Pattern recognition framework: patterns and pseudo-randomness in complex systems

Abstract can also be found here (página 197) Patterns and randomness are intuitively considered two opposite terms. Pattern recognition usually involves extracting features from abstract objects in order to classify them, while computability theory and information theory explores randomness as an information measure. Besides, the slight fuzzy line between pattern & randomness, they are two terms complementary to one another, however studied separately. Considering the point of view of chaotic systems, the frontier between regularity and randomness, involving these two terms together can be of high importance to study complex systems. Classical pattern recognition is a field based on decision theory, artificial intelligence, evolutionary computation and fuzzy logic. However, this field still presents many challenges and limitations when applied into complex systems problems. Recently, the field of chaos theory offered their tools to the pattern recognition (1) and cryptography (2), thus opening new branches of research. We proposed a pattern recognition framework to search for patterns and pseudo-randomness on complex systems. This work has focused on different complex systems such as one-dimensional dynamical systems, complex networks, cellular automata (CA), and their combinations. Thus, several methods derived from interdisciplinary tools (graph theory, chaos and complexity theory) were implemented aiming to analyze patterns & randomness on complex systems from different perspectives. During this PhD, four applications of pattern recognition (patterns & randomness) on complex systems from fields of Cryptography, Biology and Literature were analyzed. The first application was to explore the pseudo-randomness of one-dimensional dynamical systems by means of the Lyapunov exponent, from chaos theory. Thus, the well-known Logistic map was explored by removing k digits from the original orbital sequences, which we called k-logistic map. In the meantime, some initial results showed an increase of pseudo-randomness when high k values are setup, which is of interest to Cryptography. A second application of pattern recognition was applied to CA, which represents a discrete branch of chaos theory. Thus, it was proposed a prototype of CA combined with complex networks, where cells represent nodes and their dynamic is dependent on its neighborhood and their transition function. This second application allowed extracting patterns using metrics such as entropy, word-entropy and Lempel Ziv complexity, permitting the classification of various network types. A third approach of pattern recognition was applied to plant metabolic networks, which are intrinsically considered as complex systems because of their scale-free behavior. In this scenario, several topological metrics from graph theory extracted phylogenetic patterns that may trace evolutionary information. It is also expected to explore other metrics within these complex systems. A fourth application was applied in authorship recognition. A database of complex networks (3) made up from the frequency that words appear into literary text were modeled as chaotic systems, in this manner, the Lyapunov exponent calculated over these database extracted authorship patterns. Finally, the successful preliminary results obtained, until now, indicate that the proposed framework of various methods based on chaos theory, complex networks and complexity theory can bring good results for the field of pattern recognition. 1 FLORINDO, J. B. et al. Brachiaria species identification using imaging techniques based on fractal descriptors. Computers and Electronics in Agriculture, v. 103, p. 48-54, 2014. doi: 10.1016/j.compag.2014.02.005. 2 MACHICAO, J. et al. 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. 3 AMANCIO, D. R. et al. Comparing intermittency and network measurements of words and their dependence on authorship. New Journal of Physics, v. 13, n. 12, p. 123024-1-123024-17, 2011.Poster presented during the Semana integrada da graduação e pós-graduação do Instituto de Física de São Carlos, 2015, São Carlos, Brasil