A non-linear pattern recognition approach to extract patterns and pseudo-randomness

Abstract can also be found here (page 192)

Usually the terms patterns and randomness are studied separately as opposite fields. For instance, Classical pattern recognition involves extracting patterns from objects in order to systematically make predictions from them, while information theory and Cryptography explores randomness as an information measure. On the other hand, some researches explored both patterns and pseudo-randomness in a unified framework [1, 2]. Since this integration would be in accordance to how many systems in nature show a slight fuzzy line between order and chaos. In this PhD project, we proposed a pattern recognition approach that aims for two purposes: (i) to extract patterns and (ii) to take advantages of the “absence” of patterns as a source of pseudo-randomness. This work has focused on different non-linear systems such as discrete dynamical systems, complex networks, cellular automata (CA), and their combinations. Thus, several methods were implemented aiming to extract patterns & pseudo-randomness from different dataset as entrances of the proposed method. During this PhD, we proposed two pattern recognition approaches applied to four applications of pattern recognition in multidisciplinary areas such as Cryptography, Biology and Information Science. The first method was to explore the patterns and pseudo-randomness from chaotic dynamical systems such as the logistic map, tent map and Hénon map. We observed that the patterns vanishes and therefore pseudo-randomness is increased by removing k right digits from the original orbit sequences. Therefore, we found an interesting chaotic source to obtain pseudo-randomness number generators (PRNGs). A second method was proposed which is based on the combination of cellular automata and networks, also called network automata (NA). The NA dynamic allows to extract patterns from different systems modeled as networks permitting their characterization. An interesting application of the NA approach was applied to the authorship recognition, thus literary texts have been modeled as networks, where words (nodes) are linked according to textual relationships. A third approach of pattern recognition was applied to plant metabolic networks, where the nodes are the metabolites connected to others metabolites through links formed by the reagent-product. In this scenario, several topological metrics from graph theory extracted phylogenetic patterns that converge trace of evolutionary information. So far, during this PhD, the proposed pattern recognition approach based on non-linear systems allowed us to explored patterns and pseudo-randomness extracted from a myriad of systems with successful results in terms of accuracy and pseudo-randomness metrics.

1 Machicao, J., Baetens, J.M., Marco, A.M., De Baets, B., Bruno, O.M. . A dynamical systems approach to the discrimination of the modes of operation of cryptographic systems.Communications in Nonlinear Science and Numerical Simulation, v. 29, n. 1-3, p. 102-115, 2015.

2 Machicao J.. Autômatos celulares caóticos aplicados na Criptografia e Criptoanálise.2013. 121p. Dissertação (Mestrado) - Instituto de Física de São Carlos, Universide de São Paulo, São Carlos, 2013.