Balance Ratio Sum Versus Maximization Ratio Sum for Linear Discriminant Analysis.

Area of Science:

• Machine Learning
• Data Science
• Pattern Recognition

Background:

• Linear Discriminant Analysis (LDA) is a standard dimensionality reduction technique.
• Ratio Sum LDA (RSLDA) was developed to improve feature discriminability but suffers from ratio dominance.
• The dominance of maximum ratios in RSLDA hinders the selection of truly discriminative features.

Purpose of the Study:

• To analyze the dominance problem in traditional Ratio Sum LDA.
• To propose a novel discriminant feature learning method, Balance Ratio Sum Discriminant Analysis (BRSDA).
• To mitigate the ratio dominance issue and enhance feature extraction capabilities.

Main Methods:

• Introduced a minimization ratio sum (Min-RS) criterion utilizing the harmonic mean for ratio balancing.
• Integrated the Min-RS criterion with the $\ell _{p}$-norm to further balance ratios and amplify projection direction differences.
• Employed the gradient descent method for optimization due to the challenge in obtaining a closed-form solution.

Main Results:

• BRSDA effectively balances ratios, mitigating the dominance problem inherent in RSLDA.
• The method focuses on optimizing low-quality projection directions, leading to a well-balanced solution.
• Experimental results confirm BRSDA's effectiveness in extracting discriminative features.

Conclusions:

• BRSDA provides a robust solution to the ratio dominance problem in Ratio Sum LDA.
• The proposed method enhances the quality and discriminative power of extracted features.
• BRSDA represents a significant advancement in discriminant feature learning.