Chapter - Auto-Contractive Maps, H Function and Maximally Regular Graph - Theory

Abstract

This chapter presents a new paradigm of Artificial Neural Networks (ANNs): the Auto- Contractive Maps (Auto-CMs). The Auto-CM differs from the traditional ANNs under many viewpoints: the Auto-CMs 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 a development of the traditionally Minimum Spanning Tree (MST).

Keywords: Artificial Neural Networks, Contractive Maps, Artificial Adaptive Systems, Theory of Graph, Minimum Spanning Tree.

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