PCA Dimensionality Reduction Followed by LDA Classification for Face Recognition

Face Recognition Method Using PCA Dimensionality Reduction and LDA Classification

In face recognition tasks, directly processing raw image data often encounters the curse of dimensionality problem. To address this challenge, we implement a combined approach using PCA (Principal Component Analysis) and LDA (Linear Discriminant Analysis).

First, we perform data dimensionality reduction through PCA. PCA transforms high-dimensional face image data into a lower-dimensional feature space by identifying principal components that capture maximum variance. This step involves computing eigenvectors and eigenvalues from the covariance matrix of standardized face data. Implementation typically includes: data normalization, covariance matrix calculation, eigenvalue decomposition, and selecting top-k eigenvectors corresponding to the largest eigenvalues. This process not only reduces computational complexity but also effectively suppresses noise interference while preserving essential variation patterns.

Next, we utilize LDA for feature extraction and classification. Unlike PCA which focuses solely on variance maximization, LDA incorporates class label information to find optimal projection directions. The algorithm maximizes between-class scatter while minimizing within-class scatter through mathematical operations involving scatter matrices. Key implementation steps include: computing within-class and between-class scatter matrices, solving the generalized eigenvalue problem, and projecting PCA-reduced features onto LDA directions. This creates a transformed space where samples from the same class cluster together while different classes separate distinctly.

Experimental results demonstrate that this cascaded PCA+LDA approach achieves excellent recognition performance. PCA serves as a preprocessing step for dimensionality reduction, while LDA subsequently optimizes the feature space to enhance classification capability. The combination leverages the strengths of both methods effectively. This approach proves particularly suitable for high-dimensional small-sample face recognition problems, showing high accuracy and robustness in practical applications. The implementation typically involves sklearn's PCA and LDA modules or custom matrix operations for eigenvalue decomposition and projection calculations.