Source code for neurokit2.complexity.entropy_slope

import numpy as np
import pandas as pd

from .entropy_shannon import entropy_shannon

[docs] def entropy_slope(signal, dimension=3, thresholds=[0.1, 45], **kwargs): """**Slope Entropy (SlopEn)** Slope Entropy (SlopEn) uses an alphabet of three symbols, 0, 1, and 2, with positive (+) and negative versions (-) of the last two. Each symbol covers a range of slopes for the segment joining two consecutive samples of the input data, and the :func:`Shannon entropy <entropy_shannon>` of the relative frequency of each pattern is computed. .. figure:: ../img/cuestafrau2019.png :alt: Figure from Cuesta-Frau, D. (2019). :target: Parameters ---------- signal : Union[list, np.array, pd.Series] The signal (i.e., a time series) in the form of a vector of values. dimension : int Embedding Dimension (*m*, sometimes referred to as *d* or *order*). See :func:`complexity_dimension` to estimate the optimal value for this parameter. thresholds : list Angular thresholds (called *levels*). A list of monotonically increasing values in the range [0, 90] degrees. **kwargs : optional Other keyword arguments, such as the logarithmic ``base`` to use for :func:`entropy_shannon`. Returns ------- slopen : float Slope Entropy of the signal. info : dict A dictionary containing additional information regarding the parameters used. See Also -------- entropy_shannon 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) # Compute Slope Entropy slopen, info = nk.entropy_slope(signal, dimension=3, thresholds=[0.1, 45]) slopen slopen, info = nk.entropy_slope(signal, dimension=3, thresholds=[5, 45, 60, 90]) slopen # Compute Multiscale Slope Entropy (MSSlopEn) @savefig p_entropy_slope1.png scale=100% msslopen, info = nk.entropy_multiscale(signal, method="MSSlopEn", show=True) @suppress plt.close() References ---------- * Cuesta-Frau, D. (2019). Slope entropy: A new time series complexity estimator based on both symbolic patterns and amplitude information. Entropy, 21(12), 1167. """ # 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." ) # Store parameters info = {"Dimension": dimension} # We could technically expose the Delay, but the paper is about consecutive differences so... if "delay" in kwargs.keys(): delay = kwargs["delay"] kwargs.pop("delay") else: delay = 1 # each subsequence of length m drawn from x, can be transformed into another subsequence of # length m-1 with the differences of each pair of consecutive samples Tx = np.degrees(np.arctan(signal[delay:] - signal[:-delay])) N = len(Tx) # a threshold or thresholds must be applied to these differences in order to find the # corresponding symbolic representation symbols = np.zeros(N) for q in range(1, len(thresholds)): symbols[np.logical_and(Tx <= thresholds[q], Tx > thresholds[q - 1])] = q symbols[np.logical_and(Tx >= -thresholds[q], Tx < -thresholds[q - 1])] = -q if q == len(thresholds) - 1: symbols[Tx > thresholds[q]] = q + 1 symbols[Tx < -thresholds[q]] = -(q + 1) unique = np.array([symbols[k : N - dimension + k + 1] for k in range(dimension - 1)]).T _, freq = np.unique(unique, axis=0, return_counts=True) # Shannon Entropy slopen, _ = entropy_shannon(freq=freq / freq.sum(), **kwargs) return slopen, info