Source code for neurokit2.complexity.entropy_cumulativeresidual

import itertools

import numpy as np
import pandas as pd

from .entropy_shannon import _entropy_freq

[docs] def entropy_cumulativeresidual(signal, symbolize=None, show=False, freq=None): """**Cumulative residual entropy (CREn)** The cumulative residual entropy is an alternative to the Shannon differential entropy with several advantageous properties, such as non-negativity. The key idea is to use the cumulative distribution (CDF) instead of the density function in Shannon's entropy. .. math:: CREn = -\\int_{0}^{\\infty} p(|X| > x) \\log_{2} p(|X| > x) dx Similarly to :func:`Shannon entropy <entropy_shannon>` and :func:`Petrosian fractal dimension <fractal_petrosian>`, different methods to transform continuous signals into discrete ones are available. See :func:`complexity_symbolize` for details. This function can be called either via ``entropy_cumulativeresidual()`` or ``complexity_cren()``. Parameters ---------- signal : Union[list, np.array, pd.Series] The signal (i.e., a time series) in the form of a vector of values. symbolize : str Method to convert a continuous signal input into a symbolic (discrete) signal. ``None`` by default, which skips the process (and assumes the input is already discrete). See :func:`complexity_symbolize` for details. show : bool If ``True``, will show the discrete the signal. freq : np.array Instead of a signal, a vector of probabilities can be provided. Returns ------- CREn : float The cumulative residual entropy. info : dict A dictionary containing ``Values`` for each pair of events. Examples ---------- .. ipython:: python import neurokit2 as nk signal = [1, 1, 1, 3, 3, 2, 2, 1, 1, 3, 3, 3] @savefig p_entropy_cumulativeresidual1.png scale=100% cren, info = nk.entropy_cumulativeresidual(signal, show=True) @suppress plt.close() .. ipython:: python cren References ----------- * Rao, M., Chen, Y., Vemuri, B. C., & Wang, F. (2004). Cumulative residual entropy: a new measure of information. IEEE transactions on Information Theory, 50(6), 1220-1228. """ # 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." ) if freq is None: events, freq = _entropy_freq(signal, symbolize=symbolize, show=show) freq = freq / np.sum(freq) events, freq = zip(*sorted(zip(events, freq))) # Get the CDF cdf = {a: _ for a, _ in zip(events, np.cumsum(freq))} terms = np.zeros(len(events)) for i, (a, b) in enumerate(_entropy_cumulativeresidual_pairwise(events)): pgx = cdf[a] term = (b - a) * pgx * np.log2(pgx) terms[i] = term return -np.nansum(terms), {"Values": terms, "Symbolization": symbolize}
# ============================================================================= # Utilities # ============================================================================= def _entropy_cumulativeresidual_pairwise(iterable): "s -> (s0,s1), (s1,s2), (s2, s3), ..." a, b = itertools.tee(iterable) next(b, None) return zip(a, b)