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The objective of this paper is the design of an engine for the automatic generation of supervised manifold embedding models. It proposes a modular and adaptive data embedding framework for classification, referred to as DEFC, which realizes in different stages including initial data preprocessing, relation feature generation and embedding computation. For the computation of embeddings, the concepts of friend closeness and enemy dispersion are introduced, to better control at local level the relative positions of the intraclass and interclass data samples. These are shown to be general cases of the global information setup utilized in the Fisher criterion, and are employed for the construction of different optimization templates to drive the DEFC model generation. For model identification, we use a simple but effective bilevel evolutionary optimization, which searches for the optimal model and its best model parameters. The effectiveness of DEFC is demonstrated with experiments using noisy synthetic datasets possessing nonlinear distributions and real-world datasets from different application fields.