Generalized two-dimensional linear discriminant analysis with regularization.

Area of Science:

• Machine Learning
• Data Science
• Pattern Recognition

Background:

• Two-dimensional Linear Discriminant Analysis (2DLDA) is a matrix-based dimensionality reduction technique.
• Standard 2DLDA faces theoretical singularity issues and sensitivity to data outliers.
• Robustness and generalization are critical for effective dimensionality reduction in real-world applications.

Purpose of the Study:

• To propose a generalized Lp-norm 2DLDA (G2DLDA) framework with regularization.
• To enhance robustness against outliers by utilizing an arbitrary Lp-norm.
• To improve generalization performance and avoid singularity issues inherent in traditional 2DLDA.

Main Methods:

• Developed a G2DLDA model employing an arbitrary Lp-norm for scatter measurement.
• Incorporated a regularization term to enhance model stability and generalization.
• Designed an efficient learning algorithm solvable via convex problems with closed-form solutions.

Main Results:

• The G2DLDA framework demonstrates robustness by allowing selection of an appropriate 'p' value for the Lp-norm.
• Regularization successfully mitigates singularity issues and boosts generalization capabilities.
• Theoretical convergence is guaranteed for G2DLDA when 1 ≤ p ≤ 2.

Conclusions:

• G2DLDA offers a robust and effective alternative to standard 2DLDA for dimensionality reduction.
• The proposed method shows significant promise, particularly in scenarios with noisy or contaminated data.
• Experimental validation on human face databases confirms the effectiveness of G2DLDA.