abcrlda {abcrlda}

Asymptotically Bias-Corrected Regularized Linear Discriminant Analysis for Cost-Sensitive Binary Classification

Description

Constructs Asymptotically Bias-Corrected Regularized Linear Discriminant Analysis.

Usage

abcrlda(x, y, gamma = 1, cost = c(0.5, 0.5), bias_correction = TRUE)

Arguments

x

Input matrix or data.frame of dimension nobs x nvars; each row is an feature vector.

y

A numeric vector or factor of class labels. Factor should have either two levels or be a vector with two distinct values. If y is presented as a vector, it will be coerced into a factor. Length of y has to correspond to number of samples in x.

gamma

Regularization parameter \gamma in the ABC-RLDA discriminant function given by:

W_{ABC}^{RLDA} = \gamma (x-\frac{\bar{x}_0 + \bar{x}_1}{2})^T H (\bar{x}_0 - \bar{x}_1) - log(\frac{C_{01}}{C_{10}}) + \hat{\omega}_{opt}

H = (I_p + \gamma \hat{\Sigma})^{-1}

Formulas and derivations for parameters used in above equation can be found in the article under reference section.

cost

Parameter that controls the overall misclassification costs. This is a vector of length 1 or 2 where the first value is C_{10} (represents the cost of assigning label 1 when the true label is 0) and the second value, if provided, is C_{01} (represents the cost of assigning label 0 when the true label is 1). The default setting is c(0.5, 0.5), so both classes have equal misclassification costs

If a single value is provided, it should be normalized to lie between 0 and 1 (but not including 0 or 1). This value will be assigned to C_{10} while C_{01} will be equal to (1 - C_{10}).

bias_correction

Takes in a boolean value. If bias_correction is TRUE, then asymptotic bias correction will be performed. Otherwise, (if bias_correction is FALSE) asymptotic bias correction will not be performed and the ABCRLDA is the classical RLDA. The default is TRUE.

Value

An object of class "abcrlda" is returned which can be used for class prediction (see predict()).

a

Coefficient vector of a discriminant hyperplane: W(x) = a' x + m.

m

Intercept of discriminant hyperplane: W(x) = a'x + m.

cost

Vector of cost values that are used to construct ABC-RLDA.

ncost

Normalized cost such that C_{10} + C_{01} = 1.

gamma

Regularization parameter value used in ABC_RLDA discriminant function.

lev

Levels corresponding to the labels in y.

Reference

A. Zollanvari, M. Abdirash, A. Dadlani and B. Abibullaev, "Asymptotically Bias-Corrected Regularized Linear Discriminant Analysis for Cost-Sensitive Binary Classification," in IEEE Signal Processing Letters, vol. 26, no. 9, pp. 1300-1304, Sept. 2019. doi: 10.1109/LSP.2019.2918485 URL: https://ieeexplore.ieee.org/document/8720003

See Also

Other functions in the package: cross_validation(), da_risk_estimator(), grid_search(), predict.abcrlda(), risk_calculate()

Examples

data(iris)
train_data <- iris[which(iris[, ncol(iris)] == "virginica" |
                           iris[, ncol(iris)] == "versicolor"), 1:4]
train_label <- factor(iris[which(iris[, ncol(iris)] == "virginica" |
                                   iris[, ncol(iris)] == "versicolor"), 5])
model <- abcrlda(train_data, train_label, gamma = 0.5, cost = 0.75)
a <- predict(model, train_data)
# same params but more explicit
model <- abcrlda(train_data, train_label, gamma = 0.5, cost = c(0.75, 0.25))
b <- predict(model, train_data)
# same class costs ratio
model <- abcrlda(train_data, train_label, gamma = 0.5, cost = c(3, 1))
c <- predict(model, train_data)
# all this model will give the same predictions
all(a == b & a == c & b == c)
#' [1] TRUE