HiDimDA (version 0.2-0)

Mlda: Maximum uncertainty Linear Discriminant Analysis.

Description

Mlda finds the coefficients of a linear discriminant rule based on the Maximum uncertainty Linear Discriminant Analysis approach of Thomaz, Kitani and Gillies (2006).

Usage

## S3 method for class 'default':
Mlda(data, grouping, prior = "proportions", StddzData=TRUE, VSelfunct = SelectV, 
ldafun=c("canonical","classification"), PCAstep=FALSE, ...)
## S3 method for class 'data.frame':
Mlda(data, \dots)

Arguments

data

Matrix or data frame of observations.

grouping

Factor specifying the class for each observation.

prior

The prior probabilities of class membership. If unspecified, the class proportions for the training set are used. If present, the probabilities should be specified in the order of the factor levels.

StddzData

A boolean flag indicating whether the data should be standardized first (default) or used in their original scales.

VSelfunct

Variable selection function. Either the string none (no selection is to be performed) or a function that takes data and grouping as its first two arguments and returns a list with two components: (i)

ldafun

Type of discriminant linear functions computed. The alternatives are canonical for maximum-discrimination canonical functions and classification for direct-classification functions.

PCAstep

A boolean flag indicating if data should be first projected into the space spanned by the first nrow(data)-1 Principal Components in problems where nrow(data)-1 is less than the number of selected variables. In applications with a very large number of use

...

Further arguments passed to or from other methods.

Value

• If algument ldafun is set to canonical an object of class canldaRes with the following components:
• prior
  The prior probabilities used.
• means
  The class means.
• scaling
  A matrix which transforms observations to discriminant functions, normalized so that the within groups covariance matrix is spherical.
• svd
  The singular values, which give the ratio of the between- and within-group standard deviations on the linear discriminant variables. Their squares are the canonical F-statistics.
• vkpt
  A vector with the indices of the variables kept in the discriminant rule if the number of variables kept is less than ncol(data). NULL otherwise.
• nvkpt
  The number of variables kept in the discriminant rule if this number is less thanncol(data). NULL otherwise.
• N
  The number of observations used.
• call
  The (matched) function call.
• If algument ldafun is set to classification an object of class clldaRes with the following components:
• prior
  The prior probabilities used.
• means
  The class means.
• coef
  A matrix with the coefficients of the k-1 classification functions.
• cnst
  A vector with the thresholds (2nd members of linear classification rules) used in classification rules that assume equal priors.
• vkpt
  A vector with the indices of the variables kept in the discriminant rule if the number of variables kept is less than ncol(data). NULL otherwise.
• nvkpt
  The number of variables kept in the discriminant rule if this number is less thanncol(data). NULL, otherwise.
• N
  The number of observations used.
• call
  The (matched) function call.

References

Pedro Duarte Silva, A. (2011) Two Group Classification with High-Dimensional Correlated Data: A Factor Model Approach, Computational Statistics and Data Analysis, 55 (1), 2975-2990.

Thomaz, Kitani and Gillies (2006) A maximum uncertainty LDA-based approach for limited sample size problems - with application to face recognition, Journal of the Brazilian Computer Society, 12 (2), 7-18.

See Also

SelectV, MldaInvE, predict.canldaRes, predict.clldaRes, AlonDS

Examples

# train classifier on Alon's Colon Cancer Data Set (after a logarithmic transformation). 

log10genes <- log10(AlonDS[,-1])

ldarule <- Mlda(log10genes,AlonDS$grouping)     

# show classification rule

print(ldarule)

# get in-sample classification results

predict(ldarule,log10genes,grpcodes=levels(AlonDS$grouping))$class           	       

# compare classifications with true assignments

cat("Original classes:
")
print(AlonDS$grouping)             		 

# Estimate error rates by four-fold cross-validation.
# (Note: In cross-validation analysis it is recommended to set the argument 
# 'ldafun' to "classification", in order to speed up computations by avoiding 
# unecessary eigen-decompositions) 

CrosValRes <- DACrossVal(log10genes,AlonDS$grouping,TrainAlg=Mlda,ldafun="classification",
kfold=4,CVrep=1)
summary(CrosValRes[,,"Clerr"])