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This book introduces the Topological Weighed Centroid approach and describes some applications in the study of the dynamics of various spatial phenomena with a special emphasis on the spatial analysis of the relationship, influence, and dynamics of geographical phenomena. Offering a comprehensive introduction to the theory and illustrative examples from various kinds of geographical data, this book also takes an in-depth look at more complex case studies, such as the applications of the topological weighed centroid approach in the study of epidemic patterns, cultural processes, criminality, and environmental phenomena.

This book offers an introduction to artificial adaptive systems and a general model of the relationships between the data and algorithms used to analyze them. It subsequently describes artificial neural networks as a subclass of artificial adaptive systems, and reports on the backpropagation algorithm, while also identifying an important connection between supervised and unsupervised artificial neural networks. The book's primary focus is on the auto contractive map, an unsupervised artificial neural network employing a fixed point method versus traditional energy minimization. This is a powerful tool for understanding, associating and transforming data, as demonstrated in the numerous examples presented here. A supervised version of the auto contracting map is also introduced as an outstanding method for recognizing digits and defects. In closing, the book walks the readers through the theory and examples of how the auto contracting map can be used in conjunction with another artificial neural network, the “spin-net,” as a dynamic form of auto-associative memory.