Robust generalized PCA for enhancing discriminability and recoverability.

Area of Science:

• Machine Learning
• Data Science
• Statistics

Background:

• Existing robust principal component analysis (PCA) methods struggle with low-dimensional embeddings and noise-corrupted data.
• Projection onto principal component directions can impair data discriminability and recoverability.

Purpose of the Study:

• To develop a generalized principal component analysis (GPCA) model that optimizes regression bias for improved adaptability.
• To introduce a robust GPCA model mitigating outlier sensitivity and enhancing feature extraction flexibility.

Main Methods:

• Proposed a generalized PCA (GPCA) optimizing regression bias instead of sample mean.
• Developed a robust GPCA model using joint ℓ2,μ and ℓ2,ν norms for loss and regularization.
• Implemented a truncated and reweighted loss strategy to handle outliers effectively.
• Introduced a non-greedy iterative algorithm with guaranteed convergence for model solving.

Main Results:

• The proposed GPCA model demonstrates enhanced adaptability and robustness to outliers.
• The joint norm regularization mitigates outlier sensitivity while improving feature extraction.
• Truncation and reweighting strategies refine sample prioritization for better performance.
• Experimental results show superior recoverability and discrimination compared to previous robust PCA models.

Conclusions:

• The novel robust GPCA model offers significant improvements over traditional PCA techniques for noisy datasets.
• The proposed methods provide a more effective approach to dimensionality reduction and feature analysis in challenging data scenarios.