Lp- and Ls-Norm Distance Based Robust Linear Discriminant Analysis.

Area of Science:

• Machine Learning
• Computer Vision
• Pattern Recognition

Background:

• Linear Discriminant Analysis (LDA) is susceptible to outliers.
• L1-norm based LDA offers some robustness but lacks guaranteed performance.
• Existing methods struggle with insufficient outlier protection.

Purpose of the Study:

• Propose a novel robust discriminant method, Lp- and Ls-Norm Distance Based Robust Linear Discriminant Analysis (FLDA-Lsp).
• Enhance robustness against outliers in discriminant analysis.
• Provide a flexible framework encompassing previous methods.

Main Methods:

• Replace L2-norm distances in conventional LDA with Lp- and Ls-norm measures.
• Develop an efficient iterative algorithm for optimizing the objective function.
• Analyze the convergence and local minimum existence of the proposed algorithm.

Main Results:

• FLDA-Lsp demonstrates superior robustness compared to existing methods.
• The Lp/Ls-norm framework generalizes prior approaches.
• Experimental results on image databases validate the method's effectiveness.

Conclusions:

• FLDA-Lsp offers a significant advancement in robust discriminant analysis.
• The proposed iterative algorithm effectively addresses optimization challenges.
• The method shows strong potential for image analysis applications.