Projection Pursuit Optimization Using PDA Index
PDAopt_Ext(origclass, origdata, q = 1, weight = TRUE, lambda = 0.1, ...)An object of class "PPoptim", which is a list containing:
Numeric value representing the maximum PDA index achieved by the optimal projection. Higher values indicate better class separation with appropriate regularization.
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.
The original class information vector passed as input, preserved for reference.
The original data matrix without class information, preserved for reference.
Factor or numeric vector containing the class labels for each observation.
Numeric matrix or data frame containing the predictor variables without class information. Each row represents an observation and each column represents a variable.
Integer specifying the dimension of the projection space. Default is 1 for 1-dimensional projection.
Logical indicating whether to use weighted PDA index calculation.
Default is TRUE.
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.
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:
Calls PDAopt to find the optimal q-dimensional projection directions with regularization
Evaluates the PDA index for the optimal projection using PDAindex2
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.
Lee, EK, Cook, D. (2010) A Projection Pursuit Index for Large p Small n Data, Statistics and Computing, 20:381-392.
LDAopt_Ext, findproj_Ext