Worst-Case Discriminative Feature Learning via Max-Min Ratio Analysis.

Area of Science:

• Machine Learning
• Data Science

Background:

• Traditional methods struggle with 'worst-case class separation', especially with diverging intra-class sample distributions.
• Existing techniques maximize minimal pairwise distances, failing to fully separate overlapping classes.

Purpose of the Study:

• To address the challenge of worst-case class separation using a novel criterion.
• To develop discriminative feature learning models for dimensionality reduction and metric learning.

Main Methods:

• Propose Max-Min Ratio Analysis (MMRA) to maximize the minimal ratio of between-class to within-class scatter.
• Develop two novel discriminative feature learning models based on the MMRA criterion.
• Derive an iterative algorithm and a bisection search strategy for solving the optimization problem.

Main Results:

• The proposed MMRA criterion significantly enhances separability for overlapped classes.
• Developed algorithms demonstrate convergence and efficient solving of the non-smooth, non-convex problem.
• Extensive experiments on artificial and real-world ScRNA-seq datasets validate the method's effectiveness.

Conclusions:

• The novel MMRA criterion effectively tackles the worst-case class separation problem.
• The developed feature learning models and algorithms offer significant improvements in pattern classification and image retrieval.
• MMRA provides a robust approach for improving class separability in complex datasets.