Fractal Geometry Meets Computational Intelligence: Future Perspectives

Abstract

Characterizations in terms of fractals are typically employed for systems with complex and multiscale descriptions. A prominent example of such systems is provided by the human brain, which can be idealized as a complex dynamical system made of many interacting subunits. The human brain can be modeled in terms of observable variables together with their spatio-temporal-functional relations. Computational intelligence is a research field bridging many nature-inspired computational methods, such as artificial neural networks, fuzzy systems, and evolutionary and swarm intelligence optimization techniques. Typical problems faced by means of computational intelligence methods include those of recognition, such as classification and prediction. Although historically conceived to operate in some vector space, such methods have been recently extended to the so-called nongeometric spaces, considering labeled graphs as the most general example of such patterns. Here, we suggest that fractal analysis and computational intelligence methods can be exploited together in neuroscience research. Fractal characterizations can be used to (i) assess scale-invariant properties and (ii) offer numeric, feature-based representations to complement the usually more complex pattern structures encountered in neurosciences. Computational intelligence methods could be used to exploit such fractal characterizations, considering also the possibility to perform data-driven analysis of nongeometric input spaces, therby overcoming the intrinsic limits related to Euclidean geometry.

Keywords: Analysis of nongeometric input spaces; Brain research; Complex systems; Computational intelligence; Fractal analysis.