DA: 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)

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.

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.

Author

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

Run this code

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

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