Factorization machine (FM) is an effective model for feature-based recommendation which utilizes inner product to capture second-order feature interactions. However, one of the major drawbacks of FM is that it couldn't capture complex high-order interaction signals. A common solution is to change the interaction function, such as stacking deep neural networks on the top of FM. In this work, we propose an alternative approach to model high-order interaction signals in the embedding level, namely Generalized Embedding Machine (GEM). The embedding used in GEM encodes not only the information from the feature itself but also the information from other correlated features. Under such situation, the embedding becomes high-order. Then we can incorporate GEM with FM and even its advanced variants to perform feature interactions. More specifically, in this paper we utilize graph convolution networks (GCN) to generate high-order embeddings. We integrate GEM with several FM-based models and conduct extensive experiments on two real-world datasets. The results demonstrate significant improvement of GEM over corresponding baselines.