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Add weighted permutation entropy. #14

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Add weighted permutation entropy. #14

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60 changes: 60 additions & 0 deletions pyentrp/entropy.py
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Original file line number Diff line number Diff line change
Expand Up @@ -78,6 +78,12 @@ def util_granulate_time_series(time_series, scale):
return cts


def util_rolling_window(a, window):
shape = a.shape[:-1] + (a.shape[-1] - window + 1, window)
strides = a.strides + (a.strides[-1],)
return np.lib.stride_tricks.as_strided(a, shape=shape, strides=strides)


def shannon_entropy(time_series):
"""Return the Shannon Entropy of the sample data.

Expand Down Expand Up @@ -327,3 +333,57 @@ def composite_multiscale_entropy(time_series, sample_length, scale, tolerance=No
tmp = util_granulate_time_series(time_series[j:], i + 1)
cmse[i] += sample_entropy(tmp, sample_length, tolerance) / (i + 1)
return cmse


def weighted_permutation_entropy(time_series, order=3, normalize=False):
"""Calculate the Weighted Permutation Entropy.

Weighted permutation entropy is based on the regular permutation entropy,
but puts additional weight on those windows that show a high variability
in the initial time series.

Parameters
----------
time_series : list or np.array
Time series
order : int
Order of permutation entropy
normalize : bool
If True, divide by log2(factorial(m)) to normalize the entropy
between 0 and 1. Otherwise, return the permutation entropy in bit.
Returns
-------
pe : float
Weighted Permutation Entropy
References
----------
.. [1] Bilal Fadlallah et al. Weighted-permutation entropy: A complexity
measure for time series incorporating amplitude information
https://link.aps.org/accepted/10.1103/PhysRevE.87.022911
"""
x = np.array(time_series)
hashmult = np.power(order, np.arange(order))
# Embed x and sort the order of permutations

embedded = _embed(x, order=order)
sorted_idx = embedded.argsort(kind='quicksort')
weights = np.var(util_rolling_window(x, order), 1)
hashval = (np.multiply(sorted_idx, hashmult)).sum(1)
mapping = {}
for i in np.unique(hashval):
mapping[i] = np.where(hashval == i)[0]
weighted_counts = dict.fromkeys(mapping)
for k, v in mapping.items():
weighted_count = 0
for i in v:
weighted_count += weights[i]
weighted_counts[k] = weighted_count
# Associate unique integer to each permutations
# Return the counts
# Use np.true_divide for Python 2 compatibility
weighted_counts_array = np.array(list(weighted_counts.values()))
p = np.true_divide(weighted_counts_array, weighted_counts_array.sum())
pe = -np.multiply(p, np.log2(p)).sum()
if normalize:
pe /= np.log2(factorial(order))
return pe