One of the primary challenges in Electroencephalogram (EEG) emotion recognition lies in developing models that can effectively generalize to new unseen subjects, considering the significant variability in EEG signals across individuals. To address the issue of subject-specific features, a suitable approach is to employ projection dictionary learning, which enables the identification of emotion-relevant features across different subjects. To accomplish the objective of pattern representation and discrimination for subject-independent EEG emotion recognition, we utilized the fast and efficient projection dictionary pair learning (PDPL) technique. PDPL involves the joint use of a synthesis dictionary and an analysis dictionary to enhance the representation of features. Additionally, to optimize the parameters of PDPL, which depend on experience, we applied the genetic algorithm (GA) to obtain the optimal solution for the model. We validated the effectiveness of our algorithm using leave-one-subject-out cross validation on three EEG emotion databases: SEED, MPED, and GAMEEMO. Our approach outperformed traditional machine learning methods, achieving an average accuracy of 69.89% on the SEED database, 24.11% on the MPED database, 64.34% for the two-class GAMEEMO, and 49.01% for the four-class GAMEEMO. These results highlight the potential of subject-independent EEG emotion recognition algorithms in the development of intelligent systems capable of recognizing and responding to human emotions in real-world scenarios.