tda: Transformation Discriminant Analysis

In transDA: Transformation Discriminant Analysis

Transformation Discriminant Analysis

Description

Implements discriminant analysis methods including traditional linear (LDA), quadratic (QDA), transformation (TDA), mixture (MDA) discriminant analysis, and their combinations such as TQDA or TLMDA. The user chooses a specific method by specifying options for common or varying transformation parameters as well as covariance matrices.

Usage

tda(x, ID, max_k, trans = TRUE, common_lambda = FALSE,
                 common_sigma = FALSE, iter = 50, subgroup = NULL, 
                 tol= 0.001, lambda0 = 0.015, iter.max = 1,
                 nstart = 10, criterion = "BIC")

Arguments

x	A frame or matrix containing a training data set
max_k	The maximum number of mixture components within each class to be fitted
ID	A variable containing class memberships for all observations
trans	A transformation indicator: 'trans = TRUE' if transformation is needed, 'trans = FALSE' if transformation is not needed
common_lambda	A parameter that regulates transformations. If 'common_lambda = TRUE', each mixture component or class has the same transformation parameter vector. If 'common_lambda = FALSE', each component or class has a different transformation vector
common_sigma	A homoscedasticity parameter: if 'common_sigma = TRUE', all subgroups across all classes have a common covariance matrix, if 'common_sigma = FALSE', groups have varying covariance matrices
iter	A maximum number of iterations of the EM algorithm; the default value is 50
subgroup	A vector containing the number of mixture components per each class to be fitted
tol	Tolerance level for a stopping critetion based on the relative difference in two consecutive log-likelihood values
lambda0	Starting value for transformation parameters
iter.max	The maximum number of iterations for the K-means algorithm used to initialize EM; default value is 1
nstart	The number of random starts for the K-means algorithm used to initialize EM; default value is 10
criterion	BIC or AIC; BIC is chosen by default.

Value

criterion	Values of the Bayesian or Akaike’s Information Criterion calculated for each evaluated model (BIC is default).
subprior	Estimated component priors for each class.
mu	Estimated component means for each class.
sigma	Estimated component covariance matrices for each group.
lambda	Estimated transformation parameters.
loglik	The log-likelihood value for the model with the lowest BIC.
pred_ID	Estimated classification of observations in the training data set.
prior	Estimated class priors.
misclassification_rate	Misclassification rate for the training data set.
ARI	Adjusted Rand index value.
Z	Matrix of posterior probabilities for the training data set.

See Also

summary.tda, predict.tda

Examples

set.seed(123)
# Example 1:
MDA <- tda(x = iris[,1:4],ID = iris$Species, max_k = 2, trans = FALSE)
print(MDA)
summary(MDA)

# Example 2:
LDA <- tda(x = iris[,1:4], ID = iris$Species, max_k = 1, trans = FALSE,
        common_sigma = TRUE)
print(LDA)
summary(LDA)

# Example 3:
QDA <-  tda(x = iris[,1:4], ID = iris$Species, subgroup = c(1, 1, 1), 
        trans = FALSE, common_sigma = FALSE)
print(QDA)
summary(QDA)

# Example 4:
TQDA <- tda(x = iris[,1:4], ID = iris$Species, subgroup = c(1, 1, 1), 
        trans = TRUE, common_sigma = FALSE, common_lambda = TRUE)
print(TQDA)
summary(TQDA)

transDA documentation built on Aug. 21, 2026, 5:14 p.m.