Two-Dimensional Quaternion PCA and Sparse PCA.

Area of Science:

• Computer Vision
• Image Processing
• Machine Learning

Background:

• Quaternion Principle Component Analysis (QPCA) uses quaternion representation for color image feature extraction and dimension reduction.
• The standard QPCA method relies on eigen-decomposition, which is sensitive to outliers and lacks optimization flexibility.
• Existing methods struggle with outlier susceptibility and fixed solutions in feature extraction.

Purpose of the Study:

• To propose a novel quaternion ridge regression (QRR) model for two-dimensional QPCA (2D-QPCA).
• To develop a quaternion sparse regression model (2D-QSPCA) for improved classification robustness by incorporating sparsity constraints.
• To demonstrate the effectiveness and efficiency of the proposed methods in color image analysis.

Main Methods:

• A novel quaternion ridge regression (QRR) model is proposed, mathematically proven to be equivalent to the QCM model of 2D-QPCA.
• A quaternion sparse regression model (2D-QSPCA) is developed by integrating sparsity constraints into the QRR framework.
• An alternating minimization algorithm is employed for iterative learning in the complex domain for 2D-QSPCA.

Main Results:

• The proposed QRR model offers a flexible framework for 2D-QPCA, adaptable to various applications.
• 2D-QPCA and 2D-QSPCA preserve the spatial structure of color images with low computational cost.
• Experimental results show 2D-QSPCA outperforms state-of-the-art methods in color face recognition tasks.

Conclusions:

• The novel QRR model provides a robust and flexible alternative to traditional QPCA for feature extraction.
• 2D-QSPCA demonstrates superior performance in color face recognition, offering improved robustness and accuracy.
• The proposed methods are computationally efficient and preserve important spatial information in color images.