This article presents a new paradigm of Artificial Neural Networks (ANNs): the Auto-Contractive Maps (Auto- CM). The Auto-CM differ from the traditional ANNs under many viewpoints: the Auto-CM start their learning task without a random initialization of their weights, they meet their convergence criterion when all their output nodes become null, their weights matrix develops a data driven warping of the original Euclidean space, they show suitable topological properties, etc. Further two new algorithms, theoretically linked to Auto-CM are presented: the first one is useful to evaluate the complexity and the topological information of any kind of connected graph: the H Function is the index to measure the global hubness of the graph generated by the Auto-CM weights matrix. The second one is named Maximally Regular Graph (MRG) and it is an development of the traditionally Minimum Spanning Tree (MST). Finally, Auto-CM and MRG, with the support of the H Function, are applied to a real complex dataset about Alzheimer disease: this data come from the very known Nuns Study, where variables measuring the abilities of normal and Alzheimer subject during their lifespan and variables measuring the number of the plaques and of the tangles in their brain after their death. The example of the Alzheimer data base is extremely useful to figure out how this new approach can help to re design bottom-up the overall structure of factors related to a complex disease like this.
Keywords: Artificial neural networks, contractive maps, artificial adaptive systems, theory of graph, minimum spanning tree, Alzheimer disease, nun study
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