WORK IN PROGRESS This package is currently under active development. The API may change, and features are still being added.

gipsDA

An R package for discriminant analysis classification using covariance matrices with permutation symmetries.

About The Project

gipsDA is an R package that extends classical Linear Discriminant Analysis (LDA) and Quadratic Discriminant Analysis (QDA) by incorporating permutation group structures into the estimation of covariance matrices. By leveraging the methodology of the gips library, this package aims to improve classification performance in scenarios where features (variables) exhibit underlying symmetries.

The core idea is to find and impose a permutation symmetry on the covariance matrix, which acts as a form of regularization and can lead to more stable and interpretable models, especially in high-dimensional settings. The ultimate goal is to submit gipsDA to the Comprehensive R Archive Network (CRAN).

Key Features

• Implementation of four novel gips-based discriminant analysis classifiers.
• A flexible, user-friendly model API consistent with established machine learning libraries in R.
• A specialized gipsmult module for modeling class-specific covariances under a shared symmetry.
• Designed following best practices for R package development.

R Package Structure

To adopt the best practices of R package development, the repository is organized with the following standard structure:

• R/

  This directory contains the core logic of the package. All source code files are located here. To ensure proper documentation, we use the roxygen2 package, with documentation comments embedded directly above the function definitions. To maintain logical modularity within this flat directory structure, a file naming convention has been adopted, where files are prefixed to indicate their module affiliation:
  • gipsmult_: for files belonging to the gipsmult module.
  • models_: for files belonging to the models module.

• tests/

  This directory houses all testing scripts to ensure the reliability and correctness of the package. Automated unit tests are implemented using the testthat framework and are designed to verify the functionality of individual functions and methods within the modules.

Available Models in gipsDA

The gipsDA object can be configured to run one of four different classification algorithms, each with different assumptions about the data structure.

1. gipsLDA_weighted_average In this approach, a separate covariance matrix is first estimated for each class. A final, single covariance matrix is then computed as a weighted average of these individual matrices. This pooled matrix is then processed by the gips library before being used for classification.

2. gipsLDA_classic This model follows a more traditional approach by using the classic pooled covariance estimator standard in traditional LDA. This single, pooled matrix is then processed by the gips library to find the most probable permutation symmetry.

3. gipsMultQDA This model leverages the gipsmult module. The process involves first identifying the single most probable permutation structure that is common across all classes. Subsequently, a separate covariance matrix is estimated for each class, with each matrix being projected onto this shared permutation.

4. gipsQDA This represents the most flexible model. The gips library is applied independently to each class. Consequently, each class can have its own uniquely estimated permutation structure and its own distinct covariance matrix. This is analogous to the classic QDA framework but with individualized symmetry discovery for each class.