairwise variable selection for classification in local models

Description

Performs pairwise variable selection on subclasses.

Usage

locpvs(x, subclasses, subclass.labels, prior=NULL, method="lda", 
    vs.method = c("ks.test", "stepclass", "greedy.wilks"),
    niveau=0.05, fold=10, impr=0.1, direct="backward", out=FALSE, ...)

Arguments

Details

A call on pvs is performed using “subclasses” as grouping variable. See pvs for further details.

Value

An object of class ‘locpvs’ containing the following components:

Author(s)

Gero Szepannek, szepannek@statistik.tu-dortmund.de, Christian Neumann

References

Szepannek, G. and Weihs, C. (2006) Local Modelling in Classification on Different Feature Subspaces. In Advances in Data Mining., ed Perner, P., LNAI 4065, pp. 226-234. Springer, Heidelberg.

See Also

predict.locpvs for predicting ‘locpvs’ models and pvs

Examples

## this example might be a bit artificial, but it sufficiently shows how locpvs has to be used

## learn a locpvs-model on the Vehicle dataset

library("mlbench")
data("Vehicle")

subclass <- Vehicle$Class # use four car-types in dataset as subclasses
## aggregate "bus" and "van" to upper-class "big" and "saab" and "opel" to upper-class "small"
subclass_class <- matrix(c("bus","van","saab","opel","big","big","small","small"),ncol=2) 

## learn now a locpvs-model for the subclasses:
model <- locpvs(Vehicle[,1:18], subclass, subclass_class) 
model # short summary, showing the class-pairs of the submodels 
# together with the selected variables and the relation of sub- to upperclasses

## predict:
pred <- predict(model, Vehicle[,1:18])

## now you can look at the predicted classes:
pred$class
## or at the posterior probabilities:
pred$posterior
## or at the posterior probabilities for the subclasses:
pred$subclass.posteriors

Minimal Error Classification

Description

Computer intensive method for linear dimension reduction that minimizes the classification error directly.

Usage

meclight(x, ...)

## Default S3 method:
meclight(x, grouping, r = 1, fold = 10, ...)
## S3 method for class 'formula'
meclight(formula, data = NULL, ..., subset, na.action = na.fail)
## S3 method for class 'data.frame'
meclight(x, ...)
## S3 method for class 'matrix'
meclight(x, grouping, ..., subset, na.action = na.fail)

Arguments

Details

Computer intensive method for linear dimension reduction that minimizes the classification error in the projected subspace directly. Classification is done by lda. In contrast to the reference function minimization is done by Nelder-Mead in optim.

Value

Author(s)

Maria Eveslage, Karsten Luebke, karsten.luebke@fom.de

References

Roehl, M.C., Weihs, C., and Theis, W. (2002): Direct Minimization in Multivariate Classification. Computational Statistics, 17, 29-46.

See Also

predict.meclight

Examples

data(iris)
meclight.obj <- meclight(Species ~ ., data = iris)
meclight.obj

Naive Bayes Classifier

Description

Computes the conditional a-posterior probabilities of a categorical class variable given independent predictor variables using the Bayes rule.

Usage

## S3 method for class 'formula'
NaiveBayes(formula, data, ..., subset, na.action = na.pass)
## Default S3 method:
NaiveBayes(x, grouping, prior, usekernel = FALSE, fL = 0, ...)

Arguments

Details

This implementation of Naive Bayes as well as this help is based on the code by David Meyer in the package e1071 but extended for kernel estimated densities and user specified prior probabilities. The standard naive Bayes classifier (at least this implementation) assumes independence of the predictor variables.

Value

An object of class "NaiveBayes" including components:

Author(s)

Karsten Luebke, karsten.luebke@fom.de

See Also

predict.NaiveBayes,plot.NaiveBayes,naiveBayes,qda

Examples

data(iris)
m <- NaiveBayes(Species ~ ., data = iris)

Nearest Mean Classification

Description

Function for nearest mean classification.

Usage

nm(x, ...)

## Default S3 method:
nm(x, grouping, gamma = 0, ...)
## S3 method for class 'data.frame'
nm(x, ...)
## S3 method for class 'matrix'
nm(x, grouping, ..., subset, na.action = na.fail)
## S3 method for class 'formula'
nm(formula, data = NULL, ..., subset, na.action = na.fail)

Arguments

Details

nm is calling sknn with the class means as observations. If gamma>0 a gaussian like density is used to weight the distance to the class means weight=exp(-gamma*distance). This is similar to an rbf kernel. If the distances are large it may be useful to scale the data first.

Value

A list containing the function call and the class means (learn)).

Author(s)

Karsten Luebke, karsten.luebke@fom.de

See Also

sknn, rda, knn

Examples

data(B3)
x <- nm(PHASEN ~ ., data = B3)
x$learn
x <- nm(PHASEN ~ ., data = B3, gamma = 0.1)
predict(x)$post

Plotting the 2-d partitions of classification methods

Description

Provides a multiple figure array which shows the classification of observations based on classification methods (e.g. lda, qda) for every combination of two variables. Moreover, the classification borders are displayed and the apparent error rates are given in each title.

Usage

partimat(x,...)

## Default S3 method:
partimat(x, grouping, method = "lda", prec = 100, 
    nplots.vert, nplots.hor, main = "Partition Plot", name, mar, 
    plot.matrix = FALSE, plot.control = list(), ...)
## S3 method for class 'data.frame'
partimat(x, ...)
## S3 method for class 'matrix'
partimat(x, grouping, ..., subset, na.action = na.fail)
## S3 method for class 'formula'
partimat(formula, data = NULL, ..., subset, na.action = na.fail)

Arguments

.

Note

Warnings such as ‘parameter “xyz” couldn't be set in high-level plot function’ are expected, if making use of ....

Author(s)

Karsten Luebke, karsten.luebke@fom.de, Uwe Ligges, Irina Czogiel

See Also

for much more fine tuning see drawparti

Examples

library(MASS)
data(iris)
partimat(Species ~ ., data = iris, method = "lda")
## Not run: 
partimat(Species ~ ., data = iris, method = "lda", 
    plot.matrix = TRUE, imageplot = FALSE) # takes some time ...

## End(Not run)

Plotting marginal posterior class probabilities

Description

For a given variable the posteriori probabilities of the classes given by a classification method are plotted. The variable need not be used for the actual classifcation.

Usage

plineplot(formula, data, method, x, col.wrong = "red", 
          ylim = c(0, 1), loo = FALSE, mfrow, ...)

Arguments

Value

The actual error rate.

Author(s)

Karsten Luebke, karsten.luebke@fom.de

See Also

partimat

Examples

library(MASS)

# The name of the variable can be used for x
data(B3)
plineplot(PHASEN ~ ., data = B3, method = "lda", 
    x = "EWAJW", xlab = "EWAJW")

# The plotted variable need not be in the data
data(iris)
iris2 <- iris[ , c(1,3,5)]
plineplot(Species ~ ., data = iris2, method = "lda", 
    x = iris[ , 4], xlab = "Petal.Width")

Naive Bayes Plot

Description

Visualizes the marginal probabilities of predictor variables given the class.

Usage

## S3 method for class 'NaiveBayes'
plot(x, vars, n = 1000, legendplot = TRUE, lty, col,
    ylab = "Density", main = "Naive Bayes Plot", ...)

Arguments

Details

For metric variables the estimated density is plotted. For categorial variables mosaicplot is called.

Author(s)

Karsten Luebke, karsten.luebke@fom.de

See Also

NaiveBayes

Examples

data(iris)
mN <- NaiveBayes(Species ~ ., data = iris)
plot(mN)

mK <- NaiveBayes(Species ~ ., data = iris, usekernel = TRUE)
plot(mK)

Plot information values

Description

Barplot of information values to compare dicriminator of the transformed variables.

Usage

## S3 method for class 'woe'
plot(x, type = c("IV", "woes"), ...)

Arguments

Details

For type=="IV" a barplot of information values for all transformed variables. A thumb rule of interpretation is that Values above 0.3 are considered as strongly discrimative where values below 0.02 are considered to characterize unpredictive variables. For type=="woes" for each variable the relative frequencies of all transformed levels are plotted.

Value

No value is returned.

Author(s)

Gero Szepannek

References

Good, I. (1950): Probability and the Weighting of Evidences. Charles Griffin, London.

Kullback, S. (1959): Information Theory and Statistics. Wiley, New York.

See Also

woe, predict.woe

Examples

# see examples in ?woe

Localized Linear Discriminant Analysis (LocLDA)

Description

Classifies new observations using parameters determined by the loclda-function.

Usage

## S3 method for class 'loclda'
predict(object, newdata, ...)

Arguments

Value

A list with components:

Author(s)

Marc Zentgraf (marc-zentgraf@gmx.de) and Karsten Luebke (karsten.luebke@fom.de)

See Also

loclda

Examples

data(B3)
x <- loclda(PHASEN ~ ., data = B3, subset = 1:80)
predict(x, B3[-(1:80),])

predict method for locpvs objects

Description

Prediction of class membership and posterior probabilities in local models using pairwise variable selection.

Usage

## S3 method for class 'locpvs'
predict(object,newdata, quick = FALSE, return.subclass.prediction = TRUE, ...)

Arguments

Details

Posterior probabilities are predicted as if object is a standard ‘pvs’-model with the subclasses as classes. Then the posterior probabalities are summed over all subclasses for each class. The class with the highest value becomes the prediction.

If “quick=FALSE” the posterior probabilites for each case are computed using the pairwise coupling algorithm presented by Hastie, Tibshirani (1998). If “quick=FALSE” a much quicker solution is used, which leads to less accurate posterior probabalities. In almost all cases it doesn't has a negative effect on the classification result.

Value

a list with components:

Author(s)

Gero Szepannek, szepannek@statistik.tu-dortmund.de, Christian Neumann

References

Szepannek, G. and Weihs, C. (2006) Local Modelling in Classification on Different Feature Subspaces. In Advances in Data Mining., ed Perner, P., LNAI 4065, pp. 226-234. Springer, Heidelberg.

See Also

locpvs for learning ‘locpvs’-models and examples for applying this predict method, pvs for pairwise variable selection without modeling subclasses, predict.pvs for predicting ‘pvs’-models

Prediction of Minimal Error Classification

Description

Classify multivariate observations in conjunction with meclight and lda.

Usage

## S3 method for class 'meclight'
predict(object, newdata,...)

Arguments

Details

Classify multivariate observations in conjunction with meclight and lda.

Value

Author(s)

Karsten Luebke, karsten.luebke@fom.de

References

Roehl, M.C., Weihs, C., and Theis, W. (2002): Direct Minimization in Multivariate Classification. Computational Statistics, 17, 29-46.

See Also

meclight

Examples

data(iris)
meclight.obj <- meclight(Species ~ ., data = iris)
predict(meclight.obj, iris)

Naive Bayes Classifier

Description

Computes the conditional a-posterior probabilities of a categorical class variable given independent predictor variables using the Bayes rule.

Usage

## S3 method for class 'NaiveBayes'
predict(object, newdata, threshold = 0.001, ...)

Arguments

Details

This implementation of Naive Bayes as well as this help is based on the code by David Meyer in the package e1071 but extended for kernel estimated densities. The standard naive Bayes classifier (at least this implementation) assumes independence of the predictor variables. For attributes with missing values, the corresponding table entries are omitted for prediction.

Value

A list with the conditional a-posterior probabilities for each class and the estimated class are returned.

Author(s)

Karsten Luebke, karsten.luebke@fom.de

See Also

NaiveBayes,dkernelnaiveBayes,qda

Examples

data(iris)
m <- NaiveBayes(Species ~ ., data = iris)
predict(m)

predict method for pvs objects

Description

Prediction of class membership and posterior probabilities using pairwise variable selection.

Usage

## S3 method for class 'pvs'
predict(object, newdata, quick = FALSE, detail = FALSE, ...)

Arguments

Details

If “quick=FALSE” the posterior probabilites for each case are computed using the pairwise coupling algorithm presented by Hastie, Tibshirani (1998). If “quick=FALSE” a much quicker solution is used, which leads to less accurate posterior probabalities. In almost all cases it doesn't has a negative effect on the classification result.

Value

a list with components:

Author(s)

Gero Szepannek, szepannek@statistik.tu-dortmund.de, Christian Neumann

References

Szepannek, G. and Weihs, C. (2006) Variable Selection for Classification of More than Two Classes Where the Data are Sparse. In From Data and Information Analysis to Kwnowledge Engineering., eds Spiliopolou, M., Kruse, R., Borgelt, C., Nuernberger, A. and Gaul, W. pp. 700-708. Springer, Heidelberg.

See Also

For more details and examples how to use this predict method, see pvs.

Regularized Discriminant Analysis (RDA)

Description

Classifies new observations using parameters determined by the rda-function.

Usage

## S3 method for class 'rda'
predict(object, newdata, posterior = TRUE, 
    aslist = TRUE, ...)

Arguments

Value

Depends on the value of argument ‘aslist’:

Either a vector (of class factor) of classifications that (optionally) has an attribute ‘posterior’ containing the posterior probability matrix, or

A list with elements ‘class’ and ‘posterior’.

Author(s)

Christian Röver, roever@statistik.tu-dortmund.de

See Also

rda

Examples

data(iris)
x <- rda(Species ~ ., data = iris, gamma = 0.05, lambda = 0.2)
predict(x, iris[, 1:4])

Simple k Nearest Neighbours Classification

Description

Classifies new observations using the sknn learned by the sknn-function.

Usage

## S3 method for class 'sknn'
predict(object, newdata,...)

Arguments

Value

A list with elements ‘class’ and ‘posterior’.

Author(s)

Karsten Luebke, karsten.luebke@fom.de

See Also

sknn, knn

Examples

data(iris)
x <- sknn(Species ~ ., data = iris)
predict(x, iris)
x <- sknn(Species ~ ., gamma = 10, kn = 10, data = iris)
predict(x, iris)

Interface to SVMlight

Description

Predicts new observations using the SVM learned by the svmlight-function.

Usage

## S3 method for class 'svmlight'
predict(object, newdata, scal = TRUE, ...)

Arguments

Value

If a classification is learned (type="C") in svmlight a list with elements ‘class’ and ‘posterior’ (scaled, if scal = TRUE).

If a Regression is learned (type="R") in svmlight the predicted values.

Author(s)

Karsten Luebke, karsten.luebke@fom.de

See Also

svmlight, svm

Examples

## Not run: 
data(iris)
x <- svmlight(Species ~ ., data = iris)
predict(x, iris)

## End(Not run)

Weights of evidence

Description

Applies weight of evidence transform of factor variables for binary classification based on a model of class woe.

Usage

## S3 method for class 'woe'
predict(object, newdata, replace = TRUE, ...)

Arguments

Value

Data frame including the transformed numeric woe variables.

Author(s)

Gero Szepannek

References

Good, I. (1950): Probability and the Weighting of Evidences. Charles Griffin, London.

See Also

woe, plot.woe

Examples

# see examples in ?woe

Pairwise variable selection for classification

Description

Pairwise variable selection for numerical data, allowing the use of different classifiers and different variable selection methods.

Usage

pvs(x, ...)

## Default S3 method:
pvs(x, grouping, prior=NULL, method="lda", 
    vs.method=c("ks.test","stepclass","greedy.wilks"), niveau=0.05, 
    fold=10, impr=0.1, direct="backward", out=FALSE, ...)
    
## S3 method for class 'formula'
pvs(formula, data = NULL, ...)

Arguments

Details

The classification “method” (e.g. ‘lda’) must have its own ‘predict’ method (like ‘predict.lda’ for ‘lda’) returns a list with an element ‘posterior’ containing the posterior probabilties. It must be able to deal with matrices as in method(x, grouping, ...). Examples of such classification methods are ‘lda’, ‘qda’, ‘rda’, ‘NaiveBayes’ or ‘sknn’.\ For the classification methods “svm” and “randomForest” there are special routines implemented, to make them work with ‘pvs’ method even though their ‘predict’ methods don't provide the demanded posteriors. However those two classfiers can not be used together with variable selection method “stepclass”.

‘pvs’ performs a variable selection using the selection method chosen in ‘vs.method’ for each pair of classes in ‘x’. Then for each pair of classes a submodel using ‘method’ is trained (using only the earlier selected variables for this class-pair).

If ‘method’ is “ks.test”, then for each variable the empirical distribution functions of the cases of both classes are compared via “ks.test”. Only variables with a p-values below ‘niveau’ are used for training the submodel for this pair of classes.

If ‘method’ is “stepclass” the variable selection is performed using the “stepclass” method.

If ‘method’ is “greedy.wilks” the variable selection is performed using Wilk's lambda criterion.

Value

An object of class ‘pvs’ containing the following components:

Author(s)

Gero Szepannek, szepannek@statistik.tu-dortmund.de, Christian Neumann

References

• Szepannek, G. and Weihs, C. (2006) Variable Selection for Classification of More than Two Classes Where the Data are Sparse. In From Data and Information Analysis to Kwnowledge Engineering., eds Spiliopolou, M., Kruse, R., Borgelt, C., Nuernberger, A. and Gaul, W. pp. 700-708. Springer, Heidelberg.

• Szepannek, G. (2008): Different Subspace Classification - Datenanalyse, -interpretation, -visualisierung und Vorhersage in hochdimensionalen Raeumen, ISBN 978-3-8364-6302-7, vdm, Saarbruecken.

See Also

predict.pvs for predicting ‘pvs’ models and locpvs for pairwisevariable selection in local models of several subclasses

Examples

## Example 1: learn an "lda" model on the waveform data using pairwise variable 
## selection (pvs) using "ks.test" and compare it to using lda without pvs 

library("mlbench")
trainset <- mlbench.waveform(300) 
pvsmodel <- pvs(trainset$x, trainset$classes, niveau=0.05) # default: using method="lda"
## short summary, showing the class-pairs of the submodels and the selected variables
pvsmodel
 
testset <-  mlbench.waveform(500)
## prediction of the test data set: 
prediction <- predict(pvsmodel, testset$x)

## calculating the test error rate
1-sum(testset$classes==prediction$class)/length(testset$classes)
## Bayes error is 0.149

## comparison to performance of simple lda
ldamodel <- lda(trainset$x, trainset$classes)
LDAprediction <- predict(ldamodel, testset$x)

## test error rate
1-sum(testset$classes==LDAprediction$class)/length(testset$classes)


## Example 2: learn a "qda" model with pvs on half of the Satellite dataset, 
## using "ks.test" 


library("mlbench")
data("Satellite")

## takes few seconds as exact KS tests are calculated here:
model <- pvs(classes ~ ., Satellite[1:3218,], method="qda", vs.method="ks.test")
## short summary, showing the class-pairs of the submodels and the selected variables
model 

## now predict on the rest of the data set:
## pred <- predict(model,Satellite[3219:6435,]) # takes some time
pred <- predict(model,Satellite[3219:6435,], quick=TRUE) # that's much quicker

## now you can look at the predicted classes:
pred$class 
## or the posterior probabilities:
pred$posterior

Plotting of 4 dimensional membership representation simplex

Description

For a 4 class discrimination problem the membership values of each class are visualized in a 3 dimensional barycentric coordinate system.

Usage

quadplot(e = NULL, f = NULL, g = NULL, h = NULL, angle = 75, 
    scale.y = 0.6, label = 1:4, labelcol = rainbow(4), 
    labelpch = 19, labelcex = 1.5, main = "", s3d.control = list(), 
    simplex.control = list(), legend.control = list(), ...)

Arguments

Details

The membership values are calculated with quadtrafo and plotted with scatterplot3d.

Value

A scatterplot3d object.

Author(s)

Karsten Luebke, karsten.luebke@fom.de, and Uwe Ligges

References

Garczarek, Ursula Maria (2002): Classification rules in standardized partition spaces. Dissertation, University of Dortmund. URL http://hdl.handle.net/2003/2789

See Also

triplot, scatterplot3d

Examples

library("MASS")
data(B3)
opar <- par(mfrow = c(1, 2), pty = "s")
posterior <- predict(lda(PHASEN ~ ., data = B3))$post
s3d <- quadplot(posterior, col = rainbow(4)[B3$PHASEN], 
        labelpch = 22:25, labelcex = 0.8,
        pch = (22:25)[apply(posterior, 1, which.max)], 
        main = "LDA posterior assignments")
quadlines(centerlines(4), sp = s3d, lty = "dashed")

posterior <- predict(qda(PHASEN ~ ., data = B3))$post
s3d <- quadplot(posterior, col = rainbow(4)[B3$PHASEN], 
        labelpch = 22:25, labelcex = 0.8,
        pch = (22:25)[apply(posterior, 1, which.max)],
        main = "QDA posterior assignments")
quadlines(centerlines(4), sp = s3d, lty = "dashed")
par(opar)

Transforming of 4 dimensional values in a barycentric coordinate system.

Description

Transforming of 4 dimensional values in a barycentric coordinate system.

Usage

quadtrafo(e, f = NULL, g = NULL, h = NULL)
        
quadlines(e, f = NULL, g = NULL, h = NULL, sp, ...)

quadpoints(e, f = NULL, g = NULL, h = NULL, sp, ...)

Arguments

Value

For quadtrafo the 3 dimensional values in the barycentrix coordinate system.

Author(s)

Karsten Luebke, karsten.luebke@fom.de

See Also

triplot, quadplot

Examples

library(MASS)
data(B3)
posterior <- predict(lda(PHASEN ~ ., data = B3))$post
quadtrafo(posterior)

Regularized Discriminant Analysis (RDA)

Description

Builds a classification rule using regularized group covariance matrices that are supposed to be more robust against multicollinearity in the data.

Usage

rda(x, ...)

## Default S3 method:
rda(x, grouping = NULL, prior = NULL, gamma = NA, 
    lambda = NA, regularization = c(gamma = gamma, lambda = lambda), 
    crossval = TRUE, fold = 10, train.fraction = 0.5, 
    estimate.error = TRUE, output = FALSE, startsimplex = NULL, 
    max.iter = 100, trafo = TRUE, simAnn = FALSE, schedule = 2, 
    T.start = 0.1, halflife = 50, zero.temp = 0.01, alpha = 2, 
    K = 100, ...)
## S3 method for class 'formula'
rda(formula, data, ...)

Arguments

Details

J.H. Friedman (see references below) suggested a method to fix almost singular covariance matrices in discriminant analysis. Basically, individual covariances as in QDA are used, but depending on two parameters (\gamma and \lambda), these can be shifted towards a diagonal matrix and/or the pooled covariance matrix. For (\gamma=0, \lambda=0) it equals QDA, for (\gamma=0, \lambda=1) it equals LDA.

You may fix these parameters at certain values or leave it to the function to try to find “optimal” values. If one parameter is given, the other one is determined using the R-function ‘optimize’. If no parameter is given, both are determined numerically by a Nelder-Mead-(Simplex-)algorithm with the option of using Simulated Annealing. The goal function to be minimized is the (estimated) misclassification rate; the misclassification rate is estimated either by Cross-Validation or by repeatedly dividing the data into training- and test-sets (Boostrapping).

Warning: If these sets are small, optimization is expected to produce almost random results. We recommend to adjust the parameters manually in such a case. In all other cases it is recommended to run the optimization several times in order to see whether stable results are gained.

Since the Nelder-Mead-algorithm is actually intended for continuous functions while the observed error rate by its nature is discrete, a greater number of Boostrap-samples might improve the optimization by increasing the smoothness of the response surface (and, of course, by reducing variance and bias). If a set of parameters leads to singular covariance matrices, a penalty term is added to the misclassification rate which will hopefully help to maneuver back out of singularity (so do not worry about error rates greater than one during optimization).

Value

A list of class rda containing the following components:

More details

The explicit defintion of \gamma, \lambda and the resulting covariance estimates is as follows:

The pooled covariance estimate \hat{\Sigma} is given as well as the individual covariance estimates \hat{\Sigma}_k for each group.

First, using \lambda, a convex combination of these two is computed:

\hat{\Sigma}_k (\lambda) := (1-\lambda) \hat{\Sigma}_k + \lambda \hat{\Sigma}.

Then, another convex combination is constructed using the above estimate and a (scaled) identity matrix:

\hat{\Sigma}_k (\lambda,\gamma) = (1-\gamma)\hat{\Sigma}_k(\lambda)+ \gamma\frac{1}{d}\mathrm{tr}[\hat{\Sigma}_k(\lambda)]\mathrm{I}.

The factor \frac{1}{d}\mathrm{tr}[\hat{\Sigma}_k(\lambda)] in front of the identity matrix I is the mean of the diagonal elements of \hat{\Sigma}_k(\lambda), so it is the mean variance of all d variables assuming the group covariance \hat{\Sigma}_k(\lambda).

For the four extremes of (\gamma,\lambda) the covariance structure reduces to special cases:

• (\gamma=0, \lambda=0): QDA - individual covariance for each group.

• (\gamma=0, \lambda=1): LDA - a common covariance matrix.

• (\gamma=1, \lambda=0): Conditional independent variables - similar to Naive Bayes, but variable variances within group (main diagonal elements) are equal.

• (\gamma=1, \lambda=1): Classification using euclidean distance - as in previous case, but variances are the same for all groups. Objects are assigned to group with nearest mean.

Author(s)

Christian Röver, roever@statistik.tu-dortmund.de

References

Friedman, J.H. (1989): Regularized Discriminant Analysis. In: Journal of the American Statistical Association 84, 165-175.

Press, W.H., Flannery, B.P., Teukolsky, S.A., Vetterling, W.T. (1992): Numerical Recipes in C. Cambridge: Cambridge University Press.

See Also

predict.rda, lda, qda

Examples

data(iris)
x <- rda(Species ~ ., data = iris, gamma = 0.05, lambda = 0.2)
predict(x, iris)

Linear transformation of data

Description

The function performs a linear transformation of the data, such that afterwards range(data)=c(theMin,theMax).

Usage

rerange(data, min.goal = 0, max.goal = 1, min.data =
    min(data), max.data = max(data), center = NA)

Arguments

Value

vector with the transformed data

Author(s)

Dominik Reusser

Examples

   klaR:::rerange(data=1:20)
   klaR:::rerange(data=1:30, center=5)

Plotting Eight Direction Arranged Maps or Self-Organizing Maps

Description

Plotting method for objects of class EDAM or som.

Usage

shardsplot(object, plot.type = c("eight", "four", "points", "n"), 
    expand = 1, stck = TRUE, grd = FALSE, standardize = FALSE, 
    data.or = NA, label = FALSE, plot = TRUE, classes = 0, 
    vertices = TRUE, classcolors = "rainbow", wghts = 0, 
    xlab = "Dimension 1", ylab = "Dimension 2", xaxs = "i", 
    yaxs = "i", plot.data.column = NA,
    log.classes = FALSE, revert.colors = FALSE, ...)

level_shardsplot(object, par.names, rows = 1:NCOL(object$data),
    centers = rep(NA, length(par.names)), class.labels = NA,
    revert.colors = rep(FALSE, length(par.names)), 
    log.classes = rep(FALSE, length(par.names)),
    centeredcolors = colorRamp(c("red", "white", "blue")),
    mfrow = c(2, 2), plot.type = c("eight", "four", "points", "n"),
    expand = 1, stck = TRUE, grd = FALSE, standardize = FALSE,
    label = FALSE, plot = TRUE, vertices = TRUE, classcolors = "topo",
    wghts = 0, xlab = "Dimension 1", ylab = "Dimension 2",
    xaxs = "i", yaxs = "i", ...)

## S3 method for class 'EDAM'
plot(...)

Arguments

Details

level_shardsplot uses multiple shardsplot representations of a SOM in order to depict how the data used to calculate the SOM is distribution across the map. Two representations are possible for the data, first with a single color ramp from the minimum value to the maximum value. The second representation is usefull for data for which a basic value exists some where between minimum and maximum for which a special color representation should be used (e.g. 0 is indicated with white).

If plot.type is “four” or “eight”, the shape of each shard depends on the relative distances of the actual object or codebook to its up to eight neighbours. If plot.type is “eight”, shardsplot corresponds to the representation method suggested by Cottrell and de Bodt (1996) for Kohonen Self-Organizing Maps. If plot.type is “points”, shardsplot reduces to a usual scatter plot.

Value

The following list is (invisibly) returned:

Author(s)

Nils Raabe, level_shardsplot function from Dominik Reusser

References

Cottrell, M., and de Bodt, E. (1996). A Kohonen Map Representation to Avoid Misleading Interpretations. Proceedings of the European Symposium on Atrificial Neural Networks, D-Facto, pp. 103–110.

See Also

EDAM, TopoS, som

Examples

# Compute clusters and an Eight Directions Arranged Map for the 
# country data. Plotting the result.
data(countries)
logcount <- log(countries[,2:7])
sdlogcount <- apply(logcount, 2, sd)
logstand <- t((t(logcount) / sdlogcount) * c(1,2,6,5,5,3))
cclasses <- cutree(hclust(dist(logstand)), k = 6)
countryEDAM <- EDAM(logstand, classes = cclasses, sa = FALSE, 
    iter.max = 10, random = FALSE)
plot(countryEDAM, vertices = FALSE, label = TRUE, stck = FALSE)

# Compute and plot a Self-Organizing Map for the iris data
data(iris)
library(som)
irissom <- som(iris[,1:4], xdim = 6, ydim = 14)
shardsplot(irissom, data.or = iris, vertices = FALSE)
opar <- par(xpd = NA)
legend(7.5, 6.1, col = rainbow(3), xjust = 0.5, yjust = 0,
    legend = levels(iris[, 5]), pch = 16, horiz = TRUE)
par(opar)    

level_shardsplot(irissom, par.names = names(iris), 
    class.labels = NA, mfrow = c(2,2))

Simple k nearest Neighbours

Description

Function for simple knn classification.

Usage

sknn(x, ...)

## Default S3 method:
sknn(x, grouping, kn = 3, gamma=0, ...)
## S3 method for class 'data.frame'
sknn(x, ...)
## S3 method for class 'matrix'
sknn(x, grouping, ..., subset, na.action = na.fail)
## S3 method for class 'formula'
sknn(formula, data = NULL, ..., subset, na.action = na.fail)

Arguments

Details

If gamma>0 an gaussian like density is used to weight the classes of the kn nearest neighbors. weight=exp(-gamma*distance). This is similar to an rbf kernel. If the distances are large it may be useful to scale the data first.

Value

A list containing the function call.

Author(s)

Karsten Luebke, karsten.luebke@fom.de

See Also

predict.sknn, knn

Examples

data(iris)
x <- sknn(Species ~ ., data = iris)
x <- sknn(Species ~ ., gamma = 4, data = iris)

Stepwise variable selection for classification

Description

Forward/backward variable selection for classification using any specified classification function and selecting by estimated classification performance measure from ucpm.

Usage

stepclass(x, ...)

## Default S3 method:
stepclass(x, grouping, method, improvement = 0.05, maxvar = Inf, 
    start.vars = NULL, direction = c("both", "forward", "backward"), 
    criterion = "CR",  fold = 10, cv.groups = NULL, output = TRUE, 
    min1var = TRUE, ...)
## S3 method for class 'formula'
stepclass(formula, data, method, ...)

Arguments

Details

The classification “method” (e.g. ‘lda’) must have its own ‘predict’ method (like ‘predict.lda’ for ‘lda’) that either returns a matrix of posterior probabilities or a list with an element ‘posterior’ containing that matrix instead. It must be able to deal with matrices as in method(x, grouping, ...)

Then a stepwise variable selection is performed. The initial model is defined by the provided starting variables; in every step new models are generated by including every single variable that is not in the model, and by excluding every single variable that is in the model. The resulting performance measure for these models are estimated (by cross-validation), and if the maximum value of the chosen criterion is better than ‘improvement’ plus the value so far, the corresponding variable is in- or excluded. The procedure stops, if the new best value is not good enough, or if the specified maximum number of variables is reached.

If ‘direction’ is “forward”, the model is only extended (by including further variables), if ‘direction’ is “backward”, the model is only reduced (by excluding variables from the model).

Value

An object of class ‘stepclass’ containing the following components:

Author(s)

Christian Röver, roever@statistik.tu-dortmund.de, Irina Czogiel

See Also

step, stepAIC, and greedy.wilks for stepwise variable selection according to Wilk's lambda

Examples

data(iris)
library(MASS)
iris.d <- iris[,1:4]  # the data    
iris.c <- iris[,5]    # the classes 
sc_obj <- stepclass(iris.d, iris.c, "lda", start.vars = "Sepal.Width")
sc_obj
plot(sc_obj)

## or using formulas:
sc_obj <- stepclass(Species ~ ., data = iris, method = "qda", 
    start.vars = "Sepal.Width", criterion = "AS")  # same as above 
sc_obj
## now you can say stuff like
## qda(sc_obj$formula, data = B3)

Interface to SVMlight

Description

Function to call SVMlight from R for classification. Multiple group classification is done with the one-against-rest partition of data.

Usage

svmlight(x, ...)

## Default S3 method:
svmlight(x, grouping, temp.dir = NULL, pathsvm = NULL, 
    del = TRUE, type = "C", class.type = "oaa", svm.options = NULL, 
    prior = NULL, out = FALSE, ...)
## S3 method for class 'data.frame'
svmlight(x, ...)
## S3 method for class 'matrix'
svmlight(x, grouping, ..., subset, na.action = na.fail)
## S3 method for class 'formula'
svmlight(formula, data = NULL, ..., subset, 
    na.action = na.fail)

Arguments

Details

Function to call SVMlight from R for classification (type="C"). SVMlight is an implementation of Vapnik's Support Vector Machine. It is written in C by Thorsten Joachims. On the homepage (see below) the source-code and several binaries for SVMlight are available. If more then two classes are given the SVM is learned by the one-against-all scheme (class.type="oaa"). That means that each class is trained against the other K-1 classes. The class with the highest decision function in the SVM wins. So K SVMs have to be learned. If class.type="oao" each class is tested against every other and the final class is elected by a majority vote.

If type="R" a SVM Regression is performed.

Value

A list containing the function call and the result of SVMlight.

Requirements

SVMlight (http://svmlight.joachims.org/) must be installed before using this interface.

Author(s)

Karsten Luebke, karsten.luebke@fom.de, Andrea Preusser

References

http://svmlight.joachims.org/

See Also

predict.svmlight,svm,

Examples

## Not run: 
## Only works if the svmlight binaries are in the path.
data(iris)
x <- svmlight(Species ~ ., data = iris)
## Using RBF-Kernel with gamma=0.1:
data(B3)
x <- svmlight(PHASEN ~ ., data = B3, svm.options = "-t 2 -g 0.1")

## End(Not run)

Computation of criterion S of a visualization

Description

TopoS computes one version of the criterion stress as i.e. known from sammon for a given visualization.

Usage

TopoS(EV.dist, Cells.dist)

Arguments

Details

TopoS first performs a homogeneous linear regression where dx is predicted by dy. Then the residual sum of squares of this regression is computed and divided by the sum of squared dx. Finally one minus the square root of the latter result defines S.

Value

TopoS returns a numeric between zero and one which is the criterion S of the given visualization.

Author(s)

Nils Raabe

See Also

EDAM

Examples

# Compute S for the MDS visualization of the german business data
data(B3)
plot(cmdscale(dist(B3[, 2:14])), col = rainbow(4)[B3[, 1]], pch = 16)
TopoS(dist(B3[, 2:14]), dist(cmdscale(dist(B3[, 2:14]))))

Barycentric plots

Description

Function to add a frame to an existing (barycentric) plot.

Usage

triframe(label = 1:3, label.col = 1, cex = 1, ...)

Arguments

Author(s)

Christian Röver, roever@statistik.tu-dortmund.de

See Also

triplot, trilines, trigrid, centerlines

Examples

triplot(grid = TRUE, frame = FALSE)     # plot without frame 
some.triangle <- rbind(c(0, 0.65, 0.35), c(0.53, 0.47, 0), 
                       c(0.72, 0, 0.28))[c(1:3, 1), ]
trilines(some.triangle, col = "red", pch = 16, type = "b")
triframe(label = c("left", "top", "right"), col = "blue", 
         label.col = "green3")          # frame on top of points 

Barycentric plots

Description

Function to add a grid to an existing (barycentric) plot.

Usage

trigrid(x = seq(0.1, 0.9, by = 0.1), y = NULL, z = NULL, 
    lty = "dashed", col = "grey", ...)

Arguments

Details

Grid lines illustrate the set of points for which one of the dimensions is held constant; e.g. horizontal lines contain all points with a certain value y for the second dimension, connecting the two extreme points (0,y,1-y) and (1-y,y,0).

Grids may be designed more flexible than with triplot's grid option.

Author(s)

Christian Röver, roever@statistik.tu-dortmund.de

See Also

triplot, trilines, triframe, centerlines

Examples

triplot(grid = FALSE)
trigrid(c(1/3, 0.5)) # same grid for all 3 dimensions 

triplot(grid = c(1/3, 0.5))  # (same effect) 

triplot(grid = FALSE)
# different grids for all dimensions:
trigrid(x = 1/3, y = 0.5, z = seq(0.2, 0.8, by=0.2))  

triplot(grid = FALSE)
# grid for third dimension only:
trigrid(x = NA, y = NA, z = c(0.1, 0.2, 0.4, 0.8))  

Barycentric plots

Description

Function to add a point and the corresponding perpendicular lines to all three sides to an existing (barycentric) plot.

Usage

triperplines(x, y = NULL, z = NULL, lcol = "red", pch = 17, ...)

Arguments

Details

Adds a (single!) point and lines to an existing plot (generated by triplot). The lines originate from the point and run (perpendicular) towards all three sides. The lengths (and proportions) of these lines are identical to those of x, y and z.

Value

a 2-column-matrix containing plot coordinates.

Author(s)

Christian Röver, roever@statistik.tu-dortmund.de

See Also

triplot, tripoints, trilines, tritrafo

Examples

triplot()  # empty plot 
triperplines(1/2, 1/3, 1/6)

Barycentric plots

Description

Function to produce triangular (barycentric) plots illustrating proportions of 3 components, e.g. discrete 3D-distributions or mixture fractions that sum up to 1.

Usage

triplot(x = NULL, y = NULL, z = NULL, main = "", frame = TRUE, 
    label = 1:3, grid = seq(0.1, 0.9, by = 0.1), center = FALSE, 
    set.par = TRUE, ...)

Arguments

Details

The barycentric plot illustrates the set of points (x,y,z) with x,y,z between 0 and 1 and x+y+z=1; that is, the triangle spanned by (1,0,0), (0,1,0) and (0,0,1) in 3-dimensional space. The three dimensions x, y and z correspond to lower left, upper and lower right corner of the plot. The greater the share of x in the proportion, the closer the point is to the lower left corner; Points on the opposite (upper right) side have a zero x-fraction. The grid lines show the points at which one dimension is held constant, horizontal lines for example contain points with a constant second dimension.

Author(s)

Christian Röver, roever@statistik.tu-dortmund.de

See Also

tripoints, trilines, triperplines, trigrid, triframe for points, lines and layout, tritrafo for placing labels, and quadplot for the same in 4 dimensions.

Examples

# illustrating probabilities: 
triplot(label = c("1, 2 or 3", "4 or 5", "6"), 
    main = "die rolls: probabilities", pch = 17)
triperplines(1/2, 1/3, 1/6)

# expected... 
triplot(1/2, 1/3, 1/6, label = c("1, 2 or 3", "4 or 5", "6"), 
    main = "die rolls: expected and observed frequencies", pch = 17)
# ... and observed frequencies. 
dierolls <- matrix(sample(1:3, size = 50*20, prob = c(1/2, 1/3, 1/6), 
                          replace = TRUE), ncol = 50)
frequencies <- t(apply(dierolls, 1, 
    function(x)(summary(factor(x, levels = 1:3)))) / 50)
tripoints(frequencies)

# LDA classification posterior: 
data(iris)
require(MASS)
pred <- predict(lda(Species ~ ., data = iris),iris)
plotchar <- rep(1,150)
plotchar[pred$class != iris$Species] <- 19
triplot(pred$posterior, label = colnames(pred$posterior), 
        main = "LDA posterior assignments", center = TRUE, 
        pch = plotchar, col = rep(c("blue", "green3", "red"), rep(50, 3)), 
        grid = TRUE)
legend(x = -0.6, y = 0.7, col = c("blue", "green3", "red"), 
    pch = 15, legend = colnames(pred$posterior))

Barycentric plots

Description

Function to add points or lines to an existing (barycentric) plot.

Usage

tripoints(x, y = NULL, z = NULL, ...)
trilines(x, y = NULL, z = NULL, ...)

Arguments

Details

Adds points or lines to an existing plot (generated by triplot).

Author(s)

Christian Röver, roever@statistik.tu-dortmund.de

See Also

points, lines, triplot, tritrafo, centerlines

Examples

triplot()  # empty plot 
tripoints(0.1, 0.2, 0.7)                        # a point 
tripoints(c(0.2, 0.6), c(0.3, 0.3), c(0.5, 0.1),
    pch = c(2, 6))                              # two points
trilines(c(0.1, 0.6), c(0.2, 0.3), c(0.7, 0.1), 
    col = "blue", lty = "dotted")               # a line 

trilines(centerlines(3))

Barycentric plots

Description

Function to carry out the transformation into 2D space for triplot, trilines etc.

Usage

tritrafo(x, y = NULL, z = NULL, check = TRUE, tolerance = 0.0001)

Arguments

Details

Projects the mixture given by x, y, and z with x, y, z between one and zero and x+y+z=1 into a two-dimensional space.

For further details see triplot.

Value

A matrix with two columns corresponding to the two dimensions.

Author(s)

Christian Röver, roever@statistik.tu-dortmund.de

See Also

triplot, tripoints, trilines, trigrid

Examples

tritrafo(0.1, 0.2, 0.7)
tritrafo(0.1, 0.2, 0.6) # warning 

triplot()
points(tritrafo(0.1, 0.2, 0.7), col="red")
tripoints(0.1, 0.2, 0.7, col="green")  # the same

tritrafo(c(0.1,0.2), c(0.3,0.4), c(0.6,0.4))
tritrafo(diag(3))

point <- c(0.25,0.6,0.15)
triplot(point, pch=16)
text(tritrafo(point), "(0.25, 0.60, 0.15)", adj=c(0.5,2)) # add a label 

Uschi's classification performance measures

Description

Function to calculate the Correctness Rate, the Accuracy, the Ability to Seperate and the Confidence of a classification rule.

Usage

ucpm(m, tc, ec = NULL)

Arguments

Details

• The correctness rate is the estimator for the correctness of a classification rule (1-error rate).

• The accuracy is based on the euclidean distances between (scaled) membership vectors and the vectors representing the true class corner. These distances are standardized so that a measure of 1 is achieved if all vectors lie in the correct corners and 0 if they all lie in the center.

• Analougously, the ability to seperate is based on the distances between (scaled) membership vectors and the vector representing the corresponding assigned class corner.

• The confidence is the mean of the membership values of the assigned classes.

Value

A list with elements:

Author(s)

Karsten Luebke, karsten.luebke@fom.de

References

Garczarek, Ursula Maria (2002): Classification rules in standardized partition spaces. Dissertation, University of Dortmund. URL http://hdl.handle.net/2003/2789

Examples

library(MASS)
data(iris)
ucpm(predict(lda(Species ~ ., data = iris))$posterior, iris$Species)

Weights of evidence

Description

Computes weight of evidence transform of factor variables for binary classification.

Usage

woe(x, ...)
## Default S3 method:
woe(x, grouping, weights = NULL, zeroadj = 0, ids = NULL, 
                      appont = TRUE, ...)
## S3 method for class 'formula'
woe(formula, data = NULL, weights = NULL, ...)

Arguments

Details

To each factor level x a numeric value WOE(x) = ln(f(x|1)/f(x|2)) is assigned where 1 and 2 denote the class labels. The WOE transform is motivated for subsequent modelling by logistic regression. Note that the frequencies of the classes should be investigated before. Information values heuristically quantify the discriminatory power of a variable by IV = (f(x|1)-f(x|2)) ln(f(x|1)/f(x|2)).

Value

Returns an object of class woe that can be applied to new data.

Author(s)

Gero Szepannek

References

Good, I. (1950): Probability and the Weighting of Evidences. Charles Griffin, London.

Kullback, S. (1959): Information Theory and Statistics. Wiley, New York.

See Also

predict.woe, plot.woe

Examples

## load German credit data
data("GermanCredit")

## training/validation split
train <- sample(nrow(GermanCredit), round(0.6*nrow(GermanCredit)))

woemodel <- woe(credit_risk~., data = GermanCredit[train,], zeroadj=0.5, applyontrain = TRUE)
woemodel

## plot variable information values and woes
plot(woemodel)
plot(woemodel, type = "woes")

## apply woes 
traindata <- predict(woemodel, GermanCredit[train,], replace = TRUE)
str(traindata)

## fit logistic regression model
glmodel     <- glm(credit_risk~., traindata, family=binomial)
summary(glmodel)
pred.trn <- predict(glmodel, traindata, type = "response")

## predict validation data
validata <- predict(woemodel, GermanCredit[-train,], replace = TRUE)
pred.val <- predict(glmodel, validata, type = "response")

Variable clustering based variable selection

Description

Applies variable selection to data based on variable clusterings as resulting from corclust or CLV.

Usage

xtractvars(object, data, thres = 0.5)

Arguments

Details

Of each cluster the first variable is selected as well as all other variables with an average within cluster correlation below thres.

Value

The data is returned where unselected coloumns are removed.

Author(s)

Gero Szepannek

References

Roever, C. and Szepannek, G. (2005): Application of a genetic algorithm to variable selection in fuzzy clustering. In C. Weihs and W. Gaul (eds), Classification - The Ubiquitous Challenge, 674-681, Springer.

See Also

See also corclust, cvtree and CLV.

Examples

    data(B3)
    ccres <- corclust(B3)
    plot(ccres)
    cvtres <- cvtree(ccres, k = 3)
    newdata <- xtractvars(cvtres, B3, thres = 0.5)