 This paper proposes a new method called EEGG to decompose the brain into its independent and interactive components. It then uses these components to classify brain activity related to intentions. The proposed method is shown to be more robust than traditional methods when applied to low-quality data. Additionally, it is shown to have the ability to capture the known ERD-slash-ERS phenomenon, suggesting that the interaction between brain regions plays a role in intention classification. This article was authored by Geng Lu and Jing Wang.