Successful human interactions are based on becoming aware of other's emotion and making adaptations accordingly. However, understanding emotion is a complex task that has generated countless debates among researchers over the past decades. The abstractive nature of human emotion highlights the need for a new data-driven approach that can better describe and compare across fine-grained emotional states. In this study, we propose Seemo, a novel neural embedding framework, which allows us to map human emotions into vector space representations. Seemo is trained using Twitter data and is evaluated on two fundamental use cases in traditional emotion research: determining the underlying dimensions of emotions and identifying the set of basic emotions. The evaluation reveals that on both tasks Seemo can generate results consistent with the mainstream theories. Results also show that the vector space representation of Seemo can effectively decode the important relationships between emotions that were usually not explicitly presented.