Auto-contractive Maps, the H Function, and the Maximally Regular Graph (MRG): A New Methodology for Data Mining

  • Massimo Buscema
  • Pier L. Sacco


In this chapter we introduce
  1. 1.

    a new artificial neural network (ANN) architecture, the auto-contractive map (auto-CM);

  2. 2.

    a new index to measure the complexity of a-directed graphs (the H index); and

  3. 3.

    a new method to translate the results of data mining into a graph representation (the maximally regular graph).


In particular, auto-CMs squash the nonlinear correlation among variables into an embedding space where a visually transparent and cognitively natural notion such as “closeness” among variables reflects accurately their associations.

Through suitable optimization techniques that will be introduced and discussed in detail in what follows, “closeness” can be converted into a compelling graph-theoretic representation that picks all and only the relevant correlations and organizes them into a coherent picture.


Root Mean Square Error Artificial Neural Network Hide Layer Minimum Span Tree Topological Entropy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Semeion Research Center, Via SersaleRomeItaly
  2. 2.Department of Arts and Industrial DesignIuav UniversityVeniceItaly

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