Source code for neurokit2.complexity.entropy_approximate

# -*- coding: utf-8 -*-
import numpy as np
import pandas as pd

from .optim_complexity_tolerance import _entropy_apen, complexity_tolerance
from .utils_entropy import _get_count

[docs] def entropy_approximate( signal, delay=1, dimension=2, tolerance="sd", corrected=False, **kwargs ): """**Approximate entropy (ApEn) and its corrected version (cApEn)** Approximate entropy is a technique used to quantify the amount of regularity and the unpredictability of fluctuations over time-series data. The advantages of ApEn include lower computational demand (ApEn can be designed to work for small data samples (< 50 data points) and can be applied in real time) and less sensitive to noise. However, ApEn is heavily dependent on the record length and lacks relative consistency. This function can be called either via ``entropy_approximate()`` or ``complexity_apen()``, and the corrected version via ``complexity_capen()``. Parameters ---------- signal : Union[list, np.array, pd.Series] The signal (i.e., a time series) in the form of a vector of values. delay : int Time delay (often denoted *Tau* :math:`\\tau`, sometimes referred to as *lag*) in samples. See :func:`complexity_delay` to estimate the optimal value for this parameter. dimension : int Embedding Dimension (*m*, sometimes referred to as *d* or *order*). See :func:`complexity_dimension` to estimate the optimal value for this parameter. tolerance : float Tolerance (often denoted as *r*), distance to consider two data points as similar. If ``"sd"`` (default), will be set to :math:`0.2 * SD_{signal}`. See :func:`complexity_tolerance` to estimate the optimal value for this parameter. corrected : bool If true, will compute corrected ApEn (cApEn), see Porta (2007). **kwargs Other arguments. See Also -------- entropy_shannon, entropy_sample, entropy_fuzzy Returns ---------- apen : float The approximate entropy of the single time series. info : dict A dictionary containing additional information regarding the parameters used to compute approximate entropy. Examples ---------- .. ipython:: python import neurokit2 as nk signal = nk.signal_simulate(duration=2, frequency=5) apen, parameters = nk.entropy_approximate(signal) apen capen, parameters = nk.entropy_approximate(signal, corrected=True) capen References ----------- * Sabeti, M., Katebi, S., & Boostani, R. (2009). Entropy and complexity measures for EEG signal classification of schizophrenic and control participants. Artificial intelligence in medicine, 47(3), 263-274. * Shi, B., Zhang, Y., Yuan, C., Wang, S., & Li, P. (2017). Entropy analysis of short-term heartbeat interval time series during regular walking. Entropy, 19(10), 568. """ # 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, "Delay": delay, "Tolerance": complexity_tolerance( signal, method=tolerance, dimension=dimension, show=False, )[0], "Corrected": corrected, } # Compute index if corrected is False: # ApEn is implemented in '' to avoid circular imports # as one of the method for optimizing tolerance relies on ApEn out, _ = _entropy_apen(signal, delay, dimension, info["Tolerance"], **kwargs) else: out = _entropy_capen(signal, delay, dimension, info["Tolerance"], **kwargs) return out, info
# ============================================================================= # Utils # ============================================================================= def _entropy_capen(signal, delay, dimension, tolerance, **kwargs): __, count1, _ = _get_count( signal, delay=delay, dimension=dimension, tolerance=tolerance, approximate=True, **kwargs, ) __, count2, _ = _get_count( signal, delay=delay, dimension=dimension + 1, tolerance=tolerance, approximate=True, **kwargs, ) # Limit the number of vectors to N - (dimension + 1) * delay upper_limit = len(signal) - (dimension + 1) * delay # Correction to replace the ratio of count1 and count2 when either is equal to 1 # As when count = 1, only the vector itself is within r distance correction = 1 / upper_limit vector_similarity = np.full(upper_limit, np.nan) for i in np.arange(upper_limit): if count1.astype(int)[i] != 1 and count2.astype(int)[i] != 1: vector_similarity[i] = np.log(count2[i] / count1[i]) else: vector_similarity[i] = np.log(correction) return -np.mean(vector_similarity)