PDAopt_Ext: PP optimization using PDA index

In PPtreeExt: Projection Pursuit Classification Tree Extensions

PP optimization using PDA index

Description

Projection Pursuit Optimization Using PDA Index

Usage

PDAopt_Ext(origclass, origdata, q = 1, weight = TRUE, lambda = 0.1, ...)

Arguments

origclass	Factor or numeric vector containing the class labels for each observation.
origdata	Numeric matrix or data frame containing the predictor variables without class information. Each row represents an observation and each column represents a variable.
q	Integer specifying the dimension of the projection space. Default is 1 for 1-dimensional projection.
weight	Logical indicating whether to use weighted PDA index calculation. Default is TRUE.
lambda	Numeric penalty parameter for the PDA index. Controls the amount of regularization applied. Default is 0.1. Higher values increase regularization, which is useful for high-dimensional or collinear data.
...	Additional arguments to be passed to internal optimization methods.

Details

Finds the q-dimensional optimal projection using the Penalized Discriminant Analysis (PDA) projection pursuit index. This implementation follows the method described in PPtree and is particularly useful for high-dimensional data (large p, small n).

The Penalized Discriminant Analysis (PDA) projection pursuit index extends LDA by incorporating a penalty term, making it particularly suitable for:

• High-dimensional data where the number of variables exceeds the number of observations (p > n)

• Data with multicollinearity among predictor variables

• Cases where standard LDA fails due to singular covariance matrices

The function performs the following steps:

1. Calls PDAopt to find the optimal q-dimensional projection directions with regularization

2. Evaluates the PDA index for the optimal projection using PDAindex2

3. Returns both the projection matrix and its associated index value

The lambda parameter controls the trade-off between maximizing class separation and regularization. When weight = TRUE, the index calculation accounts for class proportions in the optimization.

Value

An object of class "PPoptim", which is a list containing:

indexbest	Numeric value representing the maximum PDA index achieved by the optimal projection. Higher values indicate better class separation with appropriate regularization.
projbest	Numeric matrix of optimal projection coefficients with dimensions ncol(origdata) by q. Each column represents an optimal projection direction that maximizes the PDA index for class separation.
origclass	The original class information vector passed as input, preserved for reference.
origdata	The original data matrix without class information, preserved for reference.

References

Lee, EK, Cook, D. (2010) A Projection Pursuit Index for Large p Small n Data, Statistics and Computing, 20:381-392.

See Also

LDAopt_Ext, findproj_Ext

PPtreeExt documentation built on Feb. 6, 2026, 5:06 p.m.