Noise-assisted estimation of attractor invariants

In this article, the noise-assisted correlation integral (NCI) is proposed. The purpose of the NCI is to estimate the invariants of a dynamical system, namely the correlation dimension (D), the correlation entropy (K2), and the noise level (σ). This correlation integral is induced by using random noise in a modified version of the correlation algorithm, i.e., the noise-assisted correlation algorithm. We demonstrate how the correlation integral by Grassberger et al. and the Gaussian kernel correlation integral (GCI) by Diks can be thought of as special cases of the NCI. A third particular case is the U-correlation integral proposed herein, from which we derived coarse-grained estimators of the correlation dimension (DmU), the correlation entropy (KmU), and the noise level (σmU). Using time series from the Henon map and the Mackey-Glass system, we analyze the behavior of these estimators under different noise conditions and data lengths. The results show that the estimators DmU and σmU behave in a similar manner to those based on the GCI. However, for the calculation of K2, the estimator KmU outperforms its GCI-based counterpart. On the basis of the behavior of these estimators, we have proposed an automatic algorithm to find D,K2, and σ from a given time series. The results show that by using this approach, we are able to achieve statistically reliable estimations of those invariants.Fil: Restrepo Rinckoar, Juan Felipe. Universidad Nacional de Entre Ríos. Facultad de Ingeniería. Departamento de Matemática e Informática. Laboratorio de Señales y Dinámicas no Lineales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Schlotthauer, Gaston. Universidad Nacional de Entre Ríos. Facultad de Ingeniería. Departamento de Matemática e Informática. Laboratorio de Señales y Dinámicas no Lineales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro de Investigaciones y Transferencia de Entre Ríos. Universidad Nacional de Entre Ríos. Centro de Investigaciones y Transferencia de Entre Ríos; Argentin

Transfer entropy rate through Lempel-Ziv complexity

The transfer entropy and the transfer entropy rate are closely related concepts that measure information exchange between two dynamical systems. These measures allow us to study linear and nonlinear causality relations and can be estimated through the use of different methodologies. However, some of them assume a data model and/or are computationally expensive. This article depicts a methodology to estimate the transfer entropy rate between two systems through the Lempel-Ziv complexity. This methodology offers a set of advantages: It estimates the transfer entropy rate from two single discrete series of measures, it is not computationally expensive, and it does not assume any data model. The simulation results over three different unidirectional coupled dynamical systems suggest that this methodology can be used to assess the direction and strength of the information flow between systems. Moreover, it provides good estimations for short-length time series.Fil: Restrepo Rinckoar, Juan Felipe. Consejo Nacional de Investigaciones Científicas y Técnicas. Universidad Nacional de Entre Ríos. Instituto de Investigación y Desarrollo en Bioingeniería y Bioinformática. Laboratorio de Señales y Dinámicas no Lineales; Argentina. Universidad Nacional de Entre Ríos. Facultad de Ingeniería. Departamento de Matemática e Informática. Laboratorio de Señales y Dinámicas no Lineales; ArgentinaFil: Mateos, Diego Martín. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina. Universidad Autónoma de Entre Ríos. Facultad de Ciencia y Tecnología; ArgentinaFil: Schlotthauer, Gaston. Consejo Nacional de Investigaciones Científicas y Técnicas. Universidad Nacional de Entre Ríos. Instituto de Investigación y Desarrollo en Bioingeniería y Bioinformática. Laboratorio de Señales y Dinámicas no Lineales; Argentina. Universidad Nacional de Entre Ríos. Facultad de Ingeniería. Departamento de Matemática e Informática. Laboratorio de Señales y Dinámicas no Lineales; Argentin

Automatic estimation of attractor invariants

The invariants of an attractor have been the most used resource to characterize a nonlinear dynamics. Their estimation is a challenging endeavor in short-time series and/or in presence of noise. In this article, we present two new coarse-grained estimators for the correlation dimension and for the correlation entropy. They can be easily estimated from the calculation of two U-correlation integrals. We have also developed an algorithm that is able to automatically obtain these invariants and the noise level in order to process large data sets. This method has been statistically tested through simulations in low-dimensional systems. The results show that it is robust in presence of noise and short data lengths. In comparison with similar approaches, our algorithm outperforms the estimation of the correlation entropy.Fil: Restrepo Rinckoar, Juan Felipe. Universidad Nacional de Entre Ríos. Facultad de Ingeniería. Departamento de Matemática e Informática. Laboratorio de Señales y Dinámicas no Lineales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Schlotthauer, Gaston. Universidad Nacional de Entre Ríos. Facultad de Ingeniería. Departamento de Matemática e Informática. Laboratorio de Señales y Dinámicas no Lineales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Classification of intracavitary electrograms in atrial fibrillation using information and complexity measures

Background Classification of complex fractionated atrial electrograms is crucial for the study of atrial fibrillation and the development of treatment strategies, because these electrophysiological phenomena represent a common substrate for radiofrequency ablation in treatment of this arrythmia.ObjectiveThe objective of this work is the characterization of short term atrial electrograms using nonlinear dynamics measures, helping in the automatic classification of electrograms.MethodsThe dataset consists of 113 atrial electrograms recordings from left-atrial endocardial mapping. These signals were classified by three expert electrophysiologists into four classes, from C0 (non fractionated) to C3 (high degree of fractionation). The calculated features were Approximate entropy, Dispersion entropy, Fuzzy entropy, Permutation entropy, Tsallis entropy, Shannon entropy, Renyi entropy, and Lempel-Ziv complexity. Features were selected for classification using Neighborhood Component Analysis. Different classifiers were tested using selected features, and the one with maximum sensitivity and specificity in each task was reported.ResultsWe obtained a classification performance that overcome previous works on this database and are comparable to the results of studies performed over bigger datasets. Separation between C3 signals from (C0, C1, C2) signals was performed with 99.98% sensitivity and 96.61% specificity. Non-fractionated signals (C0 + C1) were separated from fractionated signals (C2 + C3) with 96.72% sensitivity and 94.51% specificity. Moreover, the estimation times of the selected features are low enough to consider the online application of this scheme.Conclusions and significanceClassification performance obtained using information and complexity measures shown better results than previous works over this dataset, encouraging the application of these features to characterize atrial electrograms.Fil: Nicolet, Jonathan José Carlos. Universidad Nacional de Entre Ríos. Instituto de Investigación y Desarrollo en Bioingeniería y Bioinformática - Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Investigación y Desarrollo en Bioingeniería y Bioinformática; ArgentinaFil: Restrepo Rinckoar, Juan Felipe. Universidad Nacional de Entre Ríos. Instituto de Investigación y Desarrollo en Bioingeniería y Bioinformática - Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Investigación y Desarrollo en Bioingeniería y Bioinformática; ArgentinaFil: Schlotthauer, Gaston. Universidad Nacional de Entre Ríos. Instituto de Investigación y Desarrollo en Bioingeniería y Bioinformática - Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Investigación y Desarrollo en Bioingeniería y Bioinformática; Argentin

Voice Signal Typing Using a Pattern Recognition Approach

Voice signal classification in three types according to their degree of periodicity, a task known as signal typing, is a relevant preprocessing step before computing any perturbation measures. However, it is a time consuming and subjective activity. This has given rise to interest in automatic systems that use objective measures to distinguish among the different signal types. The purpose of this paper is twofold. First, to propose a pattern recognition approach for automatic voice signal typing based on a multi-class linear Support Vector Machine, and using rather well-known parameters like Jitter, Shimmer, Harmonic-to-Noise Ratio, and Cepstral Prominence Peak in combination with nonlinear dynamics measures. Two novel features are also proposed as objective parameters. Second, to validate this approach using a large amount of signals coming from two well-known corpora using cross-dataset experiments to assess the generalizability of the system. A total amount of 1262 signals labeled by professional voice pathologists were used with this purpose. Statistically significant differences between all types were found for all features. Accuracies over 82.71% were estimated in all intra-datasets and inter-datasets using cross-validation. Finally, the use of posterior probabilities is proposed as a measure of the reliability of the assigned type. This could help clinicians to make a more informed decision about the type assigned to a voice. These outcomes suggest that the proposed approach can successfully discriminate among the three voice types, paving the way to a fully automatic tool for voice signal typing in the future.Fil: Miramont, Juan Manuel. Universidad Nacional de Entre Ríos. Instituto de Investigación y Desarrollo en Bioingeniería y Bioinformática - Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Investigación y Desarrollo en Bioingeniería y Bioinformática; ArgentinaFil: Restrepo Rinckoar, Juan Felipe. Universidad Nacional de Entre Ríos. Instituto de Investigación y Desarrollo en Bioingeniería y Bioinformática - Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Investigación y Desarrollo en Bioingeniería y Bioinformática; ArgentinaFil: Codino, J.. Lakeshore Professionalvoice Center, Lakeshore Ear, Nose; Estados UnidosFil: Jackson-Menaldi, C.. Wayne State University, School Of Medicine; Estados UnidosFil: Schlotthauer, Gaston. Universidad Nacional de Entre Ríos. Instituto de Investigación y Desarrollo en Bioingeniería y Bioinformática - Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Investigación y Desarrollo en Bioingeniería y Bioinformática; Argentin