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Rmixmod a MIXture MODelling package

Description

Rmixmod is a package based on the existing MIXMOD software. MIXMOD is a tool for fitting a mixture model of multivariategaussian or multinomial components to a given data set with either a clustering, a density estimation or a discriminantanalysis point of view.

Details

The general purpose of the package is to discover, or explain, group structures in multivariate data sets with unknown(cluster analysis or clustering) or known class discriminant analysis or classification). It is an exploratory dataanalysis tool for solving clustering and classification problems. But it can also be regarded as a semi-parametric toolto estimate densities with Gaussian mixture distributions and multinomial distributions.

Mathematically, mixture probability density function (pdf)f is a weighted sum ofK components densities:

f({\bf x}_i|\theta) = \sum_{k=1}^{K}p_kh({\bf x}_i|\lambda_k)

whereh(.|{\lambda}_k) denotes ad-dimensional distribution parametrized by\lambda_k.The parameters are the mixing proportionsp_k and the component of the distribution\lambda_k.

In the Gaussian case,h is the density of a Gaussian distribution with mean\mu_k and variancematrix\Sigma_k, and thus\lambda_k = (\mu_k,\Sigma_k).

In the qualitative case,h is a multinomial distribution and\lambda_k=(a_k,\epsilon_k) is the parameterof the distribution.

Estimation of the mixture parameters is performed either through maximum likelihood via the EM(Expectation Maximization, Dempster et al. 1977), the SEM (Stochastic EM, Celeux and Diebolt 1985) algorithmor through classification maximum likelihood via the CEM algorithm (Clustering EM, Celeux and Govaert 1992).These three algorithms can be chained to obtain original fitting strategies (e.g. CEM then EM with results of CEM) to useadvantages of each of them in the estimation process. As mixture problems usually have multiple relative maxima,the program will produce different results, depending on the initial estimates supplied by the user. If the user doesnot input his own initial estimates, some initial estimates procedures are proposed (random centers for instance).

It is possible to constrain some input parameters. For example, dispersions can be equal between classes, etc.

In the Gaussian case, fourteen models are implemented. They are based on the eigenvalue decomposition, are most generallyused. They depend on constraints on the variance matrix such as same variance matrix between clusters, spherical variancematrix... and they are suitable for data sets in any dimension.

In the qualitative case, five multinomial models are available. They are based on a reparametrization of the multinomialprobabilities.

In both cases, the models and the number of clusters can be chosen by different criteria:BIC (Bayesian Information Criterion), ICL (Integrated Completed Likelihood, a classification version of BIC),NEC (Entropy Criterion), or Cross-Validation (CV).

Author(s)

Author: Florent Langrognet and Remi Lebret and Christian Poli and Serge Iovleff, with contributions from C. Biernackiand G. Celeux and G. Govaertcontact@mixmod.org

References

Biernacki C., Celeux G., Govaert G., Langrognet F., 2006. "Model-Based Cluster and Discriminant Analysis withthe MIXMOD Software". Computational Statistics and Data Analysis, vol. 51/2, pp. 587-600.

Lebret R., Iovleff S., Langrognet F., Biernacki C., Celeux G., Govaert G. (2015). "Rmixmod: The R Package of theModel-Based Unsupervised, Supervised, and Semi-Supervised Classification Mixmod Library". Journal of StatisticalSoftware, 67(6), 1–29. https://doi.org/10.18637/jss.v067.i06

Examples

## Not run: ## Clustering Analysis# load quantitative data setdata(geyser)# Clustering in gaussian casexem1 <- mixmodCluster(geyser, 3)summary(xem1)plot(xem1)hist(xem1)# load qualitative data setdata(birds)# Clustering in multinomial casexem2 <- mixmodCluster(birds, 2)summary(xem2)barplot(xem2)# load heterogeneous data setdata(finance)# Clustering in composite casexem3 <- mixmodCluster(finance, 2:6)summary(xem3)## Discriminant Analysis# start by extract 10 observations from iris data setremaining.obs <- sample(1:nrow(iris), 10)# then run a mixmodLearn() analysis without those 10 observationslearn <- mixmodLearn(iris[-remaining.obs, 1:4], iris$Species[-remaining.obs])# create a MixmodPredict to predict those 10 observationsprediction <- mixmodPredict(    data = iris[remaining.obs, 1:4],    classificationRule = learn["bestResult"])# show resultsprediction# compare prediction with real resultspaste("accuracy= ", mean(as.integer(iris$Species[remaining.obs]) == prediction["partition"]) * 100,    "%",    sep = "")## End(Not run)

Constructor of [CompositeModel] class

Description

This class defines a Composite Model. Inherits the [Model] class.

Details

variable.independency

logical

component.independency

logical

Examples

new("CompositeModel")new("CompositeModel", listModels = c("Heterogeneous_pk_E_L_B", "Heterogeneous_pk_Ekj_L_B"))new("CompositeModel", free.proportions = FALSE, variable.independency = TRUE)getSlots("CompositeModel")

Constructor of [CompositeParameter] class

Description

This class defines parameters of a Heterogeneous Mixture Model. Inherits the [Parameter] class.

Details

g_parameter

an object of class CompositeParameter

m_parameter

an object of class MultinomialParameter

factor

a numeric vector

Examples

new("CompositeParameter")getSlots("CompositeParameter")

Constructor of [GaussianModel] class

Description

This class defines a gaussian Model. Inherits the [Model] class.

Details

family

character defining a family of models.

Examples

new("GaussianModel")new("GaussianModel", family = "general")getSlots("GaussianModel")

Constructor of [GaussianParameter] class

Description

This class defines parameters of a Gaussian Mixture Model. Inherits the [Parameter] class.

Details

mean

a numeric vector containing mean of each cluster.

variance

a vector of matrix containing variance matrix of each cluster.

Examples

new("GaussianParameter")getSlots("GaussianParameter")

Constructor of [Mixmod] class

Description

This is a class to run mixmod library.

Details

data

numeric vector or a data frame of observations. Can be qualitative,quantitative or both(heterogeneous)

dataType

character. Type of data. It defines whether data is quantitative, qualitative or composite

nbCluster

integer. It indicates the number of classes.

knownLabels

numeric. It contains the known labels.

weight

numeric vector with n (number of individuals) rows. Weight is optional.This option is to be used when weight is associated to the data.

nbVariable

integer. The number of variables.

nbSample

integer. The number of observations.

criterion

list of character. This option permits to select the criterion giving the best configurationof an execution.

models

a S4 [Model] object. Defining the list of models to be tested.

error

logical. Say if at least one model finished with no error in MIXMOD.

results

a list of S4 [MixmodResults] object containing all results.Results are sorted into a ascending order according to the first criterion (descending order for the CV criterion).This order can be changed by using the sortByCriterion() method.

Examples

getSlots("Mixmod")

Constructor of [MixmodCluster] class

Description

This is a class to run clustering with mixmod. Inherits the [Mixmod] class.

Details

strategy

a S4 [Strategy] object. Defining the strategy used to run MIXMOD.

bestResult

a S4 [MixmodResults] object containing the best model results.

Examples

## A quantitative example with the famous iris data setdata(iris)## with default valuesnew("MixmodCluster", data = iris[1:4], nbCluster = 3)getSlots("MixmodCluster")

Constructor of [MixmodDAResults] class

Description

This is a class to contain results after a discriminant analysis with MIXMOD.Inherits the [MixmodResults] class.

Details

CVLabel

vector of integers containing labels defined by cross validation.

CVClassification

classification table after cross validation.

MAPErrorRate

error rate done by MAP algorithm.

MAPClassification

classification table after MAP algorithm.

Examples

getSlots("MixmodDAResults")

Constructor of [MixmodLearn] class

Description

This is a class to run discriminant analysis with mixmod. Inherits the [Mixmod] class.

Details

bestResult

a S4 [MixmodDAResults] object containing the best model results.

nbCVBlocks

integer which defines the number of block to perform the Cross Validation.

Examples

## A quantitative example with the famous iris data setnew("MixmodLearn", data = iris[1:4], knownLabels = iris$Species)getSlots("MixmodLearn")

Constructor of [MixmodPredict] class

Description

This is a class to run discriminant analysis with mixmod.

Details

data

numeric vector, matrix, or data frame of observations. Either qualitative or quantitative.

dataType

character. It defines whether data are quantitative or qualitative.

nbVariable

integer. The number of variables.

nbSample

integer. The number of observations.

error

a character. The mixmod error.

classificationRule

a [MixmodResults] object containing the classification rule.

partition

a matrix containing observations to predict.

proba

a matrix of probabilities.

Examples

# start by extract 10 observations from iris data setremaining.obs <- sample(1:nrow(iris), 10)# then run a mixmodLearn() analysis without those 10 observationslearn <- mixmodLearn(iris[-remaining.obs, 1:4], iris$Species[-remaining.obs])# create a MixmodPredict to predict those 10 observationsnew("MixmodPredict", data = iris[remaining.obs, 1:4], classificationRule = learn["bestResult"])getSlots("MixmodPredict")

Constructor of [MixmodResults] class

Description

This is a class to contain results from MIXMOD library.

Details

nbCluster

integer. It indicates the number of components.

model

character. Name of the model.

criterion

list of character. This option permits to select the criterion giving the best configuration ofan execution.

criterionValue

numeric. Values of the criterion.

parameters

a S4 [Parameter] object. The best model parameters.

likelihood

numeric. The model likelihood.

partition

vector of integers defining the partition.

proba

a matrix of probabilities.

error

a character. The mixmod error.

Examples

getSlots("MixmodResults")

Constructor of [MixmodXmlCheck] class

Description

This is a class to handle XML files (TODO: describe...)

Constructor of [MixmodXmlInput] class

Description

This is ...

Constructor of [Model] class

Description

This class defines the Mixmod models.

Details

listModels

character containing a list of models.

free.proportions

logical to include models with free proportions. Default is TRUE.

equal.proportions

logical to include models with equal proportions. Default is FALSE.

Examples

getSlots("Model")

MultinomialModel

Description

Constructor of [MultinomialModel] class

Details

This class defines a multinomial Model. Inherits the [Model] class.

variable.independency

logical

component.independency

logical

Examples

new("MultinomialModel")new("MultinomialModel", listModels = c("Binary_pk_E", "Binary_p_E"))new("MultinomialModel", free.proportions = FALSE, variable.independency = TRUE)getSlots("MultinomialModel")

Constructor of [MultinomialParameter] class

Description

This class defines parameters of a Multinomial Mixture Model. Inherits the [Parameter] class.

Details

center

a numeric vector containing center of each cluster.

scatter

a vector of matrix containing dispersion matrix of each cluster.

factor

a character vector containing the modalities.

Examples

new("MultinomialParameter")getSlots("MultinomialParameter")

Constructor of [Parameter] class

Description

This class defines parameters of a Mixture Model.

Details

proportions

a numeric vector containing proportions of the mixture model.

Examples

getSlots("Parameter")

Constructor of [Strategy] class

Description

This class defines the Mixmod strategies.

Details

algo:

list of character string with the estimation algorithm. Possible values: "EM", "SEM", "CEM", c("EM","SEM").Default value is "EM".

nbTry:

integer defining the number of tries. Default value: 1.

initMethod:

a character string with the method of initialization of the algorithm specified in thealgoargument. Possible values: "random", "smallEM", "CEM", "SEMMax", "parameter", "label". Default value: "smallEM".

nbTryInInit:

integer defining number of tries ininitMethod algorithm. Default value: 50.

nbIterationInInit:

integer defining the number of "EM" or "SEM" iterations ininitMethod. Default values: 5ifinitMethod is "smallEM" and 100 ifinitMethod is "SEMMax".

nbIterationInAlgo:

list of integers defining the number of iterations if user want to use nbIteration as rule tostop the algorithm(s). Default value: 200.

epsilonInInit:

real defining the epsilon value in the initialization step. Only available ifinitMethod is"smallEM". Default value: 0.001.

epsilonInAlgo:

list of reals defining the epsilon value for the algorithm. Warning: epsilonInAlgo doesn't have anysense ifalgo is SEM, so it needs to be set as NaN in that case. Default value: 0.001.

seed:

integer defining the seed of the random number generator. Setting a particular seed allows the user to(re)-generate a particular sequence of random numbers. Default value is NULL, i.e. a random seed.

parameter:

instance of "Parameter" subclass. Required if initMethod is "parameter", forbidden otherwise.

labels:

vector of integers containing labels. Required if initMethod is "label", forbidden otherwise.

Examples

new("Strategy")new("Strategy", algo = "SEM", initMethod = "SEMMax")getSlots("Strategy")

Extract parts of a Rmixmod class

Description

Extract parts of a Rmixmod class

Usage

## S4 method for signature 'MultinomialModel,ANY,ANY,ANY'x[i, j, drop]## S4 replacement method for signature 'MultinomialModel,ANY,ANY,ANY'x[i, j] <- value## S4 method for signature 'GaussianModel,ANY,ANY,ANY'x[i, j, drop]## S4 replacement method for signature 'GaussianModel,ANY,ANY,ANY'x[i, j] <- value## S4 method for signature 'CompositeModel,ANY,ANY,ANY'x[i, j, drop]## S4 replacement method for signature 'CompositeModel,ANY,ANY,ANY'x[i, j] <- value## S4 method for signature 'MultinomialParameter,ANY,ANY,ANY'x[i, j, drop]## S4 replacement method for signature 'MultinomialParameter,ANY,ANY,ANY'x[i, j] <- value## S4 method for signature 'GaussianParameter,ANY,ANY,ANY'x[i, j, drop]## S4 replacement method for signature 'GaussianParameter,ANY,ANY,ANY'x[i, j] <- value## S4 method for signature 'CompositeParameter,ANY,ANY,ANY'x[i, j, drop]## S4 replacement method for signature 'CompositeParameter,ANY,ANY,ANY'x[i, j] <- value## S4 method for signature 'MixmodResults,ANY,ANY,ANY'x[i, j, drop]## S4 method for signature 'Strategy,ANY,ANY,ANY'x[i, j, drop]## S4 replacement method for signature 'Strategy,ANY,ANY,ANY'x[i, j] <- value## S4 method for signature 'MixmodCluster,ANY,ANY,ANY'x[i, j, drop]## S4 replacement method for signature 'MixmodCluster,ANY,ANY,ANY'x[i, j] <- value## S4 method for signature 'MixmodLearn,ANY,ANY,ANY'x[i, j, drop]## S4 replacement method for signature 'MixmodLearn,ANY,ANY,ANY'x[i, j] <- value## S4 method for signature 'MixmodPredict,ANY,ANY,ANY'x[i, j, drop]

Arguments

Convert a data frame containing integers to a qualitative data set with factors.

Description

Convert a data frame containing integers to a qualitative data set with factors.

Usage

asQualitative(x)

Arguments

Value

a qualitative data set with factors

Barplot of a class [Mixmod]

Description

Barplot of qualitative data from a [Mixmod] object using parametersto plot probabilities of modalities.

Usage

## S4 method for signature 'Mixmod'barplot(height, ...)

Arguments

Details

Each line corresponds to one variable. Barplot is drawn for each cluster with the probabilities foreach modality to be in that cluster.

See Also

barplot

Examples

data(birds)xem2 <- mixmodCluster(birds, 2)barplot(xem2)barplot(xem2, variables = c(2, 3, 4))barplot(xem2, variables = c("eyebrow", "collar"))

Barplot of a class [MixmodResults]

Description

Barplot of qualitative data object using parameters from a [MixmodResults]to plot probabilities of modalities.

Usage

barplotCluster(  x,  data,  variables = colnames(data),  main = paste("Barplot of", variables),  ...)

Arguments

Details

Each line corresponds to one variable. A barplot is drawn for each cluster with the probabilities foreach modality to be in that cluster.

See Also

barplot

Examples

data(birds)xem <- mixmodCluster(birds, 2)barplotCluster(xem["bestResult"], birds)barplotCluster(xem["bestResult"], birds, variables = c(2, 3, 4))barplotCluster(xem["bestResult"], birds, variables = c("eyebrow", "collar"))

Qualitative data: morphological description of birds

Description

The dataset contains details on the morphology of birds (puffins). Each individual (bird) is described by 6 qualitativevariables. One variable for the gender and 5 variables giving a morphological description of the birds.There is 69 puffins divided in 2 sub-classes: lherminieri (34) and subalaris (35).

Format

A data frame with 69 observations on the following 5 variables.

gender

a numeric vector defining the gender (2 modalities, male or female).

eyebrow

a numeric vector describing the eyebrow stripe (4 modalities).

collar

a numeric vector describing the collar (5 modalities).

sub-caudal

a numeric vector describing the sub-caudal (5 modalities).

border

a numeric vector describing the border (3 modalities).

Source

Bretagnolle, V., 2007. Personal communication, source: Museum.

Examples

data(birds)

Qualitative data: Car Evaluation

Description

Car Evaluation Database was derived from a simple hierarchical decision model originally developed for the demonstrationof DEX, M. Bohanec, V. Rajkovic: Expert system for decision making.

Format

A data frame with 1728 observations on the following 6 variables.

buying

the buying price (4 modalities: vhigh, high, med, low).

maint

the price of the maintenance (4 modalities: vhigh, high, med, low).

doors

the number of doors (4 modalities: 2, 3, 4, 5more).

persons

the capacity in terms of persons to carry (3 modalities: 2, 4, more).

lug_boot

the size of luggage boot (3 modalities: small, med, big).

safety

the estimated safety of the car (3 modalities: low, med, high).

acceptability

the car acceptability (4 modalities: unacc, acc, good, vgood).

Source

Creator: Marko BohanecDonors: Marko Bohanec & Blaz Zupanhttp://archive.ics.uci.edu/ml/datasets/Car+Evaluation

Examples

data(car)

clusteringMain

Description

TODO: describe

Get the heterogeneous model name using Gaussian and Multinomial model name

Description

Get the heterogeneous model name using Gaussian and Multinomial model name

Usage

composeModelName(g_modelname, m_modelname)

Arguments

Value

name of heterogeneous model

Define function to draw an ellipse

Description

Define function to draw an ellipse

Usage

ellipse(x, i, j)

Arguments

Composite data: Financial health of companies

Description

This data set is made up of 216 healthy firms and 212 bankruptcy firms (year 2002) and also 241 healthy firms and 220bankruptcy firms (year 2003). Companies are described by four financial ratios expected to provide some meaningfulinformation about their health: EBITDA/Total Assets, Value Added/Total Sales, Quick Ratio, Accounts Payable/Total Sales.This data set offers the possibility to predict the company's ability to cover its financial obligations and also to studyits stability over the years.

Format

A data frame with 889 companies (rows) and 6 variables (columns).

Year

categorical variable with two modalities (2002 & 2003).

Health

categorical variable with two modalities (bankruptcy & healthy).

EBITDA.Total.Assets

numeric variable.

Value.Added.Total.Sales

numeric variable.

Quick.Ratio

numeric variable.

Accounts.Payable.Total.Sales

numeric variable.

Source

Lourme A, Biernacki C (2011).Simultaneous t-Model-Based Clustering for Data Differing over Time Period: Applicationfor Understanding Companies Financial Health. Case Studies in Business, Industry and Government Statistics, 4(2), 73-82.

Du Jardin P, S\'everin E (2010).Dynamic analysis of the business failure process: a study of bankruptcytrajectories. In Portuguese Finance Network. Ponte Delgada, Portugal.

Examples

data(finance)summary(finance)

Quantitative data: Old Faithful Geyser

Description

The file geyser.rda contains 272 observations from the Old Faithful Geyser in the Yellowstone National Park.Each observation consists of two measurements: the duration (in minutes) of the eruption and the waiting time(in minutes) to the next eruption.

Format

A data frame with 272 observations on the following 2 variables.

Duration

a numeric vector containing the duration (in minutes) of the eruption

Waiting.Time

a numeric vector containing the waiting time (in minutes) to the next eruption

Details

Old Faithful erupts more frequently than any other big geyser, although it is not the largest nor the most regulargeyser in the park. Its average interval between two eruptions is about 76 minutes, varying from 45 - 110 minutes.An eruption lasts from 1.1/2 to 5 minutes, expels 3,700 - 8,400 gallons (14,000 - 32,000 litres) of boiling water,and reaches heights of 106 - 184 feet (30 - 55m). It was named for its consistent performance by members of the WashburnExpedition in 1870. Old Faithful is still as spectacular and predictable as it was a century ago.

Source

https://web.archive.org/web/20191110083004/http://www.geyserstudy.org/geyser.aspx?pGeyserNo=OLDFAITHFUL

References

Hardle, W. (1991). "Smoothing Techniques with Implementation in S". Springer-Verlag, New York.

Azzalini, A. and Bowman, A. W. (1990). "A look at some data on the Old Faithful geyser". Applied Statistics 39, 357-365.

Examples

data(geyser)

Composite data with training and testing set

Description

The data set is made up of 5 variables: 3 categorical variables and 2 quantitative variables.The original data set contains 200 individuals. The training data set has 300 individuals while the testing data set has100 individuals.

Format

A data frame with 200 individuals (rows) and 5 variables (columns).

V1

categorical variable with two modalities (1 & 2).

V2

categorical variable with two modalities (1 & 2).

V3

categorical variable with two modalities (1 & 2).

V4

numeric variable.

V5

numeric variable.

See Also

heterodatatrain andheterodatatest

Examples

data(heterodata)summary(heterodata)

Composite data: A testing set

Description

The data set is made up of 5 variables: 3 categorical variables and 2 quantitative variables.The testing data set has 100 individuals.

Format

A data frame with 100 individuals (rows) and 5 variables (columns).

V1

categorical variable with two modalities (1 & 2).

V2

categorical variable with two modalities (1 & 2).

V3

categorical variable with two modalities (1 & 2).

V4

numeric variable.

V5

numeric variable.

See Also

heterodatatrain

Examples

data(heterodatatest)summary(heterodatatest)

Composite data: A training set

Description

The data set is made up of 5 variables: 3 categorical variables and 2 quantitative variables.The training data set has 300 individuals.

Format

A data frame with 300 individuals (rows) and 5 variables (columns).

V1

categorical variable with two modalities (1 & 2).

V2

categorical variable with two modalities (1 & 2).

V3

categorical variable with two modalities (1 & 2).

V4

numeric variable.

V5

numeric variable.

See Also

heterodatatest

Examples

data(heterodatatrain)summary(heterodatatrain)

Histograms of a class [Mixmod]

Description

Histograms of quantitative data from a [Mixmod] object using parametersto plot densities.

Usage

## S4 method for signature 'Mixmod'hist(x, hist_x_dim = 10000, ...)

Arguments

Details

Data with the density of each cluster and the mixture density are drawn for each variable.

See Also

hist

Examples

data(iris)xem <- mixmodCluster(iris[1:4], 3)hist(xem)hist(xem, variables = c(1, 3))hist(xem, variables = c("Sepal.Length", "Sepal.Width"))

Histogram of a class [MixmodResults]

Description

Histograms of data object using parameters from a [MixmodResults]to plot densities.

Usage

histCluster(  x,  data,  variables = colnames(data),  xlab = rep("", length(variables)),  main = paste("Histogram of", variables),  hist_x_dim = 10000,  ...)

Arguments

Details

Data with the density of each cluster and the mixture density are drawn for each variable.

See Also

hist

Examples

data(geyser)xem1 <- mixmodCluster(geyser, 3)## Not run: histCluster(xem1["bestResult"], geyser)## End(Not run)histCluster(xem1["bestResult"], geyser, variables = 1)

Create an instance of the [MultinomialModel] class using new/initialize.

Description

Initialization method. Used internally in the ‘Rmixmod’ package.

Initialization method. Used internally in the ‘Rmixmod’ package.

Initialization method. Used internally in the ‘Rmixmod’ package.

Initialization method. Used internally in the ‘Rmixmod’ package.

Initialization method. Used internally in the ‘Rmixmod’ package.

Initialization method. Used internally in the ‘Rmixmod’ package.

Initialization method. Used internally in the ‘Rmixmod’ package.

Initialization method. Used internally in the ‘Rmixmod’ package.

Usage

## S4 method for signature 'MultinomialModel'initialize(  .Object,  listModels,  free.proportions,  equal.proportions,  variable.independency,  component.independency)## S4 method for signature 'GaussianModel'initialize(.Object, listModels, family, free.proportions, equal.proportions)## S4 method for signature 'CompositeModel'initialize(  .Object,  listModels,  free.proportions,  equal.proportions,  variable.independency,  component.independency)## S4 method for signature 'Mixmod'initialize(  .Object,  data,  dataType,  models,  weight,  knownLabels,  xmlIn,  xmlOut,  seed,  trace,  massiccc)## S4 method for signature 'Strategy'initialize(  .Object,  algo,  nbTry,  initMethod,  nbTryInInit,  nbIterationInInit,  nbIterationInAlgo,  epsilonInInit,  epsilonInAlgo,  seed,  parameter,  labels)## S4 method for signature 'MixmodCluster'initialize(  .Object,  data = NULL,  nbCluster = NULL,  dataType = NULL,  models = NULL,  strategy = NULL,  criterion = NULL,  weight = NULL,  knownLabels = NULL,  seed = -1,  xmlIn = NULL,  xmlOut = NULL,  trace = 0,  massiccc = 0)## S4 method for signature 'MixmodLearn'initialize(  .Object,  data = NULL,  knownLabels = NULL,  dataType = NULL,  models = NULL,  criterion = "CV",  nbCVBlocks = 10,  weight = NULL,  seed = -1,  xmlIn = NULL,  xmlOut = NULL,  trace = 0,  massiccc = 0)## S4 method for signature 'MixmodPredict'initialize(  .Object,  data,  classificationRule,  xmlIn = NULL,  xmlOut = NULL,  trace = 0,  massiccc = 0)

See Also

initialize

initialize

initialize

initialize

initialize

initialize

initialize

initialize

Say if a data frame is quantitative, qualitative or composite

Description

Say if a data frame is quantitative, qualitative or composite

Usage

is.dataType(x)

Arguments

Value

a string with the data type

Define function to check an integer

Description

Define function to check an integer

Usage

is.wholenumber(x, tol = .Machine$double.eps^0.5)

Arguments

Value

a logical. TRUE ifx is an integer, FALSE otherwise.

Say if a data frame contains only qualitative variables.

Description

Say if a data frame contains only qualitative variables.

Usage

isQualitative(x)

Arguments

Value

a boolean

learnMain

Description

TODO: describe

Define function to transform a matrix of modalities into matrix of binary data

Description

Define function to transform a matrix of modalities into matrix of binary data

Usage

matrix2binary(x)

Arguments

Value

a matrix of binary data.

Create an instance of the [MixmodCluster] class

Description

This function computes an optimal mixture model according to the criteria furnished,and the list of model defined in [Model], using the algorithm specified in[Strategy].

Usage

mixmodCluster(...)

Arguments

Value

Returns an instance of the [MixmodCluster] class.Those two attributes will contain all outputs:

results

a list of [MixmodResults] object containing all the results sorted in ascending orderaccording to the given criterion.

bestResult

a S4 [MixmodResults] object containing the best model results.

Author(s)

Florent Langrognet and Remi Lebret and Christian Poli ans Serge Iovleff, with contributions from C. Biernackiand G. Celeux and G. Govaertcontact@mixmod.org

Examples

## A quantitative example with the famous geyser data setdata(geyser)## with default valuesmixmodCluster(geyser, nbCluster = 2:6)## A qualitative example with the birds data setdata(birds)mixmodCluster(  data = birds, nbCluster = 2:5, criterion = c("BIC", "ICL", "NEC"),  model = mixmodMultinomialModel())## use graphics functionsxem <- mixmodCluster(data = geyser, nbCluster = 3)## Not run: plot(xem)hist(xem)## End(Not run)## get summarysummary(xem)## A composite example with a heterogeneous data setdata(heterodata)mixmodCluster(heterodata, 2)

Create an instance of the [CompositeModel] class

Description

Define a list of heterogeneous model to test in MIXMOD.

Usage

mixmodCompositeModel(  listModels = NULL,  free.proportions = TRUE,  equal.proportions = TRUE,  variable.independency = NULL,  component.independency = NULL)

Arguments

Details

In heterogeneous case, Gaussian model can only belong to the diagonal family.We assume that the variance matrices\Sigma_{k} are diagonal.In the parameterization, it means that the orientation matricesD_{k} are permutation matrices.We write\Sigma_{k}=\lambda_{k}B_{k} whereB_{k} is a diagonal matrix with| B_{k}|=1.This particular parameterization gives rise to 4 models:[\lambda B],[\lambda_{k}B],[\lambda B_{k}]and[\lambda_{k}B_{k}].The multinomial distribution is associated to thejth variable of thekth component is reparameterizedby a centera_k^j and the dispersion\varepsilon_k^j around this center. Thus, it allows us to give aninterpretation similar to the center and the variance matrix used for continuous data in the Gaussian mixture context.In the following, this model will be denoted by[\varepsilon_k^j]. In this context, three other models can be easilydeduced. We note[\varepsilon_k] the model where\varepsilon_k^j is independent of the variablej,[\varepsilon^j] the model where\varepsilon_k^j is independent of the componentk and, finally,[\varepsilon] the model where\varepsilon_k^j is independent of both the variable $j$ and the componentk.In order to maintain some unity in the notation, we will denote also[\varepsilon_k^{jh}] the most general modelintroduced at the previous section.

Value

an object of [CompositeModel] which contains some of the 40 heterogeneous Models:

Author(s)

Florent Langrognet and Remi Lebret and Christian Poli ans Serge Iovleff, with contributions fromC. Biernacki and G. Celeux and G. Govaertcontact@mixmod.org

References

C. Biernacki, G. Celeux, G. Govaert, F. Langrognet. "Model-Based Cluster and Discriminant Analysis withthe MIXMOD Software". Computational Statistics and Data Analysis, vol. 51/2, pp. 587-600. (2006)

Examples

mixmodCompositeModel()# composite models with equal proportionsmixmodCompositeModel(free.proportions = FALSE)# composite models with equal proportions and independent of the variablemixmodCompositeModel(free.proportions = FALSE, variable.independency = TRUE)# composite models with a pre-defined listmixmodCompositeModel(listModels = c("Heterogeneous_pk_Ekjh_L_Bk", "Heterogeneous_pk_Ekjh_Lk_B"))

Create an instance of the [GaussianModel] class

Description

Define a list of Gaussian model to test in MIXMOD.

Usage

mixmodGaussianModel(  family = "all",  listModels = NULL,  free.proportions = TRUE,  equal.proportions = TRUE)

Arguments

Details

In the Gaussian mixture model, following Banfield and Raftery (1993) and Celeux and Govaert (1995), we consider aparameterization of the variance matrices of the mixture components consisting of expressing the variance matrix\Sigma_{k} in terms of its eigenvalue decomposition

\Sigma_{k}= \lambda_{k} D_{k} A_{k}D'_{k}

where\lambda_{k}=|\Sigma_{k}|^{1/d}, D_{k} is the matrix of eigenvectors of\Sigma_{k} andA_{k} is a diagonalmatrix, such that| A_{k} |=1, with the normalized eigenvalues of\Sigma_{k} on the diagonal in a decreasingorder. The parameter\lambda_{k} determines thevolume of thekth cluster,D_{k} itsorientation andA_{k} itsshape. By allowing some but not all of these quantities to vary betweenclusters, we obtain parsimonious and easily interpreted models which are appropriate to describe various clusteringsituations.

In general family, we can allow the volumes, the shapes and the orientations of clusters to vary or to be equal betweenclusters. Variations on assumptions on the parameters\lambda_{k}, D_{k} andA_{k}(1 \leq k \leq K)lead to 8 general models of interest. For instance, we can assume different volumes and keep the shapes and orientationsequal by requiring thatA_{k}=A (A unknown) andD_{k}=D (D unknown) fork=1,\ldots,K. Wedenote this model[\lambda_{k}DAD']. With this convention, writing[\lambda D_{k}AD'_{k}] means that we considerthe mixture model with equal volumes, equal shapes and different orientations.In diagonal family, we assume that the variance matrices\Sigma_{k} are diagonal. In the parameterization, it meansthat the orientation matricesD_{k} are permutation matrices. We write\Sigma_{k}=\lambda_{k}B_{k} whereB_{k} is a diagonal matrix with| B_{k}|=1. This particular parameterization gives rise to 4 models:[\lambda B],[\lambda_{k}B],[\lambda B_{k}] and[\lambda_{k}B_{k}].

In spherical family, we assume spherical shapes, namelyA_{k}=I,I denoting the identity matrix. In such a case,two parsimonious models are in competition:[\lambda I] and[\lambda_{k}I].

Value

an object of [GaussianModel] which contains some of the 28 Gaussian Models:

Author(s)

Florent Langrognet and Remi Lebret and Christian Poli ans Serge Iovleff, with contributions from C. Biernacki andG. Celeux and G. Govaertcontact@mixmod.org

References

C. Biernacki, G. Celeux, G. Govaert, F. Langrognet. "Model-Based Cluster and Discriminant Analysis with theMIXMOD Software". Computational Statistics and Data Analysis, vol. 51/2, pp. 587-600. (2006)

Examples

mixmodGaussianModel()# all Gaussian models with equal proportionsmixmodGaussianModel(family = "all", free.proportions = FALSE)# Diagonal and Spherical Gaussian modelsmixmodGaussianModel(family = c("diagonal", "spherical"))# Gaussian models with a pre-defined listmixmodGaussianModel(listModels = c("Gaussian_p_L_C", "Gaussian_p_L_Ck", "Gaussian_pk_L_I"))

mixmodLearn

Description

TODO: describe...

Usage

mixmodLearn(...)

Arguments

Create an instance of the [MixmodLearn] class

Description

This function computes the first step of a discriminant analysis. It will find the best classification rule by running anM step from the training observations.

Usage

mixmodLearn.default(  data,  knownLabels,  dataType = NULL,  models = NULL,  criterion = "CV",  nbCVBlocks = 10,  weight = NULL)

Arguments

Value

Returns an instance of the [MixmodLearn] class. Those two attributes will contain all outputs:

results

a list of [MixmodResults] object containing all the results sorted in ascending orderaccording to the given criterion.

bestResult

a S4 [MixmodResults] object containing the best model results.

Author(s)

Florent Langrognet and Remi Lebret and Christian Poli ans Serge Iovleff, with contributions from C. Biernacki andG. Celeux and G. Govaertcontact@mixmod.org

Examples

## A quantitative example with the famous iris data setlearn.iris <- mixmodLearn(iris[1:4], iris$Species)## get summarysummary(learn.iris)## A qualitative example with the famous birds data setdata(birds)birds.partition <- as.integer(c(rep(1, 34), rep(2, 35)))learn.birds <- mixmodLearn(data = birds, knownLabels = birds.partition)## get summarysummary(learn.birds)## A composite example with a heterogeneous data setdata(heterodatatrain)learn.hetero <- mixmodLearn(heterodatatrain[-1], knownLabels = heterodatatrain$V1)## get summarysummary(learn.hetero)

Create an instance of the [MultinomialModel] class

Description

Define a list of multinomial model to test in MIXMOD.

Usage

mixmodMultinomialModel(  listModels = NULL,  free.proportions = TRUE,  equal.proportions = TRUE,  variable.independency = NULL,  component.independency = NULL)

Arguments

Details

In the multinomial mixture model, the multinomial distribution is associated to thejth variable of thekth component is reparameterized by a centera_k^j and the dispersion\varepsilon_k^j around this center.Thus, it allows us to give an interpretation similar to the center and the variance matrix used for continuous data in theGaussian mixture context. In the following, this model will be denoted by[\varepsilon_k^j]. In this context, threeother models can be easily deduced. We note[\varepsilon_k] the model where\varepsilon_k^j is independent ofthe variablej,[\varepsilon^j] the model where\varepsilon_k^j is independent of the componentkand, finally,[\varepsilon] the model where\varepsilon_k^j is independent of both the variable $j$ and thecomponentk. In order to maintain some unity in the notation, we will denote also[\varepsilon_k^{jh}] the mostgeneral model introduced at the previous section.

Value

an object of [MultinomialModel] containing some of the 10 Binary Models:

Author(s)

Florent Langrognet and Remi Lebret and Christian Poli ans Serge Iovleff, with contributions from C. Biernacki andG. Celeux and G. Govaertcontact@mixmod.org

References

C. Biernacki, G. Celeux, G. Govaert, F. Langrognet. "Model-Based Cluster and Discriminant Analysis with theMIXMOD Software". Computational Statistics and Data Analysis, vol. 51/2, pp. 587-600. (2006)

Examples

mixmodMultinomialModel()# multinomial models with equal proportionsmixmodMultinomialModel(equal.proportions = TRUE, free.proportions = FALSE)# multinomial models with a pre-defined listmixmodMultinomialModel(listModels = c("Binary_pk_E", "Binary_p_E"))# multinomial models with equal proportions and independent of the variablemixmodMultinomialModel(free.proportions = FALSE, variable.independency = TRUE)

mixmodPredict

Description

TODO: describe

Usage

mixmodPredict(...)

Arguments

Value

A MixmodPredict object

Create an instance of [Strategy] class

Description

This class will contain all the parameters needed by the estimation algorithms.

Usage

mixmodStrategy(...)

Arguments

Details

There are different ways to initialize an algorithm :

random

Initialization from a random position is a standard way toinitialize an algorithm. This random initial position is obtained bychoosing at random centers in the data set. This simple strategy isrepeated5 times (the user can choose the number of times) fromdifferent random positions and the position that maximises thelikelihood is selected.

smallEM

A maximum of50 iterations of the EM algorithm according to the process :n_i numbers ofiterations of EM are done (with random initialization) until thesmallEM stop criterion value has beenreached. This action is repeated until the sum ofn_i

reaches50 iterations (or if in one action50 iterations are reached before the stop criterion value).\It appears that repeating runs of EM is generally profitable since using a single runof EM can often lead to suboptimal solutions.

CEM

10 repetitions of50 iterations of the CEM algorithm are done.One advantage of initializing an algorithm with CEM lies in the factthat CEM converges generally in a small number of iterations. Thus,without consuming a large amount of CPU times, several runs of CEM areperformed. Then EM is run with the best solution among the10 repetitions.

SEMMax

A run of500 iterations of SEM. The idea is that an SEM sequence isexpected to enter rapidly in the neighbourhood of the global maximumof the likelihood function.

Defining the algorithms used in the strategy, the stopping rule and when to stop.

• Algorithms :

  EM

  Expectation Maximisation

  CEM

  Classification EM

  SEM

  Stochastic EM

• Stopping rules for the algorithm :

  nbIterationInAlgo

  Sets the maximum number of iterations

  epsilonInAlgo

  Sets relative increase of the log-likelihood criterion

• Default values are200nbIterationInAlgo ofEM with anepsilonInAlgo valueof10-3.

Value

a [Strategy] object

Author(s)

Florent Langrognet and Remi Lebret and Christian Poli ans Serge Iovleff, with contributions from C. Biernackiand G. Celeux and G. Govaertcontact@mixmod.org

References

Biernacki, C., Celeux, G., Govaert, G., 2003. "Choosing starting values for the EM algorithm for getting thehighest likelihood in multivariate gaussian mixture models". Computational Statistics and Data Analysis 41, 561-575.

Examples

mixmodStrategy()mixmodStrategy(algo = "CEM", initMethod = "random", nbTry = 10, epsilonInInit = 0.00001)mixmodStrategy(  algo = c("SEM", "EM"), nbIterationInAlgo = c(200, 100),  epsilonInAlgo = c(NA, 0.000001))

mixmodXmlCheck

Description

TODO: describe...

Usage

mixmodXmlCheck(...)

Arguments

Value

Object of type MixmodXmlCheck

mixmodXmlInput

Description

TODO: describe..

Usage

mixmodXmlInput(...)

Arguments

mixmodXmlLoad

Description

TODO: describe...

Usage

mixmodXmlLoad(xmlFile, numFormat = "humanReadable")

Arguments

Value

XML output of mixmod methods

Get the number of modalities for each column of a categorical data set

Description

Get the number of modalities for each column of a categorical data set

Usage

nbFactorFromData(x)

Arguments

Value

a vector containing the number of modalities for each column

Create an instance of the [MixmodPredict] class

Description

This function computes the second step of a discriminant analysis. The aim of this step is to assign remaining observationsto one of the groups.

Usage

oldmixmodPredict(data, classificationRule, ...)

Arguments

Value

Returns an instance of the [MixmodPredict] class which contains predicted partition andprobabilities.

Author(s)

Florent Langrognet and Remi Lebret and Christian Poli ans Serge Iovleff, with contributions from C. Biernacki andG. Celeux and G. Govaertcontact@mixmod.org

Examples

# start by extract 10 observations from iris data setremaining.obs <- sample(1:nrow(iris), 10)# then run a mixmodLearn() analysis without those 10 observationslearn <- mixmodLearn(iris[-remaining.obs, 1:4], iris$Species[-remaining.obs])# create a MixmodPredict to predict those 10 observationsprediction <- mixmodPredict(  data = iris[remaining.obs, 1:4],  classificationRule = learn["bestResult"])# show resultsprediction# compare prediction with real resultspaste("accuracy= ", mean(as.integer(iris$Species[remaining.obs]) == prediction["partition"]) * 100,  "%",  sep = "")## A composite example with a heterogeneous data setdata(heterodatatrain)## Learning with training datalearn <- mixmodLearn(heterodatatrain[-1], knownLabels = heterodatatrain$V1)

Plotting of a class [Mixmod]

Description

Plotting data from a [Mixmod] object using parameters and partitionto distinguish the different clusters.

Usage

## S4 method for signature 'Mixmod'plot(x, y, showOnly = NULL, withResult = NULL, hist_x_dim = 10000, ...)

Arguments

Details

For quantitative case, ellipsoids (i.e. linear transformations of hyperspheres)centered at the mean are drawn using the parameters computed by MIXMOD.The directions of the principal axes of the ellipsoids are given by the eigenvectors of the covariance matrix\Sigma.The squared relative lengths of the principal axes are given by the corresponding eigenvalues.A 1-dimensional representation of variables with the densities is drawn on the diagonal.

For qualitative case, a Multiple Correspondence Analysis is performed to get a2-dimensional representation of the data set. Bigger symbol means that observations are similar.

See Also

plot

Examples

## for quantitative casedata(iris)xem <- mixmodCluster(iris[1:4], 3)plot(xem)plot(xem, c(1, 3))plot(xem, c("Sepal.Length", "Sepal.Width"))## for qualitative casedata(birds)xem2 <- mixmodCluster(birds, 2)plot(xem2)legend("bottomleft", c("Cluster1", "Cluster2"), col = c(2, 3), pch = c(1, 2))

Plotting of a class [MixmodResults]

Description

Biplot of two variables from a quantitative data set. Use parameters and partition from a[MixmodResults] object to distinguish the different clusters.

Usage

plotCluster(  x,  data,  variable1 = colnames(data)[1],  variable2 = colnames(data)[2],  col = x@partition + 1,  pch = x@partition,  xlab = variable1,  ylab = variable2,  add.ellipse = TRUE,  ...)

Arguments

Details

Ellipsoids (i.e. linear transformations of hyperspheres)centered at the mean can be drawn using the parameters computed by MIXMOD.The directions of the principal axes of the ellipsoids are given by the eigenvectors of the covariance matrix\Sigma.The squared relative lengths of the principal axes are given by the corresponding eigenvalues.

See Also

plot

Examples

data(geyser)xem1 <- mixmodCluster(geyser, 3)plotCluster(xem1["bestResult"], geyser)data(iris)xem2 <- mixmodCluster(iris[1:4], 2:6)plotCluster(xem2["bestResult"], iris, variable1 = "Sepal.Length", variable2 = "Sepal.Width")plotCluster(xem2["bestResult"], iris, variable1 = 1, variable2 = 4)

predictMain

Description

TODO: describe

Print a Rmixmod class to standard output.

Description

Print a Rmixmod class to standard output.

Usage

## S4 method for signature 'Model'print(x, ...)## S4 method for signature 'MultinomialParameter'print(x, ...)## S4 method for signature 'GaussianParameter'print(x, ...)## S4 method for signature 'CompositeParameter'print(x, ...)## S4 method for signature 'MixmodResults'print(x, ...)## S4 method for signature 'Mixmod'print(x, ...)## S4 method for signature 'Strategy'print(x, ...)## S4 method for signature 'MixmodCluster'print(x, ...)## S4 method for signature 'MixmodDAResults'print(x, ...)## S4 method for signature 'MixmodLearn'print(x, ...)## S4 method for signature 'MixmodPredict'print(x, ...)

Arguments

Value

NULL. Prints to standard out.

See Also

print

Examples

## for strategystrategy <- mixmodStrategy()print(strategy)## for Gaussian modelsgmodel <- mixmodGaussianModel()print(gmodel)## for multinomial modelsmmodel <- mixmodMultinomialModel()print(mmodel)## for clusteringdata(geyser)xem <- mixmodCluster(geyser, 3)print(xem)## for Gaussian parametersprint(xem["bestResult"]["parameters"])## for discriminant analysis# start by extract 10 observations from iris data setiris.partition <- sample(1:nrow(iris), 10)# then run a mixmodLearn() analysis without those 10 observationslearn <- mixmodLearn(iris[-iris.partition, 1:4], iris$Species[-iris.partition])# print learn resultsprint(learn)# create a MixmodPredict to predict those 10 observationsprediction <- mixmodPredict(  data = iris[iris.partition, 1:4],  classificationRule = learn["bestResult"])# print prediction resultsprint(prediction)

Show description of a Rmixmod class to standard output.

Description

Show description of a Rmixmod class to standard output.

Usage

## S4 method for signature 'Model'show(object)## S4 method for signature 'MultinomialParameter'show(object)## S4 method for signature 'GaussianParameter'show(object)## S4 method for signature 'CompositeParameter'show(object)## S4 method for signature 'MixmodResults'show(object)## S4 method for signature 'Mixmod'show(object)## S4 method for signature 'Strategy'show(object)## S4 method for signature 'MixmodCluster'show(object)## S4 method for signature 'MixmodDAResults'show(object)## S4 method for signature 'MixmodLearn'show(object)## S4 method for signature 'MixmodPredict'show(object)

Arguments

Value

NULL. Prints to standard out.

See Also

show

Examples

## for strategystrategy <- mixmodStrategy()show(strategy)## for Gaussian modelsgmodel <- mixmodGaussianModel()show(gmodel)## for multinomial modelsmmodel <- mixmodMultinomialModel()show(mmodel)## for clusteringdata(geyser)xem <- mixmodCluster(geyser, 3)show(xem)## for Gaussian parametersshow(xem["bestResult"]["parameters"])## for discriminant analysis# start by extract 10 observations from iris data setiris.partition <- sample(1:nrow(iris), 10)# then run a mixmodLearn() analysis without those 10 observationslearn <- mixmodLearn(iris[-iris.partition, 1:4], iris$Species[-iris.partition])# create a MixmodPredict to predict those 10 observationsprediction <- mixmodPredict(  data = iris[iris.partition, 1:4],  classificationRule = learn["bestResult"])# show resultsshow(prediction)

Sorting results of a [Mixmod] object by a given criterion

Description

After calling the mixmodCluster() or mixmodLearn() method, results will be sortedinto ascending order according to the first given criterion (descending order for CV criterion).This method is able to reorder the list of results according to a given criterion.

Usage

sortByCriterion(object, criterion)## S4 method for signature 'Mixmod,character'sortByCriterion(object, criterion)

Arguments

Value

a modified [Mixmod] object

Examples

x <- mixmodCluster(iris[1:4], 2:10, criterion = c("BIC", "ICL"))icl <- sortByCriterion(x, "ICL")icl["results"]

Produce result summaries of a Rmixmod class

Description

Produce result summaries of a Rmixmod class

Usage

## S4 method for signature 'MultinomialParameter'summary(object, ...)## S4 method for signature 'GaussianParameter'summary(object, ...)## S4 method for signature 'CompositeParameter'summary(object, ...)## S4 method for signature 'MixmodResults'summary(object, ...)## S4 method for signature 'Mixmod'summary(object, ...)## S4 method for signature 'MixmodPredict'summary(object, ...)

Arguments

Value

NULL. Summaries to standard out.

See Also

summary

Examples

data(geyser)xem <- mixmodCluster(geyser, 3)summary(xem)summary(xem["bestResult"])summary(xem["bestResult"]["parameters"])

Qualitative data: Survival of passengers on the Titanic

Description

For each person on board the fatal maiden voyage of the ocean liner Titanic, this dataset records: sex, age [adult/child],economic status [first/second/third class, or crew] and whether or not that person survived.Values are aligned and delimited by blanks. There are no missing values.

Format

A data frame with 2201 observations on the following 4 variables.

Class

0 = crew, 1 = first, 2 = second, 3 = third, which denote the economic status of the subject

Age

1 = adult, 0 = child, which denote if the subject is an adult or a child

Sex

1 = male, 0 = female, which denote the sex of the subject

Survived

1 = yes, 0 = no, which denote if the subject lived through the fatal maiden voyage of theocean liner Titanic

Details

The sinking of the Titanic is a famous event, and new books are still being published about it. Many well-known facts-fromthe proportions of first-class passengers to the "women and children first" policy, and the fact that that policy was notentirely successful in saving the women and children in the third class-are reflected in the survival rates for variousclasses of passenger.

These data were originally collected by the British Board of Trade in their investigation of the sinking. Note that thereis not complete agreement among primary sources as to the exact numbers on board, rescued, or lost.

Due in particular to the very successful film "Titanic", the last years saw a rise in public interest in the Titanic.Very detailed data about the passengers is now available on the Internet, at sites such as "Encyclopedia Titanica".

Source

The source provides a data set recording class, sex, age, and survival status for each person on board of the Titanic,and is based on data originally collected by the British Board of Trade and reprinted in:British Board of Trade (1990), "Report on the Loss of the Titanic (S.S.)". British Board of Trade InquiryReport (reprint). Gloucester, UK: Allan Sutton Publishing.

Examples

data(titanic)

Define function to transform a vector of modalities into matrix of binary data

Description

Define function to transform a vector of modalities into matrix of binary data

Usage

vector2binary(x)

Arguments

Value

a matrix of binary data.

xMain

Description

TODO: describe