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Ordinal analysis of lexical patterns
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2023 Words are fundamental linguistic units that connect thoughts and things through meaning. However, words do not appear independently in a text sequence. The existence of syntactic rules induces correlations among neighboring words. Using an ordinal pattern approach, we present an analysis of lexical statistical connections for 11 major languages.
David Sánchez +4 more
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Statistically Significant Pattern Mining with Ordinal Utility [PDF]
Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, 2020 Statistically significant patterns mining (SSPM) is an essential and challenging data mining task in the field of knowledge discovery in databases (KDD), in which each pattern is evaluated via a hypothesis test. Our study aims to introduce a preference relation into patterns and to discover the most preferred patterns under the constraint of ...
Thien Q. Tran +3 more
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Ordinal pattern dependence as a multivariate dependence measure [PDF]
Journal of Multivariate Analysis, 2021 In this article, we show that the recently introduced ordinal pattern dependence fits into the axiomatic framework of general multivariate dependence measures, i.e., measures of dependence between two multivariate random objects. Furthermore, we consider multivariate generalizations of established univariate dependence measures like Kendall's $τ ...
Annika Betken +3 more
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Proceedings of the International Florida Artificial Intelligence Research Society Conference, 2021 The estimation of the qualitative behaviour of fractional Brownian motion is an important topic for modelling real-world applications. Permutation entropy is a well-known approach to quantify the complexity of univariate time series in a scalar-valued ...
Marisa Mohr +2 more
doaj +1 more source
Ordinal patterns in the Duffing oscillator: Analyzing powers of characterization [PDF]
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2021 Ordinal patterns are a time-series data analysis tool used as a preliminary step to construct the permutation entropy, which itself allows the same characterization of dynamics as chaotic or regular as more theoretical constructs such as the Lyapunov exponent.
Ivan Gunther +2 more
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Statistical properties of the entropy from ordinal patterns
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2022 The ultimate purpose of the statistical analysis of ordinal patterns is to characterize the distribution of the features they induce. In particular, knowing the joint distribution of the pair entropy-statistical complexity for a large class of time series models would allow statistical tests that are unavailable to date.
E. T. C. Chagas +5 more
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The frequency of pattern occurrence in random walks [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 In the past decade, the use of ordinal patterns in the analysis of time series and dynamical systems has become an important tool. Ordinal patterns (otherwise known as a permutation patterns) are found in time series by taking $n$ data points at evenly ...
Sergi Elizalde, Megan Martinez
doaj +1 more source
Atom's Dynamics and Crystal Structure: An Ordinal Pattern Method. [PDF]
J Phys Chem AThe ubiquitous nature of thermal fluctuations poses a limitation on the identification of crystal structures. However, the trajectory of an atom carries a fingerprint of its surroundings. This rationalizes the search for a method that can determine the local atomic configuration via the analysis of the movement of an individual atom.
Abram R, Nowak R, Chrobak D.
europepmc +4 more sources
20 years of ordinal patterns: Perspectives and challenges
Europhysics Letters, 2022 Abstract In 2002, in a seminal article, Bandt and Pompe proposed a new methodology for the analysis of complex time series, now known as Ordinal Analysis. The ordinal methodology is based on the computation of symbols (known as ordinal patters) which are defined in terms of the temporal ordering of data points in a time series, and whose
Leyva Callejas, Inmaculada +4 more
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Ordinal patterns in long‐range dependent time series [PDF]
Scandinavian Journal of Statistics, 2020 AbstractWe analyze the ordinal structure of long‐range dependent time series. To this end, we use so called ordinal patterns which describe the relative position of consecutive data points. We provide two estimators for the probabilities of ordinal patterns and prove limit theorems in different settings, namely stationarity and (less restrictive ...
Annika Betken +5 more
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