Fisher discriminant analysis with L1-norm.

Area of Science:

• Machine Learning
• Pattern Recognition
• Computer Vision

Background:

• Fisher linear discriminant analysis (LDA) is a standard subspace learning method.
• The L2-norm formulation of LDA makes it sensitive to outliers.
• Conventional LDA faces challenges with small sample sizes and rank limitations.

Purpose of the Study:

• To propose a novel outlier-robust method for discriminant analysis.
• To enhance feature extraction in pattern recognition by addressing LDA's limitations.

Main Methods:

• Introduced LDA-L1, which maximizes the between-class to within-class dispersion ratio using the L1-norm.
• Developed an iterative algorithm for solving LDA-L1, proven to reach a local optimum.
• Demonstrated that LDA-L1 overcomes small sample size and rank deficiency issues.

Main Results:

• LDA-L1 exhibits robustness against outliers.
• The proposed iterative algorithm is easy to implement.
• Experimental results in image recognition validate the effectiveness of LDA-L1.

Conclusions:

• LDA-L1 offers a robust and effective alternative to conventional LDA for pattern recognition.
• The method shows significant improvements, particularly in the presence of outliers and with limited data.
• LDA-L1 provides a promising direction for advanced feature extraction techniques.