Feature Extraction Methods Directly Based on Image Matrix: 2DPCA, (2D) ZPCA, DiagPCA, and DiagPCA-I-2DPCA

In the feature extraction phase, we investigated multiple methods including PCA, 2DPCA, (2D) 2PCA, DiagPCA, and DiagPCA-F-2DPCA. While PCA-based feature extraction using image vectors has been widely adopted, methods such as 2DPCA, (2D) ZPCA, DiagPCA, and DiagPCA-I-2DPCA operate directly on image matrices, resulting in relatively lower computational complexity and significantly higher feature extraction speeds. These matrix-based algorithms work by computing covariance matrices from 2D image arrays without flattening them into vectors, typically involving operations like matrix multiplication and singular value decomposition (SVD) directly on the image matrix structure. The key implementation advantage lies in avoiding the high-dimensional vectorization step, which substantially reduces memory requirements and computational overhead. We believe these methods show promising application prospects for large-scale datasets since they can extract features more rapidly, thereby accelerating data processing and analysis tasks. In 2DPCA implementations, for example, the algorithm calculates the image covariance matrix directly from 2D image samples and selects dominant eigenvectors for feature projection, maintaining the original image structure throughout the process. In future work, we will continue to explore the advantages of these matrix-based approaches and validate their effectiveness in practical applications, particularly focusing on optimization techniques for handling ultra-high-resolution image datasets and parallel computing implementations for real-time processing scenarios.