Generalized Centered 2-D Principal Component Analysis.

Area of Science:

• Computer Vision
• Machine Learning
• Data Science

Background:

• Robust Principal Component Analysis (PCA) and 2-D PCA (2DPCA) methods using the l2-norm are used to reduce outlier sensitivity in image analysis and pattern recognition.
• However, current methods often fail to preserve data structure in their optimization objectives and lack generalized robustness.

Purpose of the Study:

• To introduce novel robust PCA methods that preserve data structure and enhance outlier suppression.
• To develop centered PCA (C-PCA) for vector data and generalized centered 2DPCA (GC-2DPCA) for matrix data.

Main Methods:

• Proposed C-PCA preserves data structure by measuring point similarity and retains PCA's rotational invariance.
• Developed GC-2DPCA uses row variations and l2,p-norm minimization for robust projection matrices, effectively suppressing outliers.
• Efficient algorithms were developed for C-PCA and GC-2DPCA, with theoretical convergence analysis.

Main Results:

• Experimental results on three public databases demonstrated significant performance improvements of the proposed C-PCA and GC-2DPCA models.
• The new methods outperformed existing state-of-the-art PCA and 2DPCA approaches in robustness and data structure preservation.

Conclusions:

• The proposed C-PCA and GC-2DPCA models offer superior performance in robust dimensionality reduction.
• These novel methods effectively address limitations of existing PCA techniques, particularly in handling outliers and preserving data integrity for pattern recognition tasks.