def get_nonlinear(self, cols=['ENMO', 'mean_hr', 'hrv_ms']):
nonlin = defaultdict(dict)
for col in cols:
column = defaultdict(dict)
column_sleep = defaultdict(dict)
column_wake = defaultdict(dict)
for idx in range(len(self.sleep_windows)):
params = defaultdict(dict)
params['DFA'] = nolds.dfa(self.sleep_windows[idx][col],
debug_data=False)
params['SampEn'] = nolds.sampen(self.sleep_windows[idx][col],
debug_data=False)
column_sleep[idx] = params
for idx in range(len(self.wake_windows)):
params = defaultdict(dict)
params['DFA'] = nolds.dfa(self.wake_windows[idx][col],
debug_data=False)
params['SampEn'] = nolds.sampen(self.wake_windows[idx][col],
debug_data=False)
column_wake[idx] = params
column['sleep'] = column_sleep
column['wake'] = column_wake
nonlin[col] = column
self.nonlinear = nonlin
return self
def test_complexity():
signal = np.cos(np.linspace(start=0, stop=30, num=100))
# Shannon
assert np.allclose(nk.entropy_shannon(signal) - pyentrp.shannon_entropy(signal), 0)
# Approximate
assert np.allclose(nk.entropy_approximate(signal), 0.17364897858477146)
assert np.allclose(nk.entropy_approximate(signal, 2, 0.2*np.std(signal, ddof=1)) - entropy_app_entropy(signal, 2), 0)
assert nk.entropy_approximate(signal, 2, 0.2*np.std(signal, ddof=1)) != pyeeg_ap_entropy(signal, 2, 0.2*np.std(signal, ddof=1))
# Sample
assert np.allclose(nk.entropy_sample(signal, 2, 0.2*np.std(signal, ddof=1)) - entropy_sample_entropy(signal, 2), 0)
assert np.allclose(nk.entropy_sample(signal, 2, 0.2) - nolds.sampen(signal, 2, 0.2), 0)
assert np.allclose(nk.entropy_sample(signal, 2, 0.2) - entro_py_sampen(signal, 2, 0.2, scale=False), 0)
assert np.allclose(nk.entropy_sample(signal, 2, 0.2) - pyeeg_samp_entropy(signal, 2, 0.2), 0)
assert nk.entropy_sample(signal, 2, 0.2) != pyentrp.sample_entropy(signal, 2, 0.2)[1]
assert nk.entropy_sample(signal, 2, 0.2*np.sqrt(np.var(signal))) != MultiscaleEntropy_sample_entropy(signal, 2, 0.2)[0.2][2]
# MSE
# assert nk.entropy_multiscale(signal, 2, 0.2*np.sqrt(np.var(signal))) != np.trapz(MultiscaleEntropy_mse(signal, [i+1 for i in range(10)], 2, 0.2, return_type="list"))
# assert nk.entropy_multiscale(signal, 2, 0.2*np.std(signal, ddof=1)) != np.trapz(pyentrp.multiscale_entropy(signal, 2, 0.2, 10))
# Fuzzy
assert np.allclose(nk.entropy_fuzzy(signal, 2, 0.2, 1) - entro_py_fuzzyen(signal, 2, 0.2, 1, scale=False), 0)
def get_nonlin_params(df, col):
params = defaultdict(dict)
#params['hurst'] = nolds.hurst_rs(df[col],debug_data=False)
params['DFA'] = nolds.dfa(df[col], debug_data=False)
params['sampen'] = nolds.sampen(df[col], debug_data=False)
#params['lyap1'] = nolds.lyap_r(df[col],debug_data=False)
return params
def test_complexity():
signal = np.cos(np.linspace(start=0, stop=30, num=100))
# Shannon
assert np.allclose(nk.entropy_shannon(signal),
6.6438561897747395,
atol=0.0000001)
assert nk.entropy_shannon(signal) == pyentrp.shannon_entropy(signal)
# Approximate
assert np.allclose(nk.entropy_approximate(signal),
0.17364897858477146,
atol=0.000001)
assert np.allclose(nk.entropy_approximate(np.array([85, 80, 89] * 17)),
1.0996541105257052e-05,
atol=0.000001)
# assert nk.entropy_approximate(signal, 2, 0.2) == pyeeg.ap_entropy(signal, 2, 0.2)
# Sample
assert np.allclose(nk.entropy_sample(signal,
order=2,
r=0.2 * np.std(signal)),
nolds.sampen(signal,
emb_dim=2,
tolerance=0.2 * np.std(signal)),
atol=0.000001)
# assert nk.entropy_sample(signal, 2, 0.2) == pyeeg.samp_entropy(signal, 2, 0.2)
# pyentrp.sample_entropy(signal, 2, 0.2) # Gives something different
# Fuzzy
assert np.allclose(nk.entropy_fuzzy(signal),
0.5216395432372958,
atol=0.000001)
def test_complexity_vs_Python():
signal = np.cos(np.linspace(start=0, stop=30, num=100))
# Shannon
shannon = nk.entropy_shannon(signal)
# assert scipy.stats.entropy(shannon, pd.Series(signal).value_counts())
assert np.allclose(shannon - pyentrp.shannon_entropy(signal), 0)
# Approximate
assert np.allclose(nk.entropy_approximate(signal), 0.17364897858477146)
assert np.allclose(
nk.entropy_approximate(
signal, dimension=2, r=0.2 * np.std(signal, ddof=1)) -
entropy_app_entropy(signal, 2), 0)
assert nk.entropy_approximate(
signal, dimension=2,
r=0.2 * np.std(signal, ddof=1)) != pyeeg_ap_entropy(
signal, 2, 0.2 * np.std(signal, ddof=1))
# Sample
assert np.allclose(
nk.entropy_sample(signal, dimension=2, r=0.2 * np.std(signal, ddof=1))
- entropy_sample_entropy(signal, 2), 0)
assert np.allclose(
nk.entropy_sample(signal, dimension=2, r=0.2) -
nolds.sampen(signal, 2, 0.2), 0)
assert np.allclose(
nk.entropy_sample(signal, dimension=2, r=0.2) -
entro_py_sampen(signal, 2, 0.2, scale=False), 0)
assert np.allclose(
nk.entropy_sample(signal, dimension=2, r=0.2) -
pyeeg_samp_entropy(signal, 2, 0.2), 0)
# import sampen
# sampen.sampen2(signal[0:300], mm=2, r=r)
assert nk.entropy_sample(signal,
dimension=2, r=0.2) != pyentrp.sample_entropy(
signal, 2, 0.2)[1]
assert nk.entropy_sample(
signal, dimension=2,
r=0.2 * np.sqrt(np.var(signal))) != MultiscaleEntropy_sample_entropy(
signal, 2, 0.2)[0.2][2]
# MSE
# assert nk.entropy_multiscale(signal, 2, 0.2*np.sqrt(np.var(signal))) != np.trapz(MultiscaleEntropy_mse(signal, [i+1 for i in range(10)], 2, 0.2, return_type="list"))
# assert nk.entropy_multiscale(signal, 2, 0.2*np.std(signal, ddof=1)) != np.trapz(pyentrp.multiscale_entropy(signal, 2, 0.2, 10))
# Fuzzy
assert np.allclose(
nk.entropy_fuzzy(signal, dimension=2, r=0.2, delay=1) -
entro_py_fuzzyen(signal, 2, 0.2, 1, scale=False), 0)
# DFA
assert nk.fractal_dfa(signal, windows=np.array([
4, 8, 12, 20
])) != nolds.dfa(signal, nvals=[4, 8, 12, 20], fit_exp="poly")
def calc(images, adversarial_images, measure='sampen'):
"""Calculate and returns the nonlinear measure of both original and adversarial images.
Set measure to what you want to calculate.
'sampen' : Sample entropy
'frac' : Correlation/Fractal dimension
'hurst' : Hurst exponent
'lyapr' : Largest Lyapunov exponent using Rosenstein et al. methods
Docs : https://cschoel.github.io/nolds/
If the adversarial image is found to be NaN, we output 0.
The reason some adversarial iamges are NaN is because
adversarial generation were unsuccessful for them.
There is a maximum iteration one can set for adversarial
generation, the program outputs NaN when the max iteration
is reached before an adversarial perturbation is found.
For more info look at "adversarial_gen.ipynb"
"""
imageCalc_data = []
advimageCalc_data = []
for i in tqdm(range(len(images))):
image = images[i]
image = image.flatten()
advimage = adversarial_images[i]
advimage = advimage.flatten()
if measure == 'sampen':
imageCalc_data.append(nolds.sampen(image))
if np.isnan(np.sum(advimage)):
advimageCalc_data.append(0)
else:
advimageCalc_data.append(nolds.samepn(advimage))
elif measure == 'frac':
imageCalc_data.append(nolds.corr_dim(image, 1))
if np.isnan(np.sum(advimage)):
advimageCalc_data.append(0)
else:
advimageCalc_data.append(nolds.corr_dim(advimage, 1))
elif measure == 'hurst':
imageCalc_data.append(nolds.hurst_rs(image))
if np.isnan(np.sum(advimage)):
advimageCalc_data.append(0)
else:
advimageCalc_data.append(nolds.hurst_rs(advimage))
elif measure == 'lyapr':
imageCalc_data.append(nolds.lyap_r(image))
if np.isnan(np.sum(advimage)):
advimageCalc_data.append(0)
else:
advimageCalc_data.append(nolds.lyap_r(advimage))
return imageCalc_data, advimageCalc_data
def sampen(windowed_buffers, **kwargs):
"""Find the sample entropy of the buffers"""
T, C, _ = windowed_buffers.size()
sampen_feature = torch.zeros((T, C, 1), dtype=torch.float32)
for tt in range(T):
for cc in range(C):
sampen_feature[tt, cc, 0] = nolds.sampen(windowed_buffers[tt,
cc, :])
return sampen_feature
def feature_extraction_EMG(clip_data):
#extract features for EMG
features_list = [
'RMS', 'range', 'mean', 'var', 'skew', 'kurt', 'Pdom_rel', 'Dom_freq',
'Sen', 'PSD_mean', 'PSD_std', 'PSD_skew', 'PSD_kurt'
]
trial = list(clip_data.keys())[0]
features = []
for c in range(len(clip_data[trial]['elec']['data'])):
rawdata = clip_data[trial]['elec']['data'][c]
rawdata_wmag = rawdata.copy()
N = len(rawdata)
RMS = 1 / N * np.sqrt(np.sum(rawdata**2))
r = np.max(rawdata) - np.min(rawdata)
mean = np.mean(rawdata)
var = np.std(rawdata)
sk = skew(rawdata)
kurt = kurtosis(rawdata)
Pxx = power_spectra_welch(rawdata_wmag, fm=20, fM=70)
domfreq = Pxx.iloc[:, -1].idxmax()
Pdom_rel = Pxx.loc[domfreq] / Pxx.iloc[:, -1].sum()
Pxx_moments = np.array([
np.nanmean(Pxx.values),
np.nanstd(Pxx.values),
skew(Pxx.values)[0],
kurtosis(Pxx.values)[0]
])
x = rawdata.iloc[:, 0]
x = x[::5]
n = len(x)
Fs = np.mean(1 / (np.diff(x.index) / 1000))
sH_raw = nolds.sampen(x)
X = np.concatenate(
(RMS, r, mean, var, sk, kurt, Pdom_rel, np.array([domfreq,
sH_raw])))
Y = np.concatenate((X, Pxx_moments))
features.append(Y)
F = np.asarray(features)
clip_data[trial]['elec']['features'] = pd.DataFrame(data=F,
columns=features_list,
dtype='float32')
def sample(x: np.ndarray):
""" Sample Entropy
:param x: a 1-d numeric vector
:return: scalar feature
"""
out = nolds.sampen(x)
if np.isinf(out):
out = np.nan
return out
def plot_entropy(
df1, df2
): # calculating and plotting the sample entropy for embeding dimensions in range (1-10)
cd1 = []
cd2 = []
n = []
for i in range(1, 11):
cd1.append(nolds.sampen(df1, emb_dim=i))
cd2.append(nolds.sampen(df2, emb_dim=i))
n.append(i)
print(i)
plt.grid()
plt.plot(n, cd1, color='red', label='Model 1')
plt.scatter(n, cd1, color='red')
plt.plot(n, cd2, color='green', label='Model 2')
plt.scatter(n, cd2, color='green')
plt.xlabel('Embedding dimension')
plt.ylabel('Sample entropy')
plt.legend()
plt.show()
print('Model 1 max: ', max(cd1))
print('Model 2 max: ', max(cd2))
def load_feature(s):
rw = [lwalk(i) for i in s]
sd = [np.std(i) for i in rw]
dfa = [nolds.dfa(i) for i in rw]
hurst = [nolds.hurst_rs(i) for i in rw]
sampen = [nolds.sampen(i) for i in rw]
ac = [autocorrelation(i, 100) for i in rw]
rvntsl = [ratio_value_number_to_time_series_length(i) for i in rw]
ac_200 = [autocorrelation(i, 200) for i in rw]
ac_300 = [autocorrelation(i, 300) for i in rw]
lyapr = [nolds.lyap_r(i) for i in rw]
inpv = pd.DataFrame(
[sd, dfa, hurst, sampen, ac, rvntsl, ac_200, ac_300, lyapr])
return inpv.transpose()
def sample_entropy(nni=None, rpeaks=None, dim=2, tolerance=None):
"""Computes the sample entropy (sampen) of the NNI series.
Parameters
----------
nni : array
NN intervals in [ms] or [s].
rpeaks : array
R-peak times in [ms] or [s].
dim : int, optional
Entropy embedding dimension (default: 2).
tolerance : int, float, optional
Tolerance distance for which the vectors to be considered equal (default: std(NNI) * 0.2).
Returns (biosppy.utils.ReturnTuple Object)
------------------------------------------
[key : format]
Description.
sample_entropy : float
Sample entropy of the NNI series.
Raises
------
TypeError
If 'tolerance' is no numeric value.
"""
# Check input values
nn = pu.check_input(nni, rpeaks)
if tolerance is None:
tolerance = np.std(nn, ddof=-1) * 0.2
else:
try:
tolerance = float(tolerance)
except:
raise TypeError(
'Tolerance level cannot be converted to float.'
'Please verify that tolerance is a numeric (int or float).')
# Compute Sample Entropy
sampen = float(nolds.sampen(nn, dim, tolerance))
# Output
args = (sampen, )
names = ('sampen', )
return biosppy.utils.ReturnTuple(args, names)
def extractNonLinear(self, x):
'''
:param x: raw respiration data
:return: zeros-crossing features (mean, min, max) and respiration rate (mean, min, max, vector) and nonlinear
'''
zeros = self.extracRate(x, self.fs)[0]
zeros_diff = np.insert(np.diff(zeros), 0, zeros[0]).astype(np.float)
# interpolate zeros_diff
f = interpolate.interp1d(np.arange(0, len(zeros_diff)), zeros_diff)
xnew = np.arange(0, len(zeros_diff) - 1, 0.5)
zeros_diff_new = f(xnew)
# nonlinear
sample_ent = nolds.sampen(zeros_diff_new, emb_dim=1)
lypanov_exp = nolds.lyap_e(zeros_diff_new, emb_dim=2, matrix_dim=2)[0]
return np.array([sample_ent, lypanov_exp])
def extractNonLinear(self, x):
'''
:param x: raw PPG
:return: zeros-crossing features (mean, min, max) and respiration rate (mean, min, max, vector) and nonlinear
'''
onsets, = biosppy.signals.bvp.find_onsets(x, sampling_rate=self.fs)
onsets_diff = np.insert(np.diff(onsets), 0, onsets[0]).astype(np.float)
# interpolate zeros_diff
f = interpolate.interp1d(np.arange(0, len(onsets_diff)), onsets_diff)
xnew = np.arange(0, len(onsets_diff) - 1, 0.5)
onsets_diff_new = f(xnew)
# nonlinear
sample_ent = nolds.sampen(onsets_diff_new, emb_dim=1)
lypanov_exp = nolds.lyap_e(onsets_diff_new, emb_dim=2, matrix_dim=2)[0]
return np.array([sample_ent, lypanov_exp])
def test_complexity():
signal = np.cos(np.linspace(start=0, stop=30, num=100))
# Shannon
assert np.allclose(
nk.entropy_shannon(signal) - pyentrp.shannon_entropy(signal), 0)
# Approximate
assert np.allclose(nk.entropy_approximate(signal), 0.17364897858477146)
assert np.allclose(
nk.entropy_approximate(signal, 2, 0.2 * np.std(signal, ddof=1)) -
entropy_app_entropy(signal, 2), 0)
assert nk.entropy_approximate(
signal, 2, 0.2 * np.std(signal, ddof=1)) != pyeeg_ap_entropy(
signal, 2, 0.2 * np.std(signal, ddof=1))
# Sample
assert np.allclose(
nk.entropy_sample(signal, 2, 0.2 * np.std(signal, ddof=1)) -
entropy_sample_entropy(signal, 2), 0)
assert np.allclose(
nk.entropy_sample(signal, 2, 0.2) - nolds.sampen(signal, 2, 0.2), 0)
assert np.allclose(
nk.entropy_sample(signal, 2, 0.2) -
entro_py_sampen(signal, 2, 0.2, scale=False), 0)
assert np.allclose(
nk.entropy_sample(signal, 2, 0.2) - pyeeg_samp_entropy(signal, 2, 0.2),
0)
assert nk.entropy_sample(signal, 2, 0.2) != pyentrp.sample_entropy(
signal, 2, 0.2)[1]
# Fuzzy
assert np.allclose(
nk.entropy_fuzzy(signal, 2, 0.2, 1) -
entro_py_fuzzyen(signal, 2, 0.2, 1, scale=False), 0)
def get_sampen(nn_intervals: List[float]) -> dict:
"""
Function computing the sample entropy of the given data.
Must use this function on short term recordings, from 1 minute window.
Parameters
---------
nn_intervals : list
Normal to Normal Interval
Returns
---------
sampen : float
The sample entropy of the data
References
----------
.. [5] Physiological time-series analysis using approximate entropy and sample entropy, \
JOSHUA S. RICHMAN1, J. RANDALL MOORMAN - 2000
"""
sampen = nolds.sampen(nn_intervals, emb_dim=2)
return {'sampen': sampen}
def complexity(signal,
shannon=True,
sampen=True,
multiscale=True,
fractal_dim=True,
hurst=True,
dfa=True,
lyap_r=False,
lyap_e=False,
emb_dim=2,
tolerance="default"):
"""
Returns several chaos/complexity indices of a signal (including entropy, fractal dimensions, Hurst and Lyapunov exponent etc.).
Parameters
----------
signal : list or array
List or array of values.
shannon : bool
Computes Shannon entropy.
sampen : bool
Computes approximate sample entropy (sampen) using Chebychev and Euclidean distances.
multiscale : bool
Computes multiscale entropy (MSE). Note that it uses the 'euclidean' distance.
fractal_dim : bool
Computes the fractal (correlation) dimension.
hurst : bool
Computes the Hurst exponent.
dfa : bool
Computes DFA.
lyap_r : bool
Computes Positive Lyapunov exponents (Rosenstein et al. (1993) method).
lyap_e : bool
Computes Positive Lyapunov exponents (Eckmann et al. (1986) method).
emb_dim : int
The embedding dimension (*m*, the length of vectors to compare). Used in sampen and fractal_dim.
tolerance : float
Distance *r* threshold for two template vectors to be considered equal. Default is 0.2*std(signal). Used in sampen and fractal_dim.
Returns
----------
complexity : dict
Dict containing values for each indices.
Example
----------
>>> import neurokit as nk
>>> import numpy as np
>>>
>>> signal = np.sin(np.log(np.random.sample(666)))
>>> complexity = nk.complexity(signal)
Notes
----------
*Details*
- **shannon entropy**: Entropy is a measure of unpredictability of the state, or equivalently, of its average information content.
- **sample entropy (sampen)**: Measures the complexity of a time-series, based on approximate entropy. The sample entropy of a time series is defined as the negative natural logarithm of the conditional probability that two sequences similar for emb_dim points remain similar at the next point, excluding self-matches. A lower value for the sample entropy therefore corresponds to a higher probability indicating more self-similarity.
- **multiscale entropy**: Multiscale entropy (MSE) analysis is a new method of measuring the complexity of finite length time series.
- **fractal dimension**: A measure of the fractal (or correlation) dimension of a time series which is also related to complexity. The correlation dimension is a characteristic measure that can be used to describe the geometry of chaotic attractors. It is defined using the correlation sum C(r) which is the fraction of pairs of points X_i in the phase space whose distance is smaller than r.
- **hurst**: The Hurst exponent is a measure of the "long-term memory" of a time series. It can be used to determine whether the time series is more, less, or equally likely to increase if it has increased in previous steps. This property makes the Hurst exponent especially interesting for the analysis of stock data.
- **dfa**: DFA measures the Hurst parameter H, which is very similar to the Hurst exponent. The main difference is that DFA can be used for non-stationary processes (whose mean and/or variance change over time).
- **lyap**: Positive Lyapunov exponents indicate chaos and unpredictability. Provides the algorithm of Rosenstein et al. (1993) to estimate the largest Lyapunov exponent and the algorithm of Eckmann et al. (1986) to estimate the whole spectrum of Lyapunov exponents.
*Authors*
- Christopher Schölzel (https://github.com/CSchoel)
- tjugo (https://github.com/nikdon)
- Dominique Makowski (https://github.com/DominiqueMakowski)
*Dependencies*
- nolds
- numpy
*See Also*
- nolds package: https://github.com/CSchoel/nolds
- pyEntropy package: https://github.com/nikdon/pyEntropy
References
-----------
- Richman, J. S., & Moorman, J. R. (2000). Physiological time-series analysis using approximate entropy and sample entropy. American Journal of Physiology-Heart and Circulatory Physiology, 278(6), H2039-H2049.
- Costa, M., Goldberger, A. L., & Peng, C. K. (2005). Multiscale entropy analysis of biological signals. Physical review E, 71(2), 021906.
"""
if tolerance == "default":
tolerance = 0.2 * np.std(signal)
# Initialize results storing
complexity = {}
# Shannon
if shannon is True:
try:
complexity["Shannon_Entropy"] = entropy_shannon(signal)
except:
print(
"NeuroKit warning: complexity(): Failed to compute Shannon entropy."
)
complexity["Shannon_Entropy"] = np.nan
# Sampen
if sampen is True:
try:
complexity["Sample_Entropy_Chebychev"] = nolds.sampen(
signal,
emb_dim,
tolerance,
dist="chebychev",
debug_plot=False,
plot_file=None)
except:
print(
"NeuroKit warning: complexity(): Failed to compute sample entropy (sampen) using chebychev distance."
)
complexity["Sample_Entropy_Chebychev"] = np.nan
try:
complexity["Sample_Entropy_Euclidean"] = nolds.sampen(
signal,
emb_dim,
tolerance,
dist="euclidean",
debug_plot=False,
plot_file=None)
except:
try:
complexity["Sample_Entropy_Euclidean"] = nolds.sampen(
signal,
emb_dim,
tolerance,
dist="euler",
debug_plot=False,
plot_file=None)
except:
print(
"NeuroKit warning: complexity(): Failed to compute sample entropy (sampen) using euclidean distance."
)
complexity["Sample_Entropy_Euclidean"] = np.nan
# multiscale
if multiscale is True:
try:
complexity["Multiscale_Entropy"] = entropy_multiscale(
signal, emb_dim, tolerance)
except:
print(
"NeuroKit warning: complexity(): Failed to compute Multiscale Entropy (MSE)."
)
complexity["Multiscale_Entropy"] = np.nan
# fractal_dim
if fractal_dim is True:
try:
complexity["Fractal_Dimension"] = nolds.corr_dim(signal,
emb_dim,
rvals=None,
fit="RANSAC",
debug_plot=False,
plot_file=None)
except:
print(
"NeuroKit warning: complexity(): Failed to compute fractal_dim."
)
complexity["Fractal_Dimension"] = np.nan
# Hurst
if hurst is True:
try:
complexity["Hurst"] = nolds.hurst_rs(signal,
nvals=None,
fit="RANSAC",
debug_plot=False,
plot_file=None)
except:
print("NeuroKit warning: complexity(): Failed to compute hurst.")
complexity["Hurst"] = np.nan
# DFA
if dfa is True:
try:
complexity["DFA"] = nolds.dfa(signal,
nvals=None,
overlap=True,
order=1,
fit_trend="poly",
fit_exp="RANSAC",
debug_plot=False,
plot_file=None)
except:
print("NeuroKit warning: complexity(): Failed to compute dfa.")
complexity["DFA"] = np.nan
# Lyap_r
if lyap_r is True:
try:
complexity["Lyapunov_R"] = nolds.lyap_r(signal,
emb_dim=10,
lag=None,
min_tsep=None,
tau=1,
min_vectors=20,
trajectory_len=20,
fit="RANSAC",
debug_plot=False,
plot_file=None)
except:
print("NeuroKit warning: complexity(): Failed to compute lyap_r.")
complexity["Lyapunov_R"] = np.nan
# Lyap_e
if lyap_e is True:
try:
result = nolds.lyap_e(signal,
emb_dim=10,
matrix_dim=4,
min_nb=None,
min_tsep=0,
tau=1,
debug_plot=False,
plot_file=None)
for i, value in enumerate(result):
complexity["Lyapunov_E_" + str(i)] = value
except:
print("NeuroKit warning: complexity(): Failed to compute lyap_e.")
complexity["Lyapunov_E"] = np.nan
return (complexity)
# Save response time
RT_series = pd.DataFrame({
"Time": response["SpawnTime"].values,
"RT": response["RT"].values
})
RT_series.to_csv(result_path + f_name + "_RTSeries.csv")
# compute gaze velocity
skip = 1
time = gaze_data["Time"].values
gazex = gaze_data["GazeX"].values
gazey = gaze_data["GazeY"].values
gaze_avg = np.array([gazex, gazey]).transpose()
velocity = gaze_data["Velocity"].values
acceleration = gaze_data["Acceleration"].values
sampen_velocity = sampen(velocity,
2) # computed sample entropy of gaze velocity
sampen_acceleration = sampen(
acceleration, 2) # compute sample entropy of gaze acceleration
# compute sample entropy and angle (1e-25 to avoid NAN)
dist_avg = euclidianDistT(
gaze_avg,
skip=2) # compute euclidian distance for consecutive gaze
angle_avg = anglesEstimation(
gaze_avg, skip=2) # compute angle distance for consecutive gaze
# compute sample entropy of gaze distance
sampen_dist = sampen(dist_avg, 2)
sampen_angle = sampen(angle_avg, 2)
# FEATURE 1: MEAN
all_mean = np.mean(all_raw_pos, axis=0)
# FEATURE 2: MAX
all_max = np.max(all_raw_pos, axis=0)
# FEATURE 3: MIN
all_min = np.min(all_raw_pos, axis=0)
# FEATURE 4: VAR
all_var = np.var(all_raw_pos, axis=0)
# FEATURE 5: MEDIAN
all_med = np.median(all_raw_pos, axis=0)
# FEATURE 6: SKEW
all_skew = skew(all_raw_pos, axis=0)
# FEATURE 7: KURIOSIS
all_kuriosis = kurtosis(all_raw_pos, axis=0)
# FEATURE 8: SAMPLE ENTROPY
all_se = nolds.sampen(all_raw_pos)
# FEATURE 9: PCA
#pca = PCA(n_components=30)
#pca.fit(all_raw)
#all_pca = pca.components_[1,:]
# FEATURE 10: FFT
quat_head = np.transpose(np.array(data['quat_head']))
head_fft = np.absolute(
np.sqrt(
np.sum(np.square(np.fft.fft(quat_head, axis=1)),
axis=0)))[1:6]
quat_left = np.transpose(np.array(data['quat_left']))
left_fft = np.absolute(
np.sqrt(
np.sum(np.square(np.fft.fft(quat_left, axis=1)),
axis=0)))[1:6]
def sampE(y):
return nolds.sampen(y)
hurst = m[0]*2.0 hurst #farctal dimension (correlation dimension)= slope of the line fitted to log(r) vs log(C(r)) # If the correlation dimension is constant for all ‘m’ the time series will be deterministic #if the correlation exponentincreases with increase in ‘m’ the time series will be stochastic. h01 = nolds.corr_dim(F,2,debug_plot=True) h01 #lyap_r = estimate largest lyapunov exponent h1=nolds.lyap_r(F,emb_dim=2,debug_plot=True) h1 #lyap_e = estimate whole spectrum of lyapunov exponents h2=nolds.lyap_e(F) h2 from pyentrp import entropy as ent T1=np.std(F) T1 k= 0.2*T1 k #sample entropy h = nolds.sampen(F,3,tolerance=k) h #permutation entropy h2=ent.permutation_entropy(F,order=3,normalize=True) h2
def complexity(signal,
sampling_rate=1000,
shannon=True,
sampen=True,
multiscale=True,
spectral=True,
svd=True,
correlation=True,
higushi=True,
petrosian=True,
fisher=True,
hurst=True,
dfa=True,
lyap_r=False,
lyap_e=False,
emb_dim=2,
tolerance="default",
k_max=8,
bands=None,
tau=1):
"""
Computes several chaos/complexity indices of a signal (including entropy, fractal dimensions, Hurst and Lyapunov exponent etc.).
Parameters
----------
signal : list or array
List or array of values.
sampling_rate : int
Sampling rate (samples/second).
shannon : bool
Computes Shannon entropy.
sampen : bool
Computes approximate sample entropy (sampen) using Chebychev and Euclidean distances.
multiscale : bool
Computes multiscale entropy (MSE). Note that it uses the 'euclidean' distance.
spectral : bool
Computes Spectral Entropy.
svd : bool
Computes the Singular Value Decomposition (SVD) entropy.
correlation : bool
Computes the fractal (correlation) dimension.
higushi : bool
Computes the Higushi fractal dimension.
petrosian : bool
Computes the Petrosian fractal dimension.
fisher : bool
Computes the Fisher Information.
hurst : bool
Computes the Hurst exponent.
dfa : bool
Computes DFA.
lyap_r : bool
Computes Positive Lyapunov exponents (Rosenstein et al. (1993) method).
lyap_e : bool
Computes Positive Lyapunov exponents (Eckmann et al. (1986) method).
emb_dim : int
The embedding dimension (*m*, the length of vectors to compare). Used in sampen, fisher, svd and fractal_dim.
tolerance : float
Distance *r* threshold for two template vectors to be considered equal. Default is 0.2*std(signal). Used in sampen and fractal_dim.
k_max : int
The maximal value of k used for Higushi fractal dimension. The point at which the FD plateaus is considered a saturation point and that kmax value should be selected (Gómez, 2009). Some studies use a value of 8 or 16 for ECG signal and other 48 for MEG.
bands : int
Used for spectral density. A list of numbers delimiting the bins of the frequency bands. If None the entropy is computed over the whole range of the DFT (from 0 to `f_s/2`).
tau : int
The delay. Used for fisher, svd, lyap_e and lyap_r.
Returns
----------
complexity : dict
Dict containing values for each indices.
Example
----------
>>> import neurokit as nk
>>> import numpy as np
>>>
>>> signal = np.sin(np.log(np.random.sample(666)))
>>> complexity = nk.complexity(signal)
Notes
----------
*Details*
- **Entropy**: Entropy is a measure of unpredictability of the state, or equivalently, of its average information content.
- *Shannon entropy*: Shannon entropy was introduced by Claude E. Shannon in his 1948 paper "A Mathematical Theory of Communication". Shannon entropy provides an absolute limit on the best possible average length of lossless encoding or compression of an information source.
- *Sample entropy (sampen)*: Measures the complexity of a time-series, based on approximate entropy. The sample entropy of a time series is defined as the negative natural logarithm of the conditional probability that two sequences similar for emb_dim points remain similar at the next point, excluding self-matches. A lower value for the sample entropy therefore corresponds to a higher probability indicating more self-similarity.
- *Multiscale entropy*: Multiscale entropy (MSE) analysis is a new method of measuring the complexity of finite length time series.
- *SVD Entropy*: Indicator of how many vectors are needed for an adequate explanation of the data set. Measures feature-richness in the sense that the higher the entropy of the set of SVD weights, the more orthogonal vectors are required to adequately explain it.
- **fractal dimension**: The term *fractal* was first introduced by Mandelbrot in 1983. A fractal is a set of points that when looked at smaller scales, resembles the whole set. The concept of fractak dimension (FD) originates from fractal geometry. In traditional geometry, the topological or Euclidean dimension of an object is known as the number of directions each differential of the object occupies in space. This definition of dimension works well for geometrical objects whose level of detail, complexity or *space-filling* is the same. However, when considering two fractals of the same topological dimension, their level of *space-filling* is different, and that information is not given by the topological dimension. The FD emerges to provide a measure of how much space an object occupies between Euclidean dimensions. The FD of a waveform represents a powerful tool for transient detection. This feature has been used in the analysis of ECG and EEG to identify and distinguish specific states of physiologic function. Many algorithms are available to determine the FD of the waveform (Acharya, 2005).
- *Correlation*: A measure of the fractal (or correlation) dimension of a time series which is also related to complexity. The correlation dimension is a characteristic measure that can be used to describe the geometry of chaotic attractors. It is defined using the correlation sum C(r) which is the fraction of pairs of points X_i in the phase space whose distance is smaller than r.
- *Higushi*: Higuchi proposed in 1988 an efficient algorithm for measuring the FD of discrete time sequences. As the reconstruction of the attractor phase space is not necessary, this algorithm is simpler and faster than D2 and other classical measures derived from chaos theory. FD can be used to quantify the complexity and self-similarity of a signal. HFD has already been used to analyse the complexity of brain recordings and other biological signals.
- *Petrosian Fractal Dimension*: Provide a fast computation of the FD of a signal by translating the series into a binary sequence.
- **Other**:
- *Fisher Information*: A way of measuring the amount of information that an observable random variable X carries about an unknown parameter θ of a distribution that models X. Formally, it is the variance of the score, or the expected value of the observed information.
- *Hurst*: The Hurst exponent is a measure of the "long-term memory" of a time series. It can be used to determine whether the time series is more, less, or equally likely to increase if it has increased in previous steps. This property makes the Hurst exponent especially interesting for the analysis of stock data.
- *DFA*: DFA measures the Hurst parameter H, which is very similar to the Hurst exponent. The main difference is that DFA can be used for non-stationary processes (whose mean and/or variance change over time).
- *Lyap*: Positive Lyapunov exponents indicate chaos and unpredictability. Provides the algorithm of Rosenstein et al. (1993) to estimate the largest Lyapunov exponent and the algorithm of Eckmann et al. (1986) to estimate the whole spectrum of Lyapunov exponents.
*Authors*
- Dominique Makowski (https://github.com/DominiqueMakowski)
- Christopher Schölzel (https://github.com/CSchoel)
- tjugo (https://github.com/nikdon)
- Quentin Geissmann (https://github.com/qgeissmann)
*Dependencies*
- nolds
- numpy
*See Also*
- nolds package: https://github.com/CSchoel/nolds
- pyEntropy package: https://github.com/nikdon/pyEntropy
- pyrem package: https://github.com/gilestrolab/pyrem
References
-----------
- Accardo, A., Affinito, M., Carrozzi, M., & Bouquet, F. (1997). Use of the fractal dimension for the analysis of electroencephalographic time series. Biological cybernetics, 77(5), 339-350.
- Pierzchalski, M. Application of Higuchi Fractal Dimension in Analysis of Heart Rate Variability with Artificial and Natural Noise. Recent Advances in Systems Science.
- Acharya, R., Bhat, P. S., Kannathal, N., Rao, A., & Lim, C. M. (2005). Analysis of cardiac health using fractal dimension and wavelet transformation. ITBM-RBM, 26(2), 133-139.
- Richman, J. S., & Moorman, J. R. (2000). Physiological time-series analysis using approximate entropy and sample entropy. American Journal of Physiology-Heart and Circulatory Physiology, 278(6), H2039-H2049.
- Costa, M., Goldberger, A. L., & Peng, C. K. (2005). Multiscale entropy analysis of biological signals. Physical review E, 71(2), 021906.
"""
if tolerance == "default":
tolerance = 0.2 * np.std(signal)
# Initialize results storing
complexity = {}
# ------------------------------------------------------------------------------
# Shannon
if shannon is True:
try:
complexity["Entropy_Shannon"] = entropy_shannon(signal)
except:
print(
"NeuroKit warning: complexity(): Failed to compute Shannon entropy."
)
complexity["Entropy_Shannon"] = np.nan
# Sampen
if sampen is True:
try:
complexity["Entropy_Sample"] = nolds.sampen(signal,
emb_dim,
tolerance,
dist="chebychev",
debug_plot=False,
plot_file=None)
except:
print(
"NeuroKit warning: complexity(): Failed to compute sample entropy (sampen)."
)
complexity["Entropy_Sample"] = np.nan
# multiscale
if multiscale is True:
try:
complexity["Entropy_Multiscale"] = entropy_multiscale(
signal, emb_dim, tolerance)
except:
print(
"NeuroKit warning: complexity(): Failed to compute Multiscale Entropy (MSE)."
)
complexity["Entropy_Multiscale"] = np.nan
# spectral
if spectral is True:
try:
complexity["Entropy_Spectral"] = entropy_spectral(
signal, sampling_rate=sampling_rate, bands=bands)
except:
print(
"NeuroKit warning: complexity(): Failed to compute Spectral Entropy."
)
complexity["Entropy_Spectral"] = np.nan
# SVD
if svd is True:
try:
complexity["Entropy_SVD"] = entropy_svd(signal,
tau=tau,
emb_dim=emb_dim)
except:
print(
"NeuroKit warning: complexity(): Failed to compute SVD Entropy."
)
complexity["Entropy_SVD"] = np.nan
# ------------------------------------------------------------------------------
# fractal_dim
if correlation is True:
try:
complexity["Fractal_Dimension_Correlation"] = nolds.corr_dim(
signal,
emb_dim,
rvals=None,
fit="RANSAC",
debug_plot=False,
plot_file=None)
except:
print(
"NeuroKit warning: complexity(): Failed to compute fractal_dim."
)
complexity["Fractal_Dimension_Correlation"] = np.nan
# higushi
if higushi is True:
try:
complexity["Fractal_Dimension_Higushi"] = fd_higushi(signal, k_max)
except:
print("NeuroKit warning: complexity(): Failed to compute higushi.")
complexity["Fractal_Dimension_Higushi"] = np.nan
# petrosian
if petrosian is True:
try:
complexity["Fractal_Dimension_Petrosian"] = fd_petrosian(signal)
except:
print(
"NeuroKit warning: complexity(): Failed to compute petrosian.")
complexity["Fractal_Dimension_Petrosian"] = np.nan
# ------------------------------------------------------------------------------
# Fisher
if fisher is True:
try:
complexity["Fisher_Information"] = fisher_info(signal,
tau=tau,
emb_dim=emb_dim)
except:
print(
"NeuroKit warning: complexity(): Failed to compute Fisher Information."
)
complexity["Fisher_Information"] = np.nan
# Hurst
if hurst is True:
try:
complexity["Hurst"] = nolds.hurst_rs(signal,
nvals=None,
fit="RANSAC",
debug_plot=False,
plot_file=None)
except:
print("NeuroKit warning: complexity(): Failed to compute hurst.")
complexity["Hurst"] = np.nan
# DFA
if dfa is True:
try:
complexity["DFA"] = nolds.dfa(signal,
nvals=None,
overlap=True,
order=1,
fit_trend="poly",
fit_exp="RANSAC",
debug_plot=False,
plot_file=None)
except:
print("NeuroKit warning: complexity(): Failed to compute dfa.")
complexity["DFA"] = np.nan
# Lyap_r
if lyap_r is True:
try:
complexity["Lyapunov_R"] = nolds.lyap_r(signal,
emb_dim=10,
lag=None,
min_tsep=None,
tau=tau,
min_vectors=20,
trajectory_len=20,
fit="RANSAC",
debug_plot=False,
plot_file=None)
except:
print("NeuroKit warning: complexity(): Failed to compute lyap_r.")
complexity["Lyapunov_R"] = np.nan
# Lyap_e
if lyap_e is True:
try:
result = nolds.lyap_e(signal,
emb_dim=10,
matrix_dim=4,
min_nb=None,
min_tsep=0,
tau=tau,
debug_plot=False,
plot_file=None)
for i, value in enumerate(result):
complexity["Lyapunov_E_" + str(i)] = value
except:
print("NeuroKit warning: complexity(): Failed to compute lyap_e.")
complexity["Lyapunov_E"] = np.nan
return (complexity)
def feature_extraction(clip_data):
features_list = [
'RMSX', 'RMSY', 'RMSZ', 'rangeX', 'rangeY', 'rangeZ', 'meanX', 'meanY',
'meanZ', 'varX', 'varY', 'varZ', 'skewX', 'skewY', 'skewZ', 'kurtX',
'kurtY', 'kurtZ', 'xcor_peakXY', 'xcorr_peakXZ', 'xcorr_peakYZ',
'xcorr_lagXY', 'xcorr_lagXZ', 'xcorr_lagYZ', 'Dom_freq', 'Pdom_rel',
'PSD_mean', 'PSD_std', 'PSD_skew', 'PSD_kur', 'jerk_mean', 'jerk_std',
'jerk_skew', 'jerk_kur', 'Sen_X', 'Sen_Y', 'Sen_Z', 'RMS_mag',
'range_mag', 'mean_mag', 'var_mag', 'skew_mag', 'kurt_mag', 'Sen_mag'
]
#cycle through all clips for current trial and save dataframe of features for current trial and sensor
features = []
for c in range(len(clip_data['data'])):
rawdata = clip_data['data'][c]
#acceleration magnitude
rawdata_wmag = rawdata.copy()
rawdata_wmag['Accel_Mag'] = np.sqrt((rawdata**2).sum(axis=1))
#extract features on current clip
#Root mean square of signal on each axis
N = len(rawdata)
RMS = 1 / N * np.sqrt(np.asarray(np.sum(rawdata**2, axis=0)))
RMS_mag = 1 / N * np.sqrt(np.sum(rawdata_wmag['Accel_Mag']**2, axis=0))
#range on each axis
min_xyz = np.min(rawdata, axis=0)
max_xyz = np.max(rawdata, axis=0)
r = np.asarray(max_xyz - min_xyz)
r_mag = np.max(rawdata_wmag['Accel_Mag']) - np.min(
rawdata_wmag['Accel_Mag'])
#Moments on each axis
mean = np.asarray(np.mean(rawdata, axis=0))
var = np.asarray(np.std(rawdata, axis=0))
sk = skew(rawdata)
kurt = kurtosis(rawdata)
mean_mag = np.mean(rawdata_wmag['Accel_Mag'])
var_mag = np.std(rawdata_wmag['Accel_Mag'])
sk_mag = skew(rawdata_wmag['Accel_Mag'])
kurt_mag = kurtosis(rawdata_wmag['Accel_Mag'])
#Cross-correlation between axes pairs
xcorr_xy = np.correlate(rawdata.iloc[:, 0],
rawdata.iloc[:, 1],
mode='same')
# xcorr_xy = xcorr_xy/np.abs(np.sum(xcorr_xy)) #normalize values
xcorr_peak_xy = np.max(xcorr_xy)
xcorr_lag_xy = (np.argmax(xcorr_xy)) / len(xcorr_xy) #normalized lag
xcorr_xz = np.correlate(rawdata.iloc[:, 0],
rawdata.iloc[:, 2],
mode='same')
# xcorr_xz = xcorr_xz/np.abs(np.sum(xcorr_xz)) #normalize values
xcorr_peak_xz = np.max(xcorr_xz)
xcorr_lag_xz = (np.argmax(xcorr_xz)) / len(xcorr_xz)
xcorr_yz = np.correlate(rawdata.iloc[:, 1],
rawdata.iloc[:, 2],
mode='same')
# xcorr_yz = xcorr_yz/np.abs(np.sum(xcorr_yz)) #normalize values
xcorr_peak_yz = np.max(xcorr_yz)
xcorr_lag_yz = (np.argmax(xcorr_yz)) / len(xcorr_yz)
#pack xcorr features
xcorr_peak = np.array([xcorr_peak_xy, xcorr_peak_xz, xcorr_peak_yz])
xcorr_lag = np.array([xcorr_lag_xy, xcorr_lag_xz, xcorr_lag_yz])
#Dominant freq and relative magnitude (on acc magnitude)
Pxx = power_spectra_welch(rawdata_wmag, fm=0, fM=10)
domfreq = np.asarray([Pxx.iloc[:, -1].idxmax()])
Pdom_rel = Pxx.loc[domfreq].iloc[:, -1].values / Pxx.iloc[:, -1].sum(
) #power at dominant freq rel to total
#moments of PSD
Pxx_moments = np.array([
np.nanmean(Pxx.values),
np.nanstd(Pxx.values),
skew(Pxx.values),
kurtosis(Pxx.values)
])
#moments of jerk magnitude
jerk = rawdata_wmag['Accel_Mag'].diff().values
jerk_moments = np.array([
np.nanmean(jerk),
np.nanstd(jerk),
skew(jerk[~np.isnan(jerk)]),
kurtosis(jerk[~np.isnan(jerk)])
])
#sample entropy raw data (magnitude) and FFT
sH_raw = []
sH_fft = []
for a in range(3):
x = rawdata.iloc[:, a]
n = len(x) #number of samples in clip
Fs = np.mean(1 / (np.diff(x.index) / 1000)) #sampling rate in clip
sH_raw.append(nolds.sampen(x)) #samp entr raw data
#for now disable SH on fft
# f,Pxx_den = welch(x,Fs,nperseg=min(256,n/4))
# sH_fft.append(nolds.sampen(Pxx_den)) #samp entr fft
sH_mag = nolds.sampen(rawdata_wmag['Accel_Mag'])
#Assemble features in array
Y = np.array(
[RMS_mag, r_mag, mean_mag, var_mag, sk_mag, kurt_mag, sH_mag])
X = np.concatenate(
(RMS, r, mean, var, sk, kurt, xcorr_peak, xcorr_lag, domfreq,
Pdom_rel, Pxx_moments, jerk_moments, sH_raw, Y))
features.append(X)
F = np.asarray(features) #feature matrix for all clips from current trial
clip_data['features'] = pd.DataFrame(data=F,
columns=features_list,
dtype='float32')
def entropy_multiscale(signal, emb_dim=2, tolerance="default"):
"""
Returns the Multiscale Entropy. Copied from the `pyEntropy <https://github.com/nikdon/pyEntropy>`_ repo by tjugo. Uses sample entropy with 'chebychev' distance.
Parameters
----------
signal : list or array
List or array of values.
emb_dim : int
The embedding dimension (*m*, the length of vectors to compare).
tolerance : float
Distance *r* threshold for two template vectors to be considered equal. Default is 0.2*std(signal).
Returns
----------
multiscale_entropy : float
The Multiscale Entropy as float value.
Example
----------
>>> import neurokit as nk
>>>
>>> signal = [5, 1, 7, 2, 5, 1, 7, 4, 6, 7, 5, 4, 1, 1, 4, 4]
>>> multiscale_entropy = nk.entropy_multiscale(signal)
Notes
----------
*Details*
- **multiscale entropy**: Entropy is a measure of unpredictability of the state, or equivalently, of its average information content. Multiscale entropy (MSE) analysis is a new method of measuring the complexity of finite length time series.
*Authors*
- tjugo (https://github.com/nikdon)
- Dominique Makowski (https://github.com/DominiqueMakowski)
*Dependencies*
- numpy
*See Also*
- pyEntropy package: https://github.com/nikdon/pyEntropy
References
-----------
- Richman, J. S., & Moorman, J. R. (2000). Physiological time-series analysis using approximate entropy and sample entropy. American Journal of Physiology-Heart and Circulatory Physiology, 278(6), H2039-H2049.
- Costa, M., Goldberger, A. L., & Peng, C. K. (2005). Multiscale entropy analysis of biological signals. Physical review E, 71(2), 021906.
"""
if tolerance == "default":
tolerance = 0.2 * np.std(signal)
n = len(signal)
mse = np.zeros((1, emb_dim))
for i in range(emb_dim):
b = int(np.fix(n / (i + 1)))
temp_ts = [0] * int(b)
for j in range(b):
num = sum(signal[j * (i + 1):(j + 1) * (i + 1)])
den = i + 1
temp_ts[j] = float(num) / float(den)
# Replaced the sample entropy computation with nolds' one...
# se = sample_entropy(temp_ts, 1, tolerance)
try:
se = nolds.sampen(temp_ts,
1,
tolerance,
dist="euclidean",
debug_plot=False,
plot_file=None)
except:
se = nolds.sampen(temp_ts,
1,
tolerance,
dist="euler",
debug_plot=False,
plot_file=None)
mse[0, i] = se
multiscale_entropy = mse[0][emb_dim - 1]
return (multiscale_entropy)
def processSingleFile(self, file):
self.logger.log(
"INFO",
"EXTRACTING FEATURE {} FROM FILE: {}".format(self.algorithm, file))
res = self.readFile(file)
if (self.algorithm == 'DfaMeanCorr'):
feature = np.zeros([378, 1])
else:
feature = np.zeros([26, 1])
if (res["error"]):
return (feature)
if (res["data"].shape[0] == 0):
return (feature)
if (res["data"].shape[1] < 10):
return (feature)
data = self.prepareMetrics(res["data"])
try:
if (self.algorithm == 'correlation'):
feature = self.correlation(data)
elif (self.algorithm == 'dfa'):
feature = np.zeros([26, 1])
for i in range(0, data.shape[1]):
feature[i] = nolds.dfa(data[:, i])
elif (self.algorithm == 'sampen'):
feature = np.zeros([26, 1])
for i in range(0, data.shape[1]):
feature[i] = nolds.sampen(data[:,i],emb_dim=2,\
tolerance=0.2*np.std(data[:,i]))
elif (self.algorithm == 'hurst'):
feature = np.zeros([26, 1])
for i in range(0, data.shape[1]):
feature[i] = nolds.hurst_rs(data[:, i])
elif (self.algorithm == 'DfaMeanCorr'):
cache_filename = file + ".pkl"
if (os.path.exists(cache_filename)):
self.logger.log("INFO", "CACHE FOUND, USING IT")
file = open(cache_filename, 'rb')
cache = pickle.load(file)
else:
cache = {}
if (not "corr" in cache):
featureCorr = self.correlation(data)
cache["corr"] = featureCorr
else:
featureCorr = cache["corr"]
if (not "cons" in cache):
featureConsump = self.consumption(res["data"])
cache["featureConsump"] = featureConsump
else:
featureConsump = cache["cons"]
if (not "dfa" in cache):
featureDfa = np.zeros([26, 1])
for i in range(0, int(data.shape[1])):
featureDfa[i] = nolds.dfa(data[:, i])
cache["dfa"] = featureDfa
else:
featureDfa = cache["dfa"]
if (not "entropy" in cache):
featureEntropy = np.zeros([26, 1])
for i in range(0, int(data.shape[1])):
featureEntropy[i] = nolds.sampen(data[:, i], 2)
cache["entropy"] = featureEntropy
with open(cache_filename, 'wb') as output:
pickle.dump(cache, output, pickle.HIGHEST_PROTOCOL)
feature = np.vstack(
[featureDfa, featureConsump, featureEntropy, featureCorr])
except Exception as e:
self.logger.log("ERROR","ERROR EXTRACTING FEATURE {} FROM FILE: {}, SKIPPING"\
.format(self.algorithm,file))
print(e)
traceback.print_exc()
for i in range(0, feature.shape[0]):
feature[i] = 0
return (feature)
def r_features(r_peaks):
# Sanity check after artifact removal
if len(r_peaks) < 5:
print(
"NeuroKit Warning: ecg_hrv(): Not enough normal R peaks to compute HRV :/"
)
r_peaks = [1000, 2000, 3000, 4000]
hrv_dict = dict()
RRis = np.diff(r_peaks)
RRis = RRis / 500
RRis = RRis.astype(float)
# Artifact detection - Statistical
rr1 = 0
rr2 = 0
rr3 = 0
rr4 = 0
median_rr = np.median(RRis)
for index, rr in enumerate(RRis):
# Remove RR intervals that differ more than 25% from the previous one
if rr < 0.6:
rr1 += 1
if rr > 1.3:
rr2 += 1
if rr < median_rr * 0.75:
rr3 += 1
if rr > median_rr * 1.25:
rr4 += 1
# Artifacts treatment
hrv_dict["n_Artifacts1"] = rr1 / len(RRis)
hrv_dict["n_Artifacts2"] = rr2 / len(RRis)
hrv_dict["n_Artifacts3"] = rr3 / len(RRis)
hrv_dict["n_Artifacts4"] = rr4 / len(RRis)
hrv_dict["RMSSD"] = np.sqrt(np.mean(np.diff(RRis)**2))
hrv_dict["meanNN"] = np.mean(RRis)
hrv_dict["sdNN"] = np.std(RRis, ddof=1) # make it calculate N-1
hrv_dict["cvNN"] = hrv_dict["sdNN"] / hrv_dict["meanNN"]
hrv_dict["CVSD"] = hrv_dict["RMSSD"] / hrv_dict["meanNN"]
hrv_dict["medianNN"] = np.median(abs(RRis))
hrv_dict["madNN"] = mad(RRis, constant=1)
hrv_dict["mcvNN"] = hrv_dict["madNN"] / hrv_dict["medianNN"]
nn50 = sum(abs(np.diff(RRis)) > 50)
nn20 = sum(abs(np.diff(RRis)) > 20)
hrv_dict["pNN50"] = nn50 / len(RRis) * 100
hrv_dict["pNN20"] = nn20 / len(RRis) * 100
hrv_dict["Shannon"] = complexity_entropy_shannon(RRis)
hrv_dict["Sample_Entropy"] = nolds.sampen(RRis, emb_dim=2)
#mse = complexity_entropy_multiscale(RRis, max_scale_factor=20, m=2)
#hrv_dict["Entropy_Multiscale_AUC"] = mse["MSE_AUC"]
hrv_dict["Entropy_SVD"] = complexity_entropy_svd(RRis, emb_dim=2)
hrv_dict["Entropy_Spectral_VLF"] = complexity_entropy_spectral(
RRis, 500, bands=np.arange(0.0033, 0.04, 0.001))
hrv_dict["Entropy_Spectral_LF"] = complexity_entropy_spectral(
RRis, 500, bands=np.arange(0.04, 0.15, 0.001))
hrv_dict["Entropy_Spectral_HF"] = complexity_entropy_spectral(
RRis, 500, bands=np.arange(0.15, 0.40, 0.001))
hrv_dict["Fisher_Info"] = complexity_fisher_info(RRis, tau=1, emb_dim=2)
#hrv_dict["FD_Petrosian"] = complexity_fd_petrosian(RRis)
#hrv_dict["FD_Higushi"] = complexity_fd_higushi(RRis, k_max=16)
hrv_dict.update(hrv.time_domain(RRis))
hrv_dict.update(hrv.frequency_domain(RRis))
# RRI Velocity
diff_rri = np.diff(RRis)
hrv_dict.update(add_suffix(hrv.time_domain(diff_rri), "fil1"))
hrv_dict.update(add_suffix(hrv.frequency_domain(diff_rri), "fil1"))
# RRI Acceleration
diff2_rri = np.diff(diff_rri)
hrv_dict.update(add_suffix(hrv.time_domain(diff2_rri), "fil2"))
hrv_dict.update(add_suffix(hrv.frequency_domain(diff2_rri), "fil2"))
return hrv_dict
def sample_entropy(y):
# Sample Entropy
return nolds.sampen(y)
# 100 dp sliding windows with 10 step jump between each window to save space
window_size = 100
window_size = 2000
emb_dim = 4
rolling = rolling_window(df.logR_ask, window_size, 10)
rolling = rolling_window(df_std.logR_ask, window_size, window_size)
rolling = rolling_window(df_QN_laplace_std.values.transpose()[0], window_size, window_size)
rolling_ns = rolling_window(df.ask, window_size, 10)
rolling_ts = rolling_window(df.index, window_size, 10)
df_ = pd.DataFrame(rolling)
sw_1 = rolling[1]
sw_1_ns = rolling[1]
nolds.lyap_r(sw_1, emb_dim = emb_dim)
nolds.lyap_e(sw_1, emb_dim = emb_dim)
nolds.sampen(sw_1, emb_dim= emb_dim)
nolds.hurst_rs(sw_1)
nolds.corr_dim(sw_1, emb_dim=emb_dim)
nolds.dfa(sw_1)
ent.shannon_entropy(sw_1) # is this even valid? we do not have any p_i states i ALSO IGNORES TEMPORAL ORDER - Practical consideration of permutation entropy
ent.sample_entropy(sw_1, sample_length = 10) #what is sample length?
#ent.multiscale_entropy(sw_1, sample_length = 10, tolerance = 0.1*np.std(sw_1)) # what is tolerance?
"Practical considerations of permutation entropy: A Tutorial review - how to choose parameters in permutation entropy"
ent.permutation_entropy(sw_1, m=8, delay = emd_dim ) #Reference paper above
#ent.composite_multiscale_entropy()
lempel_ziv_complexity(sw_1)
gzip_compress_ratio(sw_1_ns, 9)
#https://www.researchgate.net/post/How_can_we_find_out_which_value_of_embedding_dimensions_is_more_accurate
for sheet in worksheets:
# Activate worksheet to write dataframe
active = workbook[sheet]
# load dataset
series = read_csv('../data/datasets/' + sheet + '_final_week.csv',
header=0, index_col=0, parse_dates=True, squeeze=True)
x = series.values
x = x.astype('float32')
# x = np.fromiter(series.values, dtype="float32")
columns = list(range(2, 5))
emb_dim = -1
for column in columns:
if column == 2:
emb_dim = 3
elif column == 3:
emb_dim = 5
elif column == 4:
emb_dim = 4
# Do the calculation and put it on a specific cell
sample_entropy = nolds.sampen(x, emb_dim=emb_dim, tolerance=None)
print("Sample entropy: " + str(sample_entropy))
active.cell(row=27, column=column).value = sample_entropy
# Save workbook to write
workbook.save("../data/chaos_data/results_presentation.xlsx")
workbook.close()
def calculate_approximate_entropy(traffic):
return nolds.sampen(traffic)