Event detection from social media has been researched intensively and applied to many social problems such as disaster monitoring, rumor detection, and product sales prediction. In this paper, we deal with the underlying task of event representation. Existing works use topic modeling or graph embedding to extract events from text corpora, but have not fully utilized the available information. We propose a novel model called Graph Topic Model Autoencoder (GTMA) for improving event representation quality. The model combines non-negative matrix factorization and graph autoencoder to take advantages of the document-word matrix and the word-word co-occurrence graph. The model outputs event embeddings that can be used for topic-based event detection. We test our approach with two real-world social media datasets. Compared to several embedding learning baselines, our model generally achieves better topic quality in event detection evaluation.