Mathematics techniques with machine learning implementation for facial recognition

Abstract

The rapid evolution of facial recognition technology has elevated its signi cance across diverse applications, ranging from security systems to human-computer interaction. This thesis focuses on the intricate challenges faced by facial recognition systems, particularly emphasizing the im- pact of facial occlusion heightened by the widespread use of face masks during the COVID-19 pandemic. The study advances the eld by exploring dimension reduction techniques, encom- passing established methods such as Principal Component Analysis (PCA), Linear Discriminant Analysis (LDA) and Auto-Encoter-based, alongside innovative approaches hybrid methodolo- gies such as PCA-Autoencoder and LDA-Autoencoder. Notably, the study introduces Higher- Order Singular Value Decomposition (HOSVD) as a novel avenue for dimension reduction in facial recognition. The examination of facial occlusion yields nuanced insights into the challenges faced by recog- nition systems in real-world scenarios. Techniques developed in response aim to e ectively mitigate the adverse e ects of facial occlusion, ensuring precision and reliability in identi ca- tion processes, by developing face mask datasets adequate for the study. In the dimension reduction realm, the study meticulously evaluates traditional and innovative techniques. PCA and LDA are scrutinized for e ectiveness, while Autoencoder-based methods prove instrumental in facial feature extraction and dimension reduction. The innovative hybrid methodologies, PCA-Autoencoder and LDA-Autoencoder, demonstrate synergistic potential by capitalizing on the strengths of individual techniques. Tensor decomposition (HOSVD) e- merges as a novel mathematical approach, providing a fresh perspective on dimension reduction strategies. The ndings of this research signi cantly contribute to the theoretical foundations and practi- cal applications of facial recognition technology. Recommendations for future research include further exploration of diverse facial occlusion scenarios, real-time adaptive systems, and the integration of deep learning architectures to enhance dimension reduction methodologies. As technology advances, this thesis stands as a catalyst for ongoing innovation, fostering a deeper understanding of the intricate dynamics inherent in facial recognition systems.