Machine Learning with Eigenvector-Based Feature Representation: A Mathematical Analysis Using SVM for Robust Face Recognition

This paper proposes an enhanced framework for facial expression classification that integrates eigenvector-based feature extraction with an optimized Support Vector Machine (SVM) learning strategy. While Principal Component Analysis (PCA) and SVM are classical tools, the novelty of this work lies in a joint optimization scheme that couples adaptive eigenvector selection with kernel-driven margin optimization, leading to improved robustness and generalization under challenging imaging conditions. Unlike standard Eigenface approaches that retain components based solely on variance, the proposed method introduces a discriminative eigenvector selection criterion, ensuring that the retained subspace maximizes inter-class separability while minimizing intra-class variability. This is further reinforced by a systematic exploration and tuning of SVM kernels (linear, polynomial, and radial basis function), combined with cross-validated hyperparameter optimization to stabilize the decision boundary in noisy and high-dimensional settings. The framework is evaluated on the Extended Cohn–Kanade (CK+) dataset under controlled degradations, including noise perturbation and illumination variation. Comparative experiments against baseline models (standard PCA+SVM and raw-feature SVM) demonstrate that the proposed approach achieves consistent performance gains, reaching a classification accuracy above 97% while maintaining robustness across degraded scenarios. In addition, the analysis highlights the role of support vector sparsity control in improving generalization and reducing overfitting, providing further insight into the interaction between feature space structure and margin-based learning. These results suggest that embedding discriminative criteria within the eigen-decomposition stage, combined with kernel-aware optimization, constitutes an effective strategy for enhancing classical machine learning pipelines in real-world visual recognition tasks.