Related papers: On the Automatic Parameter Selection for Permutati…
Permutation Entropy, introduced by Bandt and Pompe, is a widely used complexity measure for real-valued time series that is based on the relative order of values within consecutive segments of fixed length. After standardizing each segment…
Estimation of permutation entropy (PE) using Bayesian statistical methods is presented for systems where the ordinal pattern sampling follows an independent, multinomial distribution. It is demonstrated that the PE posterior distribution is…
We show that the same maximum entropy principle applied to recurrence microstates configures a new way to properly compute the time delay necessary to correctly sample a data set. The new method retrieves results obtained using traditional…
Reconstructing state-space dynamics from scalar data using time-delay embedding requires choosing values for the delay $\tau$ and the dimension $m$. Both parameters are critical to the success of the procedure and neither is easy to…
Permutation Entropy ($PE$) is a powerful nonlinear analysis technique for univariate time series. Recently, Permutation Entropy for Graph signals ($PEG$) has been proposed to extend PE to data residing on irregular domains. However, $PEG$…
Reconstruction of a dynamical system from a time series requires the selection of two parameters, the embedding dimension $d_e$ and the embedding lag $\tau$. Many competing criteria to select these parameters exist, and all are heuristic.…
Shannon Entropy is the preeminent tool for measuring the level of uncertainty (and conversely, information content) in a random variable. In the field of communications, entropy can be used to express the information content of given…
Empirical Mode Decomposition(EMD) is an adaptive data analysis technique for analyzing nonlinear and nonstationary data[1]. EMD decomposes the original data into a number of Intrinsic Mode Functions(IMFs)[1] for giving better physical…
Entropy metrics are nonlinear measures to quantify the complexity of time series. Among them, permutation entropy is a common metric due to its robustness and fast computation. Multivariate entropy metrics techniques are needed to analyse…
Entropy metrics (for example, permutation entropy) are nonlinear measures of irregularity in time series (one-dimensional data). Some of these entropy metrics can be generalised to data on periodic structures such as a grid or lattice…
We propose two algorithms for discrete-time parameter estimation, one for time-varying parameters under persistent excitation (PE) condition, another for constant parameters under no PE condition. For the first algorithm, we show that in…
On account of a greater need for understanding the complexity of time series like physiological time series, financial time series, and many more that enter into picture for their inculpation with real-world problems, several complexity…
Permutation patterns-based approaches, such as permutation entropy (PerEn), have been widely and successfully used to analyze data. However, these methods have two main shortcomings. First, when a series is symbolized based on permutation…
Permutation tests are widely used for statistical hypothesis testing when the sampling distribution of the test statistic under the null hypothesis is analytically intractable or unreliable due to finite sample sizes. One critical challenge…
Permutation patterns and pattern avoidance are central, well-studied concepts in combinatorics and computer science. Given two permutations $\tau$ and $\pi$, the pattern matching problem (PPM) asks whether $\tau$ contains $\pi$. This…
Here, we propose a new tool to estimate the complexity of a time series: the entropy of difference (ED). The method is based solely on the sign of the difference between neighboring values in a time series. This makes it possible to…
While it is tempting in experimental practice to seek as high a data rate as possible, oversampling can become an issue if one takes measurements too densely. These effects can take many forms, some of which are easy to detect: e.g., when…
Fourier transform methods are used to analyze functions and data sets to provide frequencies, amplitudes, and phases of underlying oscillatory components. Fast Fourier transform (FFT) methods offer speed advantages over evaluation of…
Permutation Entropy and statistiCal Complexity Analysis for astRophYsics (PECCARY) is a computationally inexpensive, statistical method by which any time-series can be characterized as predominantly regular, complex, or stochastic. Elements…
Adapting models pre-trained on large-scale datasets is a proven way to reach strong performance quickly for down-stream tasks. However, the growth of state-of-the-art mod-els makes traditional full fine-tuning unsuitable and difficult,…