Long-Range Correlations in Sentence Series from A Story of the Stone

Abstract

A sentence is the natural unit of language. Patterns embedded in series of sentences can be used to model the formation and evolution of languages, and to solve practical problems such as evaluating linguistic ability. In this paper, we apply de-trended fluctuation analysis to detect long-range correlations embedded in sentence series from A Story of the Stone, one of the greatest masterpieces of Chinese literature. We identified a weak long-range correlation, with a Hurst exponent of 0.575±0.002 up to a scale of 104. We used the structural stability to confirm the behavior of the long-range correlation, and found that different parts of the series had almost identical Hurst exponents. We found that noisy records can lead to false results and conclusions, even if the noise covers a limited proportion of the total records (e.g., less than 1%). Thus, the structural stability test is an essential procedure for confirming the existence of long-range correlations, which has been widely neglected in previous studies. Furthermore, a combination of de-trended fluctuation analysis and diffusion entropy analysis demonstrated that the sentence series was generated by a fractional Brownian motion.

Robustness of sentence length measures in written texts

“…Detrended fluctuation analysis (DFA) have been largely used to study long-range correlations in time series [38,39]. Texts, for instance, were mapped using the sentence length measured as the number of characters and investigated via DFA [40,26,27]. To exemplify the method, consider a generic sentence length series W = {w 1 , w 2 , · · · , w N }.…”

“…Therefore, mapping a text into a time series of sentence lengths is a natural way to investigate text structures. Recent methods applied to study texts at sentence level include probability distributions [24,25,26,27] and correlations [26,27,17,28]. In recent studies, sentence length analysis have been related to style and authorship [29,26,27].…”

“…In general, sentence lengths have been quantified by the number of words [24,29,25,28] or characters [30,31,26,27]. Also, note that the recurrence time of full stops also quantifies the sentence length [3].…”

Quantifying Evolution of Short and Long‐Range Correlations in Chinese Narrative Texts across 2000 Years

“…In a written text, there are temporal correlations among segments between short and long distances [29,30]. These correlations can be found in word length series, word frequency series, unicode (of word/character) series, and so on.…”

Linguistic data mining with complex networks: A stylometric-oriented approach

“…Likewise, knowing the meaning of separate words does not necessarily provide the understanding of a sentence composed of them, as a sentence can carry additional information, like an emotional load or a metaphorical message. Other features of natural language that are typical for complex systems have also been studied, for example long-range correlations [47], fractal and multifractal properties [5,10,13], self-organization [9,40] or lack of characteristic scale, which manifests itself in power laws such as the well-known Zipf's law or Heaps' law (the latter also referred to as the Herdan's law) [14,35,48].The network formalism has proven to be useful in studying and processing natural language. It allows to represent language on many levels of its structure -the linguistic networks can be constructed to reflect word co-occurrence, semantic similarity, grammatical relationships etc.…”