DA {MVar}

Linear (LDA) and quadratic discriminant analysis (QDA).

Description

Perform linear and quadratic discriminant analysis.

Usage

DA(data, class = NA, type = "lda", validation = "learning", 
   method = "moment", prior = NA, testing = NA)

Arguments

data

Data to be classified.

class

Vector with data classes names.

type

"lda": linear discriminant analysis (default), or
"qda": quadratic discriminant analysis.

validation

Type of validation:
"learning" - data training (default), or
"testing" - classifies the data of the vector "testing".

method

Classification method:
"mle" to MLEs,
"mve" to use cov.mv,
"moment" (default) for standard mean and variance estimators, or
"t" for robust estimates based on the t distribution.

prior

Probabilities of occurrence of classes. If not specified, it will take the proportions of the classes. If specified, probabilities must follow the order of factor levels.

testing

Vector with indices that will be used in data as test. For validation = "learning", one has testing = NA.

Value

confusion

Confusion table.

error.rate

Overall error ratio.

prior

Probability of classes.

type

Type of discriminant analysis.

validation

Type of validation.

num.class

Number of classes.

class.names

Class names.

method

Classification method.

num.correct

Number of correct observations.

results

Matrix with comparative classification results.

Author(s)

Paulo Cesar Ossani

Marcelo Angelo Cirillo

References

Ferreira, D. F. Estatistica Multivariada. 2a ed. revisada e ampliada. Lavras: Editora UFLA, 2011. 676 p.

Mingoti, S. A. Analise de dados atraves de metodos de estatistica multivariada: uma abordagem aplicada. Belo Horizonte: UFMG, 2005. 297 p.

Rencher, A. C. Methods of multivariate analysis. 2th. ed. New York: J.Wiley, 2002. 708 p.

Ripley, B. D. Pattern Recognition and Neural Networks. Cambridge University Press, 1996.

Venabless, W. N.; Ripley, B. D. Modern Applied Statistics with S. Fourth edition. Springer, 2002.

Examples

data(iris) # data set

data  = iris[,1:4] # data to be classified
class = iris[,5]   # data class
prior = c(1,1,1)/3 # a priori probability of the classs

res <- DA(data, class, type = "lda", validation = "learning", 
          method = "mle", prior = prior, testing = NA)

print("confusion table:"); res$confusion
print("Overall hit ratio:"); 1 - res$error.rate
print("Probability of classes:"); res$prior
print("classification method:"); res$method
print("type of discriminant analysis:"); res$type
print("class names:"); res$class.names
print("Number of classess:"); res$num.class
print("type of validation:"); res$validation
print("Number of correct observations:"); res$num.correct
print("Matrix with comparative classification results:"); res$results


### cross-validation ###
amostra   = sample(2, nrow(data), replace = TRUE, prob = c(0.7,0.3))
datatrain = data[amostra == 1,] # training data
datatest  = data[amostra == 2,] # test data

dim(datatrain) # training data dimension
dim(datatest)  # test data dimension

testing  = as.integer(rownames(datatest)) # test data index

res <- DA(data, class, type = "qda", validation = "testing", 
          method = "moment", prior = NA, testing = testing)

print("confusion table:"); res$confusion
print("Overall hit ratio:"); 1 - res$error.rate
print("Number of correct observations:"); res$num.correct
print("Matrix with comparative classification results:"); res$results