gipsmultqda: Quadratic Discriminant Analysis with multiple gips-projected...

In gipsDA: Training DA Models Utilizing 'gips'

Quadratic Discriminant Analysis with multiple gips-projected covariances

Description

Quadratic Discriminant Analysis (QDA) in which each class covariance matrix is projected using the gipsmult framework, allowing for structured permutation symmetry across multiple covariance matrices.

Usage

gipsmultqda(x, ...)

## S3 method for class 'formula'
gipsmultqda(formula, data, ..., subset, na.action)

## Default S3 method:
gipsmultqda(x, grouping, prior = proportions,
  nu = 5, MAP = TRUE, optimizer = NULL, max_iter = NULL, ...)

## S3 method for class 'data.frame'
gipsmultqda(x, ...)

## S3 method for class 'matrix'
gipsmultqda(x, grouping, ..., subset, na.action)

Arguments

x	(required if no formula is given as the principal argument) a matrix or data frame containing the explanatory variables.
...	Arguments passed to or from other methods.
formula	A formula of the form groups ~ x1 + x2 + .... The response is the grouping factor and the right-hand side specifies the (non-factor) discriminators.
data	An optional data frame, list or environment from which variables specified in formula are preferentially taken.
grouping	A factor specifying the class for each observation.
prior	Prior probabilities of class membership. Must sum to one.
nu	Degrees of freedom parameter used internally during covariance projection.
MAP	Logical; if TRUE, a maximum a posteriori covariance projection is used.
optimizer	Character string specifying the optimization method used for covariance projection. If NULL, a default choice is made based on the problem dimension.
max_iter	Maximum number of iterations for stochastic optimizers.
subset	An index vector specifying the cases to be used in the training sample. (NOTE: must be named.)
na.action	A function specifying the action to be taken if NAs are found.

Details

This function is a modification of qda in which the class-specific covariance matrices are jointly projected to improve numerical stability and exploit shared symmetry assumptions.

In contrast to classical QDA, which estimates each class covariance matrix independently, gipsmultqda performs a joint projection of all class covariance matrices using the gipsmult framework. This allows the incorporation of shared permutation symmetries and can improve classification performance in high-dimensional or small-sample regimes.

Several classification rules are available via predict.gipsmultqda, including plug-in, predictive, debiased, and leave-one-out cross-validation.

Value

An object of class "gipsmultqda" containing:

• prior: prior probabilities of the groups

• counts: number of observations per group

• means: group means

• scaling: array of group-specific scaling matrices derived from the projected covariance matrices

• ldet: log-determinants of the projected covariance matrices

• lev: class labels

• N: total number of observations

• optimization_info: information returned by the covariance projection optimizer

• call: the matched call

Note

This function is not a drop-in replacement for qda. The covariance estimation, returned object, and classification rules differ substantially.

The theoretical background and details of the covariance projection are documented in the gipsmult package.

See Also

qda, predict.gipsmultqda, gipsqda, gipslda

Examples

tr <- sample(1:50, 25)
train <- rbind(iris3[tr, , 1], iris3[tr, , 2], iris3[tr, , 3])
test <- rbind(iris3[-tr, , 1], iris3[-tr, , 2], iris3[-tr, , 3])
cl <- factor(c(rep("s", 25), rep("c", 25), rep("v", 25)))
z <- gipsmultqda(train, cl)
predict(z, test)$class

gipsDA documentation built on Feb. 3, 2026, 5:07 p.m.