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LPDA: A new classification method based on linear programming.

María J Nueda1, Carmen Gandía1, Mariola D Molina1

  • 1Mathematics Department, University of Alicante, Alicante, Spain.

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Summary
This summary is machine-generated.

This study introduces a new method for finding discriminant hyperplanes, called Linear Programming Discriminant Analysis (LPDA). LPDA offers an effective approach for classification tasks across various data dimensions.

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Area of Science:

  • Machine Learning
  • Mathematical Optimization
  • Data Mining

Background:

  • Separation hyperplanes are crucial for classification tasks.
  • Existing methods for finding discriminant hyperplanes have limitations.
  • Mathematical programming offers potential for improved hyperplane determination.

Purpose of the Study:

  • To present an alternative mathematical programming formulation for finding a discriminant hyperplane.
  • To introduce a novel method called Linear Programming Discriminant Analysis (LPDA).
  • To demonstrate the existence and effectiveness of the proposed method.

Main Methods:

  • Formulating the search for a discriminant hyperplane as a convex optimization problem.
  • Deriving an equivalent linear programming problem.
  • Minimizing the sum of distances to assigned group areas for hyperplane determination.
  • Implementing dimension reduction techniques to prevent overfitting.

Main Results:

  • The existence of the discriminant hyperplane (H) is proven when group centroids differ.
  • The LPDA method is effective for both low and high-dimensional data.
  • Performance is validated through comparisons with existing classification methods on diverse datasets.

Conclusions:

  • LPDA provides an efficient and effective approach for classification.
  • The method is robust across different data dimensionalities.
  • An R package for LPDA is publicly available for practical application.