Auto-contractive maps, H function, and the maximally regular graph: A new methodology for data mining

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Abstract

Data mining can be described as a process of discovering knowledge from a large dataset and depicting it in a human-understandable structure. It involves the disciplines of artificial intelligence, machine learning, database systems, and, of course, mathematics. A specialized data mining tool called the auto-contractive map (AutoCM) is defined and illustrated. After the AutoCM has discovered the relationships contained within the dataset, it is depicted in the form of a minimal spanning tree. An example is given to illustrate how to interpret the tree. A measure to determine the degree to which the tree is hub-oriented is developed and called the hubness index. Finally, a new index to measure the relevance and contribution of any node with a graph generated by a dataset is defined and called the delta H function.

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Buscema, M. (2013). Auto-contractive maps, H function, and the maximally regular graph: A new methodology for data mining. In Intelligent Data Mining in Law Enforcement Analytics: New Neural Networks Applied to Real Problems (Vol. 9789400749146, pp. 315–381). Springer Netherlands. https://doi.org/10.1007/978-94-007-4914-6_15

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