Nested Pattern Detection and Unidimensional Process Characterization

Abstract

This document introduces methods for describing long texts as groups of repeating symbols or patterns. The process converts a series of real-number values into texts. Developed tailored algorithms for identifying repeated sequences in the text are applied to decompose the text into nested tree-like structures of repeating symbols and is called the Nested Repeated Sequence Decomposition Model (NRSDM). The NRSDM is especially valuable for extracting repetitive behaviors in oscillatory but non-periodic and chaotic processes where the classical Fourier transform has limited application. The NRSDM along with the two graphical representations proposed here form a promising tool for characterizing long texts configured to represent the behavior of unidimensional processes.