Statistical Analysis of Long-Range Correlations in Textual Data
Summary
Long-range correlations in textual data refer to persistent dependencies between elements—words, characters or sentences—that extend across large spans of text. Unlike short-range associations captured by word-frequency statistics, these correlations reveal deeper organisation, such as thematic development, rhetorical structure and authorial style. Techniques borrowed from statistical physics and time-series analysis—such as detrended fluctuation analysis, mutual information decay and point-process modelling—have been adapted to quantify these effects in corpora spanning multiple languages and genres. Analyses consistently demonstrate that textual elements often follow power-law or stretched-exponential scaling, indicating that fluctuations at one point in a text can influence patterns many thousands of tokens away. This framework has enhanced our understanding of cognitive processing, stylistic fingerprinting, authorship attribution and the limitations of current language models in capturing genuine long-term dependencies. Practical applications range from improving natural language generation to developing more sensitive measures of textual complexity and coherence.
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Statistical Analysis of Long-Range Correlations in Textual Data publication trend
The graph below shows the total number of articles in statistical analysis of long-range correlations in textual data across all publications each year (not limited to Nature Index journals).
Technical terms
Long-range correlation: Dependence between elements in a sequence that decays slowly, often following a power law.
Hurst exponent: Quantifier of long-term memory in a time series, indicating persistence or anti-persistence of fluctuations.
Detrended fluctuation analysis: Method for detecting and characterising power-law correlations by removing local trends from a time series.
Hawkes process: Self-exciting point process in which each event increases the probability of future events within a memory kernel.
Natural visibility graph: Procedure that converts a time series into a network by linking points based on geometric visibility criteria.
Power law: Scaling relationship in which the frequency of an event varies as a constant multiplied by a power of its size.
References
- Long-Range Memory in Literary Texts: On the Universal Clustering of the Rare Words. PLOS ONE (2016).
- Word-Length Correlations and Memory in Large Texts: A Visibility Network Analysis. Entropy (2015).
- Modeling Long-Range Dynamic Correlations of Words in Written Texts with Hawkes Processes. Entropy (2022).
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