Abstract
In this chapter we introduce
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1.
a new artificial neural network (ANN) architecture, the auto-contractive map (auto-CM);
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2.
a new index to measure the complexity of a-directed graphs (the H index); and
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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.
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Notes
- 1.
The “B” matrix operator was ideated by Massimo Buscema at Semeion Research Center in 1999. The “B” operator is implemented in Buscema (2002).
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Buscema, M., Sacco, P.L. (2010). Auto-contractive Maps, the H Function, and the Maximally Regular Graph (MRG): A New Methodology for Data Mining. In: Capecchi, V., Buscema, M., Contucci, P., D'Amore, B. (eds) Applications of Mathematics in Models, Artificial Neural Networks and Arts. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-8581-8_11
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