Permutation Entropy (PE) is a time series complexity measure commonly used in a variety of contexts, with medicine being the prime example. In its general form, it requires three input parameters for its calculation: time series length N, embedded dimension m, and embedded delay τ . Inappropriate choices of these parameters may potentially lead to incorrect interpretations. However, there are no specific guidelines for an optimal selection of N, m, or τ , only general recommendations such as N > > m ! , τ = 1 , or m = 3 , … , 7 . This paper deals specifically with the study of the practical implications of N > > m ! , since long time series are often not available, or non-stationary, and other preliminary results suggest that low N values do not necessarily invalidate PE usefulness. Our study analyses the PE variation as a function of the series length N and embedded dimension m in the context of a diverse experimental set, both synthetic (random, spikes, or logistic model time series) and real–world (climatology, seismic, financial, or biomedical time series), and the classification performance achieved with varying N and m. The results seem to indicate that shorter lengths than those suggested by N > > m ! are sufficient for a stable PE calculation, and even very short time series can be robustly classified based on PE measurements before the stability point is reached. This may be due to the fact that there are forbidden patterns in chaotic time series, not all the patterns are equally informative, and differences among classes are already apparent at very short lengths.
This paper presents a dimensionality reduction study based on fuzzy rough sets with the aim of increasing the discriminant capability of the representation of normal ECG beats and those that contain ischemic events. A novel procedure is proposed to obtain the fuzzy equivalence classes based on entropy and neighborhood techniques and a modification of the Quick Reduct Algorithm is used to select the relevant features from a large feature space by a dependency function. The tests were carried out on a feature space made up by 840 wavelet features extracted from 900 ECG normal beats and 900 ECG beats with evidence of ischemia. Results of around 99% classification accuracy are obtained. This methodology provides a reduced feature space with low complexity and high representation capability. Additionally, the discriminant strength of entropy in terms of representing ischemic disorders from time-frequency information in ECG signals is highlighted.
The heart's mechanical activity can be appraised by auscultation recordings, taken from the 4-Standard Auscultation Areas (4-SAA), one for each cardiac valve, as there are invisible murmurs when a single area is examined. This paper presents an effective approach for cardiac murmur detection based on adaptive neuro-fuzzy inference systems (ANFIS) over acoustic representations derived from Empirical Mode Decomposition (EMD) and Hilbert-Huang Transform (HHT) of 4-channel phonocardiograms (4-PCG). The 4-PCG database belongs to the National University of Colombia. Mel-Frequency Cepstral Coefficients (MFCC) and statistical moments of HHT were estimated on the combination of different intrinsic mode functions (IMFs). A fuzzy-rough feature selection (FRFS) was applied in order to reduce complexity. An ANFIS network was implemented on the feature space, randomly initialized, adjusted using heuristic rules and trained using a hybrid learning algorithm made up by least squares and gradient descent. Global classification for 4-SAA was around 98.9% with satisfactory sensitivity and specificity, using a 50-fold cross-validation procedure (70/30 split). The representation capability of the EMD technique applied to 4-PCG and the neuro-fuzzy inference of acoustic features offered a high performance to detect cardiac murmurs.
Abstract-In recent years several investigation prove the effects of air pollutants over human health, in this regard is necessary develop systems that allow people reduce the exposure to unhealthy air quality conditions. In This paper we propose a methodology to predict Critical Air Quality Events (CAQE) in Aburrá Valley based on Support Vector Machines (SVM) optimized with Particle Swarm Optimization (PSO) and a characterization scheme to asses the current and past tendencies of pollutants and weather behavior, analyzing the statistical behavior at different time intervals. We use a three stage methodology consisting in prepossessing, characterizations and CAQE prediction. The proposed method shows the better result for ozone CAQE prediction with an error of 30%. Due to low sensitivity among the pollutants is necessary use another machine learning technique that warranty a robust behavior working with unbalanced data.
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