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Visualization of non-linear time-series transformed as networks for pattern recognition


Prof. Odemir M. Bruno was one of the participants of the WWU-USP Workshop in Munster in January 2018. In this workshop, several research collaboration opportunities arose. One of those is the collaboration with Prof. Lars Linsen, where the main purpose is to combine the research of both groups, visualization of dynamical systems by the German side and patterns in complex systems and chaos by the Brazilian side. Our main research of joining efforts of both teams is in the areas of non-linear systems and complex networks and its applications to the pattern recognition field. Both team's work has been consolidated as promising and relevant to these areas as both teams have published articles in high impact factor journals regarding the main objective.Our main motivation is dedicated to the analysis of time-series data generated from non-linear systems. Since, the SCG-USP group has developed a pseudo-random number generator (PRNG) based on a well-known chaotic dynamical system, namely the logistic map, that allows parameterizing the quality of the pseudo-random sequences. Within this framework, a new context in pattern recognition has been opened that seek to explore pseudo-random sequences aiming to distinguish the quality of PRNGs. The abstraction of pseudo-random sequences, first represented as time series and then modeled as complex networks, opens up the possibility of using pattern recognition methods in networks to be able to study PRNGs in order to "measure pseudo-randomness" in such systems. However, there is lack of visualization tools that may aid the task to understand preliminaries abstraction of data. Typically, we use 2D projections: time-space evolution, scatter plots, recurrence matrix, network layouts, etc. However, these classical tools are not useful for visualization of networks because of several issues: e.g. randomized structure as a consequence of the non-linearity source, huge network size, and heterogeneity. Thus, within this context, we aim to explore new visualization tools that facilitate the visualization/interaction of patterns from time-series networks.The main reason behind the interest in sequences of pseudo-random numbers is because they are the backbone of the most diverse fields of application: statistical mechanics, decision theory, calculus, game industry, computer simulations, cryptography, etc. Therefore, the functioning of various sectors, such as the industrial and financial sectors, the need for secure communication and transactions, information shielding, among others, have become strongly dependent on the advances in cryptology in general, and particularly on the sources of pseudo-randomness. (AU)

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