We propose an amelioration of proposed Graph Embedding (GEM) method in previous work that takes advantages of structural pattern representation and the structured distortion. it models an Attributed Graph (AG) as a Probabilistic Graphical Model (PGM). Then, it learns the parameters of this PGM presented by a vector, as new signature of AG in a lower dimensional vectorial space. We focus to adapt the structured learning algorithm via 1-slack formulation with a suitable risk function, called Graph Edit Distance (GED). It defines the dissimilarity of the ground truth and predicted graph labels. It determines by the error tolerant graph matching using bipartite graph matching algorithm. We apply Structured Support Vector Machines (SSVM) to process classification task. During our experiments, we got our results on the GREC dataset.