Multifractal Characterization of Texts for Pattern Recognition: on the Complexity of Morphological Structures in Modern and Ancient Languages

The study of languages' structure and their organization in a set of well-defined relation schemes is a delicate matter. In the last decades, the convergence of traditional conflicting views by linguists is supported by an interdisciplinary approach that involves not only genetics or bio-archelogy but nowadays even the science of complexity. In light of this new and useful approach, this study proposes an in-depth analysis of the complexity underlying the morphological organization, in terms of multifractality and long-range correlations, of several modern and ancient texts pertaining to various linguistic strains (including ancient Greek, Arabic, Coptic, Neo-Latin and Germanic languages). The methodology is grounded on the mapping procedure between lexical categories belonging to text excerpts and time series, which is based on the rank of the frequency occurrence. Through the well-known MFDFA technique and a specific multifractal formalism, several multifractal indexes are then extracted for characterizing texts and the multifractal signature has been adopted for characterizing several language families, such as Indo-European, Semitic and Hamito-Semitic. The regularities and differences in the linguistic strains are assessed within a multivariate statistical framework and corroborated with a Machine Learning approach that is dedicated, in turn, to investigate the predictive power of the multifractal signature pertinent to text excerpts. The obtained results show a strong presence of persistence, i.e., memory, in the morphological structure of analyzed texts and we claim that this property has a role in characterizing the studied linguistic families. In fact, for example, the proposed analysis framework – grounded on complexity indexes – is able to easily distinguish ancient Greek texts from Arabic ones, as they belong to different language strains, i.e. indo-European and Semitic, respectively. The proposed approach has been proven effective and can be adopted for further comparative studies and for designing new informetrics for further advances in the fields of information retrieval and Artificial Intelligence.