Automatic emotion analysis is a highly challenging task for Natural Language Processing, which has so far mainly relied on textual contents to determine the emotion of text. However, words are not the only media that carry emotional information. In social media, people also use emojis to convey their feelings. Recently, researchers have studied emotional aspects of emojis, and use emoji information to improve the emotion detection and classification, but many issues remain to be addressed. In this study, we examine the impact of emoji embedding on emotion classification and intensity prediction on four individual emotion categories, including anger, fear, joy, and sadness, in order to investigate how emojis affect the automatic analysis of individual emotion categories and intensity. We conducted a comparative study by testing five machine learning models with and without emoji embeddings involved. Our experiment demonstrates that emojis have varying impact on different emotion categories, and there is potential that emojis can be used to enhance emotion information processing.