Extracting frequency-derived parameters allows for the identification and characterization of acoustic events, such as those obtained in passive acoustic monitoring applications. Situations where it is difficult to achieve the desired frequency resolution to distinguish between similar events occur, for example, in short time oscillating events. One feasible approach to make discrimination among such events is by measuring the complexity or the presence of non-linearities in a time series. Available techniques include the delay vector variance (DVV) and recurrence plot (RP) analysis, which have been used independently for statistical testing, however, the similarities between these two techniques have so far been overlooked. This work suggests a method that combines the DVV method with the recurrence quantification analysis parameters of the RP graphs for the characterization of short oscillating events. In order to establish the confidence intervals, a variant of the pseudo-periodic surrogate algorithm is proposed. This allows one to eliminate the fine details that may indicate the presence of non-linear dynamics, without having to add a large amount of noise, while preserving more efficiently the phase-space shape. The algorithm is verified on both synthetic and real world time series.
This paper evaluates the performance of first generation entropy metrics, featured by the well known and widely used Approximate Entropy (ApEn) and Sample Entropy (SampEn) metrics, and what can be considered an evolution from these, Fuzzy Entropy (FuzzyEn), in the Electroencephalogram (EEG) signal classification context. The study uses the commonest artifacts found in real EEGs, such as white noise, and muscular, cardiac, and ocular artifacts. Using two different sets of publicly available EEG records, and a realistic range of amplitudes for interfering artifacts, this work optimises and assesses the robustness of these metrics against artifacts in class segmentation terms probability. The results show that the qualitative behaviour of the two datasets is similar, with SampEn and FuzzyEn performing the best, and the noise and muscular artifacts are the most confounding factors. On the contrary, there is a wide variability as regards initialization parameters. The poor performance achieved by ApEn suggests that this metric should not be used in these contexts.
Many measures to quantify the nonlinear dynamics of a time series are based on estimating the probability of certain features from their relative frequencies. Once a normalised histogram of events is computed, a single result is usually derived. This process can be broadly viewed as a nonlinear I R n mapping into I R , where n is the number of bins in the histogram. However, this mapping might entail a loss of information that could be critical for time series classification purposes. In this respect, the present study assessed such impact using permutation entropy (PE) and a diverse set of time series. We first devised a method of generating synthetic sequences of ordinal patterns using hidden Markov models. This way, it was possible to control the histogram distribution and quantify its influence on classification results. Next, real body temperature records are also used to illustrate the same phenomenon. The experiments results confirmed the improved classification accuracy achieved using raw histogram data instead of the PE final values. Thus, this study can provide a very valuable guidance for the improvement of the discriminating capability not only of PE, but of many similar histogram-based measures.
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