Source code for neurokit2.complexity.entropy_ofentropy

import numpy as np
import pandas as pd

from .entropy_shannon import entropy_shannon

[docs] def entropy_ofentropy(signal, scale=10, bins=10, **kwargs): """**Entropy of entropy (EnofEn)** Entropy of entropy (EnofEn or EoE) combines the features of :func:`MSE <entropy_multiscale>` with an alternate measure of information, called *superinformation*, used in DNA sequencing. Parameters ---------- signal : Union[list, np.array, pd.Series] The signal (i.e., a time series) in the form of a vector of values. scale : int The size of the windows that the signal is divided into. Also referred to as Tau :math:`\\tau`, it represents the scale factor and corresponds to the amount of coarsegraining. bins : int The number of equal-size bins to divide the signal's range in. **kwargs : optional Other keyword arguments, such as the logarithmic ``base`` to use for :func:`entropy_shannon`. Returns -------- enofen : float The Entropy of entropy of the signal. info : dict A dictionary containing additional information regarding the parameters used, such as the average entropy ``AvEn``. See Also -------- entropy_shannon, entropy_multiscale Examples ---------- .. ipython:: python import neurokit2 as nk # Simulate a Signal signal = nk.signal_simulate(duration=2, sampling_rate=200, frequency=[5, 6], noise=0.5) # EnofEn enofen, _ = nk.entropy_ofentropy(signal, scale=10, bins=10) enofen References ----------- * Hsu, C. F., Wei, S. Y., Huang, H. P., Hsu, L., Chi, S., & Peng, C. K. (2017). Entropy of entropy: Measurement of dynamical complexity for biological systems. Entropy, 19(10), 550. """ # Sanity checks if isinstance(signal, (np.ndarray, pd.DataFrame)) and signal.ndim > 1: raise ValueError( "Multidimensional inputs (e.g., matrices or multichannel data) are not supported yet." ) info = {"Scale": scale, "Bins": bins} # divide a one-dimensional discrete time series of length n into consecutive # non-overlapping windows w where each window is of length 'scale' n_windows = int(np.floor(len(signal) / scale)) windows = np.reshape(signal[: n_windows * scale], (n_windows, scale)) # Divide the range into s1 slices into n equal width bins corresponding to a discrete state k sigrange = (np.min(signal), np.max(signal)) edges = np.linspace(sigrange[0], sigrange[1], bins + 1) # Compute the probability for a sample in each window to occur in state k freq = [np.histogram(windows[w, :], edges)[0] for w in range(n_windows)] # Next, we calculate the Shannon entropy value of each window. shanens = [entropy_shannon(freq=w / w.sum(), **kwargs)[0] for w in freq] info["AvEn"] = np.nanmean(shanens) # Number of unique ShanEn values (depending on the scale) _, freq2 = np.unique(np.round(shanens, 12), return_counts=True) freq2 = freq2 / freq2.sum() # Shannon entropy again to measure the degree of the "changing" enofen, _ = entropy_shannon(freq=freq2, **kwargs) return enofen, info