Multiple patterning lithography decomposition (MPLD) has been widely investigated, but so far there is no decomposer that dominates others in terms of both the optimality and the efficiency. This observation motivates us exploring how to adaptively select the most suitable MPLD strategy for a given layout graph, which is non-trivial and still an open problem. In this paper, we propose a layout decomposition framework based on graph convolutional networks to obtain the graph embeddings of the layout. The graph embeddings are used for graph library construction, decomposer selection and graph matching. Experimental results show that our graph embedding based framework can achieve optimal decompositions under negligible runtime overhead even comparing with fast but non-optimal heuristics.