For graph classification tasks, many traditional kernel methods focus on measuring the similarity between graphs. These methods have achieved great success on resolving graph isomorphism problems. However, in some classification problems, the graph class depends on not only the topological similarity of the whole graph, but also constituent subgraph patterns. To this end, we propose a novel graph embedding method using a multi-layer adjacent point merging model. This embedding method allows us to extract different subgraph patterns from train-data. Then we present a flexible loss function for feature selection which enhances the robustness of our method for different classification problems. Finally, numerical evaluations demonstrate that our proposed method outperforms many state-of-the-art methods.