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 dfa(nni=None,
short=(4, 16),
long=(17, 64),
show=False,
figsize=None,
legend=True):
"""Conducts Detrended Fluctuation Analysis for short and long-term fluctuation of an NNI series.
References: [Joshua2008][Kuusela2014][Fred2017]
Docs: https://pyhrv.readthedocs.io/en/latest/_pages/api/nonlinear.html#sample-entropy-sample-entropy
Parameters
----------
nn : array
NN intervals in [ms] or [s].
rpeaks : array
R-peak times in [ms] or [s].
short : array, 2 elements
Interval limits of the short term fluctuations (default: None: [4, 16]).
long : array, 2 elements
Interval limits of the long term fluctuations (default: None: [17, 64]).
show : bool
If True, shows DFA plot (default: True)
legend : bool
If True, adds legend with alpha1 and alpha2 values to the DFA plot (default: True)
Returns (biosppy.utils.ReturnTuple Object)
------------------------------------------
[key : format]
Description.
dfa_short : float
Alpha value of the short term fluctuations
dfa_long : float
Alpha value of the long term fluctuations
dfa_plot : matplotlib plot figure
Matplotlib plot figure of the DFA
"""
# Create arrays
short = range(short[0], short[1] + 1)
long = range(long[0], long[1] + 1)
alpha1, dfa_short = nolds.dfa(nni, short, debug_data=True, overlap=False)
alpha2, dfa_long = nolds.dfa(nni, long, debug_data=True, overlap=False)
# Output
args = (alpha1, alpha2, short, long)
return biosppy.utils.ReturnTuple(
args,
('dfa_alpha1', 'dfa_alpha2', 'dfa_alpha1_beats', 'dfa_alpha2_beats'))
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_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 newHurst(ts):
# Create the range of lag values
window_len = 70
hurst_ts = np.zeros(window_len, dtype=np.int)
for tail in range(window_len, len(ts)):
cur_ts = ts[max(1, tail - window_len):tail]
hurst_ts = np.append(hurst_ts, nolds.dfa(cur_ts))
return hurst_ts
def DFA(self):
'''
Returns the H exponent from detrended fluctuation analysis
Seems like the number of points needs to be over 70 or so for good results
'''
if not self.cleaned:
self.removeNoise()
return dfa(self.points)
def feature_extraction(data):
"""
Input:
- data: 4 * 15360
Output:
- feature array: 18*1
"""
fq1, pxx1 = psd(data[0,:], fs, seglength)
fq2, pxx2 = psd(data[1,:], fs, seglength)
fq3, pxx3 = psd(data[2,:], fs, seglength)
fq4, pxx4 = psd(data[3,:], fs, seglength)
f1 = rela_alpha(fq2, pxx1) # feature 1: relative alpha power of channel 1
f2 = rela_delta(fq1, pxx1) # feature 2: relative delta power of channel 1
f3 = rela_theta(fq1, pxx1) # feature 3: relative theta power of channel 1
f4 = rela_alpha(fq2, pxx2) # feature 4: relative alpha power of channel 2
f5 = rela_delta(fq2, pxx2) # feature 5: relative delta power of channel 2
f6 = rela_theta(fq2, pxx2) # feature 6: relative theta power of channel 2
f7 = rela_alpha(fq3, pxx3) # feature 7: relative alpha power of channel 3
f8 = rela_delta(fq3, pxx3) # feature 8: relative delta power of channel 3
f9 = rela_theta(fq3, pxx3) # feature 9: relative theta power of channel 3
f10 = rela_alpha(fq4, pxx4) # feature 10: relative alpha power of channel 4
f11 = rela_delta(fq4, pxx4) # feature 11: relative delta power of channel 4
f12 = rela_theta(fq4, pxx4) # feature 12: relative theta power of channel 4
f13 = hemi_ratio(f1, f4) # feature 13: hemi-ratio of alpha band between front channels (C1, C2)
f14 = hemi_ratio(f2, f5)
f15 = hemi_ratio(f3, f6)
f16 = hemi_ratio(f7, f10)
f17 = hemi_ratio(f8, f11)
f18 = hemi_ratio(f9, f12)
"""
multi-domain
"""
f19 = nolds.dfa(data[0,:])
f20 = nolds.dfa(data[1,:])
f21 = nolds.dfa(data[2,:])
f22 = nolds.dfa(data[3,:])
#f = np.array([f1,f2,f3,f4,f5,f6,f7,f8,f9,f10,f11,f12,f13,f14,f15,f16,f17,f18])
f = np.array([f1, f2, f3, f4, f5, f6, f7, f8, f9, f10, f11, f12, f13, f14, f15, f16, f17, f18, f19, f20, f21, f22])
return f
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 feature_extract(ep):
feature_mtrx = []
scale = 6
up_to = 3
for i in range(np.shape(ep)[1]):
##DWT
coeff = wavedec(ep[:,i],'db4',level = scale)
#Select decomposition bands up to scale #
##Features on each scale
E = []
FI = []
AE = []
CoV = []
#LE = [] #Lyapunov Exponent
CD = []
DFA = []
for j in range(up_to+1):
length = len(coeff[j])
#Relative Energy
if j == 0:
tau = (2 ** (scale - 1)) / freq
else:
tau = j * (2**(scale-1)) / freq
E.append(sum([x**2 for x in coeff[j]]) * tau / length)
#Fluctuation Index
FI.append( sum( np.abs(coeff[j][1:] - coeff[j][0:len(coeff[j])-1]) ) / length )
#Detrended Fluctuation Analysis
DFA.append(nolds.dfa(coeff[j]))
#Approximate Entropy
#AE.append(shannon_entropy(coeff[j]))
AE.append(ApEn(coeff[j],2,3))
#Coefficient of Variation
u = np.mean(coeff[j])
v = np.std(coeff[j])
CoV.append(v**2/u**2)
#Lyapunov Exponent
#LE.append(nolds.lyap_r(coeff[j],emb_dim=5))
#Correlation Dimension
#CD.append(nolds.corr_dim(coeff[j],2))
feature_mtrx.append([E,FI,AE,CoV,DFA])
#Normalization?
##Output
return(feature_mtrx)
def test_hurst(self):
st = datetime.datetime(2018, 5, 17, 1, 0, 0)
et = datetime.datetime(2018, 5, 17, 2, 0, 0)
_, trades, _ = DataLoader.load_split_data("/Users/jamesprince/project-data/data/consolidated-feed/LTC-USD/", st,
et, "LTC-USD")
prices = np.asarray(trades['price'].dropna(), dtype=np.float32)
print(prices)
# print(len(prices))
# res = nolds.hurst_rs(prices)
res = nolds.dfa(prices)
print(res)
def ft_dfa(cls,
ts: np.ndarray,
pol_order: int = 1,
overlap_windows: bool = True) -> float:
"""Calculate the Hurst parameter from Detrended fluctuation analysis.
Note that the ``Hurst parameter`` is not the same quantity as the
``Hurst exponent``. The Hurst parameter `H` is defined as the quantity
such that the following holds: std(ts, l * n) = l ** H * std(ts, n),
where `ts` is the time-series, `l` is a constant factor, `n` is some
window length of `ts`, and std(ts, k) is the standard deviation of
`ts` within a window of size `k`.
Check `nolds.dfa` documentation for a clear explanation about the
underlying function.
Parameters
----------
ts : :obj:`np.ndarray`
One-dimensional time-series values.
pol_order : int, optional (default=1)
Order of the detrending polynomial within each window of the
analysis.
overlap_windows : bool, optional (default=True)
If True, overlap the windows used while performing the analysis.
Returns
-------
float
Hurst parameter.
References
----------
.. [1] C.-K. Peng, S. V. Buldyrev, S. Havlin, M. Simons,
H. E. Stanley, and A. L. Goldberger, Mosaic organization of
DNA nucleotides, Physical Review E, vol. 49, no. 2, 1994.
.. [2] R. Hardstone, S.-S. Poil, G. Schiavone, R. Jansen,
V. V. Nikulin, H. D. Mansvelder, and K. Linkenkaer-Hansen,
Detrended fluctuation analysis: A scale-free view on neuronal
oscillations, Frontiers in Physiology, vol. 30, 2012.
.. [3] "nolds" Python package: https://pypi.org/project/nolds/
"""
hurst_coeff = nolds.dfa(ts, order=pol_order, overlap=overlap_windows)
return hurst_coeff
def dfa_fd(timeseries):
"""Detrended Fluctuation Analysis (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 time series\
(whose mean and/or variance change over time).
:param timeseries: Your time series.
:type timeseries: numpy.ndarray
:return dfa: Detrended Fluctuation Analysis.
.. Note::
This functions uses the dfa implementation from the Nolds package.
"""
ts = utils.fixseries(timeseries)
return utils.truncate(nolds.dfa(ts))
def dfa_fd(series):
"""Detrended Fluctuation Analysis (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).
Keyword arguments:
series : numpy.array
One dimensional time series.
Returns
-------
dfa : float
Detrended Fluctuation Analysis.
Notes:
------
This functions uses the dfa implementation from the Nolds package.
"""
dfa = nolds.dfa(series)
return dfa
def dfa_fd(timeseries, nvals=None, overlap=True, order=1, nodata=-9999):
"""Detrended Fluctuation Analysis (DFA) measures the Hurst \
parameter H, which is very similar to the Hurst Exponent (HE).
The main difference is that DFA can be used for non-stationary \
time series.
:param timeseries: Time series.
:type timeseries: numpy.ndarray
:param nvals: Sizes of subseries to use.
:type nvals: int
:param overlap: if True, there will be a 50% overlap on windows \
otherwise non-overlapping windows will be used.
:type overlap: Boolean
:param order: Polynomial order of trend to remove.
:type order: Boolean
:param nodata: nodata of the time series. Default is -9999.
:type nodata: int
:return dfa: Detrended Fluctuation Analysis.
.. Note::
This function uses the Detrended Fluctuation Analysis (DFA) \
implementation from the Nolds package. Due to time series \
characteristcs we use by default the 'RANSAC' \
fitting method as it is more robust to outliers.
For more details regarding the hurst implementation, check Nolds \
documentation page.
"""
import nolds
ts = fixseries(timeseries, nodata)
return truncate(nolds.dfa(ts, nvals, overlap, order))
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 sig_dfa(sig):
return nolds.dfa(sig)
def prepareLRMData(data):
dg = pd.DataFrame(columns=[
'uhid', 'dischargestatus', 'ecg_resprate_SE', 'ecg_resprate_DFA',
'ecg_resprate_ADF', 'ecg_resprate_Mean', 'ecg_resprate_Var', 'spo2_SE',
'spo2_DFA', 'spo2_ADF', 'spo2_Mean', 'spo2_Var', 'heartrate_SE',
'heartrate_DFA', 'heartrate_ADF', 'heartrate_Mean', 'heartrate_Var',
'peep_SE', 'peep_DFA', 'peep_ADF', 'peep_Mean', 'peep_Var', 'pip_SE',
'pip_DFA', 'pip_ADF', 'pip_Mean', 'pip_Var', 'map_SE', 'map_DFA',
'map_ADF', 'map_Mean', 'map_Var', 'tidalvol_SE', 'tidalvol_DFA',
'tidalvol_ADF', 'tidalvol_Mean', 'tidalvol_Var', 'minvol_SE',
'minvol_DFA', 'minvol_ADF', 'minvol_Mean', 'minvol_Var', 'ti_SE',
'ti_DFA', 'ti_ADF', 'ti_Mean', 'ti_Var', 'fio2_SE', 'fio2_DFA',
'fio2_ADF', 'fio2_Mean', 'fio2_Var', 'abdomen_girth', 'urine',
'totalparenteralvolume', 'new_ph', 'gender', 'birthweight',
'birthlength', 'birthheadcircumference', 'inout_patient_status',
'gestation', 'baby_type', 'central_temp', 'apgar_onemin',
'apgar_fivemin', 'apgar_tenmin', 'motherage', 'conception_type',
'mode_of_delivery', 'steroidname', 'numberofdose', 'rbs', 'temp',
'currentdateweight', 'currentdateheight', 'tpn-tfl', 'mean_bp',
'sys_bp', 'dia_bp', 'abd_difference', 'stool_day_total',
'total_intake', 'typevalue_Antibiotics', 'typevalue_Inotropes'
])
for i in data.uhid.unique():
try:
print(i)
t = data[data['uhid'] == i]
t.fillna(t.mean(), inplace=True)
t.fillna(0, inplace=True)
#t = t.apply(pd.to_numeric, errors='coerce')
dg = dg.append(
{
'uhid':
i,
'dischargestatus':
t['dischargestatus'].iloc[0],
'ecg_resprate_SE':
sample_entropy(t.ecg_resprate, order=2,
metric='chebyshev'),
'ecg_resprate_DFA':
nolds.dfa(t.ecg_resprate),
'ecg_resprate_ADF':
adfuller(t.ecg_resprate)[0],
'ecg_resprate_Mean':
np.mean(t.ecg_resprate),
'ecg_resprate_Var':
np.var(t.ecg_resprate),
'spo2_SE':
sample_entropy(t.spo2, order=2, metric='chebyshev'),
'spo2_DFA':
nolds.dfa(t.spo2),
'spo2_ADF':
adfuller(t.spo2)[0],
'spo2_Mean':
np.mean(t.spo2),
'spo2_Var':
np.var(t.spo2),
'heartrate_SE':
sample_entropy(t.heartrate, order=2, metric='chebyshev'),
'heartrate_DFA':
nolds.dfa(t.heartrate),
'heartrate_ADF':
adfuller(t.heartrate)[0],
'heartrate_Mean':
np.mean(t.heartrate),
'heartrate_Var':
np.var(t.heartrate),
'peep_SE':
sample_entropy(t.peep, order=2, metric='chebyshev'),
'peep_DFA':
nolds.dfa(t.peep),
'peep_ADF':
adfuller(t.peep)[0],
'peep_Mean':
np.mean(t.peep),
'peep_Var':
np.var(t.peep),
'pip_SE':
sample_entropy(t.pip, order=2, metric='chebyshev'),
'pip_DFA':
nolds.dfa(t.pip),
'pip_ADF':
adfuller(t.pip)[0],
'pip_Mean':
np.mean(t.pip),
'pip_Var':
np.var(t.pip),
'map_SE':
sample_entropy(t.map, order=2, metric='chebyshev'),
'map_DFA':
nolds.dfa(t.map),
'map_ADF':
adfuller(t.map)[0],
'map_Mean':
np.mean(t.map),
'map_Var':
np.var(t.map),
'tidalvol_SE':
sample_entropy(t.tidalvol, order=2, metric='chebyshev'),
'tidalvol_DFA':
nolds.dfa(t.tidalvol),
'tidalvol_ADF':
adfuller(t.tidalvol)[0],
'tidalvol_Mean':
np.mean(t.tidalvol),
'tidalvol_Var':
np.var(t.tidalvol),
'minvol_SE':
sample_entropy(t.minvol, order=2, metric='chebyshev'),
'minvol_DFA':
nolds.dfa(t.minvol),
'minvol_ADF':
adfuller(t.minvol)[0],
'minvol_Mean':
np.mean(t.minvol),
'minvol_Var':
np.var(t.minvol),
'ti_SE':
sample_entropy(t.ti, order=2, metric='chebyshev'),
'ti_DFA':
nolds.dfa(t.ti),
'ti_ADF':
adfuller(t.ti)[0],
'ti_Mean':
np.mean(t.ti),
'ti_Var':
np.var(t.ti),
'fio2_SE':
sample_entropy(t.fio2, order=2, metric='chebyshev'),
'fio2_DFA':
nolds.dfa(t.fio2),
'fio2_ADF':
adfuller(t.fio2)[0],
'fio2_Mean':
np.mean(t.fio2),
'fio2_Var':
np.var(t.fio2),
'abdomen_girth':
np.mean(t.abdomen_girth),
'urine':
np.nansum(t.urine),
'totalparenteralvolume':
np.nansum(t.totalparenteralvolume),
'total_intake':
np.nansum(t.total_intake),
'new_ph':
np.mean(t.new_ph),
'gender':
t['gender'].iloc[0],
'birthweight':
t['birthweight'].iloc[0],
'birthlength':
t['birthlength'].iloc[0],
'birthheadcircumference':
t['birthheadcircumference'].iloc[0],
'inout_patient_status':
t['inout_patient_status'].iloc[0],
'gestation':
t['gestation'].iloc[0],
'baby_type':
t['baby_type'].iloc[0],
'central_temp':
np.nanmean(t.central_temp),
'apgar_onemin':
t['apgar_onemin'].iloc[0],
'apgar_fivemin':
t['apgar_fivemin'].iloc[0],
'apgar_tenmin':
t['apgar_tenmin'].iloc[0],
'motherage':
t['motherage'].iloc[0],
'conception_type':
t['conception_type'].iloc[0],
'mode_of_delivery':
t['mode_of_delivery'].iloc[0],
'numberofdose':
np.nansum(t.numberofdose),
'rbs':
np.nanmean(t.rbs),
'temp':
np.nanmean(t.temp),
'currentdateweight':
np.nanmean(t.currentdateweight),
'currentdateheight':
np.nanmean(t.currentdateheight),
'mean_bp':
np.nanmean(t.mean_bp),
'dia_bp':
np.nanmean(t.dia_bp),
'sys_bp':
np.nanmean(t.sys_bp),
'stool_day_total':
np.nanmean(t.stool_day_total),
'tpn-tfl':
np.nansum(t['tpn-tfl']),
'typevalue_Inotropes':
np.nansum(t.typevalue_Inotropes),
'typevalue_Antibiotics':
np.nansum(t.typevalue_Antibiotics),
'steroidname':
np.nansum(t.steroidname),
},
ignore_index=True)
except Exception as e:
print(e, "error")
dg.to_csv('LRM_all_data.csv')
return dg
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
#when choosing emb_dim for Takens, each dimension should have at least 10 dp ==> 10^1 == 1D, 10^2 == 2D, ..., 10^6 == 6D
#FALSE NEAREST NEIGHBOR FOR DETERMINING MINIMAL EMBEDDING DIMENSION
def compute_params(df, number_of_epochs, structure):
total_len = int(number_of_epochs * 20) #in sec
if structure == 'spindle':
profile_type = 'energy'
bin_width = 20
elif structure == 'SWA':
profile_type = 'energy'
bin_width = 20
df_hist = _get_histogram_values_in_sec(df,
total_len,
bin_width,
profile_type=profile_type) #in sec
occ = df_hist.occurences
time = df_hist.time
dt = time[1] - time[0]
if (structure == 'SWA') and (profile_type == 'percent'):
occ[occ < 20.] = 0
#power = np.sum(df['amplitude']**2) / total_len
power = np.sum(df['modulus']) / total_len
profile_dfa = nolds.dfa(occ)
if len(df) > 2:
if structure == 'spindle':
frequency_mse = np.sum(
(df['frequency'] - 13)**2) / (len(df['frequency']) - 1)
frequency_var = np.var(df['frequency'], ddof=1)
df_params = pd.DataFrame([[power, frequency_mse, frequency_var, \
profile_dfa]],
columns=['power_spindle', 'frequency_mse_spindle', 'frequency_var', \
'profile_dfa_spindle'])
elif structure == 'SWA':
df_hist_deep = _get_histogram_values_in_sec(df,
total_len,
20,
profile_type='percent')
occ_deep_sleep = df_hist_deep.occurences
min_deep_sleep = len(
occ_deep_sleep[occ_deep_sleep >= 20.]) * 20. / 60. #in min
min_deep_sleep_50 = len(
occ_deep_sleep[occ_deep_sleep >= 50.]) * 20. / 60. #in min
occ_deep_sleep[occ_deep_sleep < 20.] = 0.
dfa_deep_sleep = nolds.dfa(occ_deep_sleep)
deep_sleep_ratio = min_deep_sleep**dfa_deep_sleep
occ_deep_sleep[occ_deep_sleep < 50.] = 0.
dfa_deep_sleep_50 = nolds.dfa(occ_deep_sleep)
deep_sleep_ratio_50 = min_deep_sleep_50**dfa_deep_sleep_50
df_params = pd.DataFrame([[power, profile_dfa, min_deep_sleep, \
dfa_deep_sleep, deep_sleep_ratio, min_deep_sleep_50, \
dfa_deep_sleep_50, deep_sleep_ratio_50]],
columns=['power_SWA', 'profile_dfa_SWA', 'min_deep_sleep', \
'dfa_deep_sleep', 'deep_sleep_ratio', 'min_deep_sleep_50', \
'dfa_deep_sleep_50', 'deep_sleep_ratio_50'])
else:
if structure == 'spindle':
df_params = pd.DataFrame([[0, np.inf, np.inf, \
0.5]],
columns=['power_spindle', 'frequency_mse_spindle', 'frequency_var', \
'profile_dfa_spindle'])
elif structure == 'SWA':
df_params = pd.DataFrame([[0, 0.5, 0, \
0.5, 0, 0, \
0.5, 0]],
columns=['power_SWA', 'profile_dfa_SWA', 'min_deep_sleep', \
'dfa_deep_sleep', 'deep_sleep_ratio', 'min_deep_sleep_50', \
'dfa_deep_sleep_50', 'deep_sleep_ratio_50'])
return df_params
import pyflux as pf
from datetime import datetime
import matplotlib.pyplot as plt
%matplotlib inline
from sklearn.metrics import mean_absolute_error, mean_squared_error, r2_score
data = pd.read_csv('dataset-2007.csv', usecols=['wind direction at 100m (deg)', 'wind speed at 100m (m/s)', 'air temperature at 2m (K)', 'surface air pressure (Pa)', 'density at hub height (kg/m^3)'], skiprows=3)
data.columns = ['direction', 'speed', 'temp', 'pressure', 'density']
data.head(3)
D=data['speed'].values
T=D[0:105120:12]
F=T[0:2000]
h = nolds.dfa(F)
h
RS=nolds.hurst_rs(F)
RS
# calculate standard deviation of differenced series using various lags
lags = range(2, 20)
tau = [sqrt(std(subtract(F[lag:], F[:-lag]))) for lag in lags]
# plot on log-log scale
plot(log(lags), log(tau)); show()
# calculate Hurst as slope of log-log plot
m = polyfit(log(lags), log(tau), 1)
hurst = m[0]*2.0
#else:
# return_exmo = None
# return_exmos.append(return_exmo)
if(row[6] != ''):
return_binance = np.float(row[6])
return_binances.append(return_binance)
#else:
# return_binance = None
# return_binances.append(return_binance)
#calculating the bds test for coinbase exchange
i = 0
while((i + size) < len(return_coinbases)):
temp1 = return_coinbases[i:i + size]
date1 = dates[i:i+size]
dfa_coinbase = nolds.dfa(temp1)
H_coinbases.append(dfa_coinbase)
temp_coinbase_date = dates[i]
Hdate_coinbases.append(temp_coinbase_date)
Ljung(temp1,date1)
flag_coinbase = flag_coinbase + 1
i = i + step
#calculating the bds test for exmo exchange
j = 0
while((j + size) < len(return_exmos)):
temp2 = return_exmos[j:j + size]
date2=dates[j:j+size]
dfa_exmo = nolds.dfa(temp2)
Ljung(temp2,date2)
H_exmos.append(dfa_exmo)
def eeg_fractal_dim(epochs, entropy=True, hurst=True, dfa=False, lyap_r=False, lyap_e=False):
"""
"""
clock = Time()
df = epochs.to_data_frame(index=["epoch", "time", "condition"])
# Separate indexes
index = df.index.tolist()
epochs = []
times = []
events = []
for i in index:
epochs.append(i[0])
times.append(i[1])
events.append(i[2])
data = {}
if entropy == True:
data["Entropy"] = {}
if hurst == True:
data["Hurst"] = {}
if dfa == True:
data["DFA"] = {}
if lyap_r == True:
data["Lyapunov_R"] = {}
if lyap_e == True:
data["Lyapunov_E"] = {}
clock.reset()
for epoch in set(epochs):
subset = df.loc[epoch]
if entropy == True:
data["Entropy"][epoch] = []
if hurst == True:
data["Hurst"][epoch] = []
if dfa == True:
data["DFA"][epoch] = []
if lyap_r == True:
data["Lyapunov_R"][epoch] = []
if lyap_e == True:
data["Lyapunov_E"][epoch] = []
for channel in subset:
if entropy == True:
data["Entropy"][epoch].append(nolds.sampen(subset[channel]))
if hurst == True:
data["Hurst"][epoch].append(nolds.hurst_rs(subset[channel]))
if dfa == True:
data["DFA"][epoch].append(nolds.dfa(subset[channel]))
if lyap_r == True:
data["Lyapunov_R"][epoch].append(nolds.lyap_r(subset[channel]))
if lyap_e == True:
data["Lyapunov_E"][epoch].append(nolds.lyap_e(subset[channel]))
if entropy == True:
data["Entropy"][epoch] = np.mean(data["Entropy"][epoch])
if hurst == True:
data["Hurst"][epoch] = np.mean(data["Hurst"][epoch])
if dfa == True:
data["DFA"][epoch] = np.mean(data["DFA"][epoch])
if lyap_r == True:
data["Lyapunov_R"][epoch] = np.mean(data["Lyapunov_R"][epoch])
if lyap_e == True:
data["Lyapunov_E"][epoch] = np.mean(data["Lyapunov_E"][epoch])
time = clock.get(reset=False)/1000
time = time/(epoch+1)
time = (time * (len(set(epochs))-epoch))/60
print(str(round((epoch+1)/len(set(epochs))*100,2)) + "% complete, remaining time: " + str(round(time, 2)) + 'min')
df = pd.DataFrame.from_dict(data)
list_events = []
for i in range(len(events)):
list_events.append(events[i] + "_" + str(epochs[i]))
list_events = list_events[np.where(find_following_duplicates(list_events))]
list_events = [re.sub('_\d+', '', i) for i in list_events]
df["Epoch"] = list_events
return(df)
def dfa(nn=None,
rpeaks=None,
short=None,
long=None,
show=True,
figsize=None,
legend=True):
"""Conducts Detrended Fluctuation Analysis for short and long-term fluctuation of an NNI series.
References: [Joshua2008][Kuusela2014][Fred2017]
Docs: https://pyhrv.readthedocs.io/en/latest/_pages/api/nonlinear.html#sample-entropy-sample-entropy
Parameters
----------
nn : array
NN intervals in [ms] or [s].
rpeaks : array
R-peak times in [ms] or [s].
short : array, 2 elements
Interval limits of the short term fluctuations (default: None: [4, 16]).
long : array, 2 elements
Interval limits of the long term fluctuations (default: None: [17, 64]).
show : bool
If True, shows DFA plot (default: True)
legend : bool
If True, adds legend with alpha1 and alpha2 values to the DFA plot (default: True)
Returns (biosppy.utils.ReturnTuple Object)
------------------------------------------
[key : format]
Description.
dfa_short : float
Alpha value of the short term fluctuations
dfa_long : float
Alpha value of the long term fluctuations
dfa_plot : matplotlib plot figure
Matplotlib plot figure of the DFA
"""
# Check input values
nn = pu.check_input(nn, rpeaks)
# Check intervals
short = pu.check_interval(short, default=(4, 16))
long = pu.check_interval(long, default=(17, 64))
# Create arrays
short = range(short[0], short[1] + 1)
long = range(long[0], long[1] + 1)
# Prepare plot
if figsize is None:
figsize = (6, 6)
fig = plt.figure(figsize=figsize)
ax = fig.add_subplot(111)
ax.set_title('Detrended Fluctuation Analysis (DFA)')
ax.set_xlabel('log n [beats]')
ax.set_ylabel('log F(n)')
# try:
# Compute alpha values
try:
alpha1, dfa_short = nolds.dfa(nn,
short,
debug_data=True,
overlap=False)
alpha2, dfa_long = nolds.dfa(nn, long, debug_data=True, overlap=False)
except ValueError:
# If DFA could not be conducted due to insufficient number of NNIs, return an empty graph and 'nan' for alpha1/2
warnings.warn(
"Not enough NNI samples for Detrended Fluctuations Analysis.")
ax.axis([0, 1, 0, 1])
ax.text(0.5,
0.5,
'[Insufficient number of NNI samples for DFA]',
horizontalalignment='center',
verticalalignment='center')
alpha1, alpha2 = 'nan', 'nan'
else:
# Plot DFA results if number of NNI were sufficent to conduct DFA
# Plot short term DFA
vals, flucts, poly = dfa_short[0], dfa_short[1], np.polyval(
dfa_short[2], dfa_short[0])
label = r'$ \alpha_{1}: %0.2f$' % alpha1
ax.plot(vals, flucts, 'bo', markersize=1)
ax.plot(vals, poly, 'b', label=label, alpha=0.7)
# Plot long term DFA
vals, flucts, poly = dfa_long[0], dfa_long[1], np.polyval(
dfa_long[2], dfa_long[0])
label = r'$ \alpha_{2}: %0.2f$' % alpha2
ax.plot(vals, flucts, 'go', markersize=1)
ax.plot(vals, poly, 'g', label=label, alpha=0.7)
# Add legend
if legend:
ax.legend()
ax.grid()
# Plot axis
if show:
plt.show()
# Output
args = (fig, alpha1, alpha2, short, long)
return biosppy.utils.ReturnTuple(args,
('dfa_plot', 'dfa_alpha1', 'dfa_alpha2',
'dfa_alpha1_beats', 'dfa_alpha2_beats'))
def pdfret(x, xm, t, sl, z, beta, q):
val2 = np.float(1 / nolds.dfa(k1.Close))
global lim
return -(1 / z) * (t**val2) * (1 + beta * (q - 1) *
((x - xm) * (t**val2))**2)**(-1 / (q - 1))
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)
def scaledpdfret(x, t, xm, sl, z, beta, q):
global k1
val1 = 1 / (nolds.dfa(k1.Close))
return -(1 / z) * (1 + beta * (q - 1) * (x / (t**val1) - xm /
(t**val1))**2)**(-1 / (q - 1))
def dfa(y):
# Detrended fluctuation analysis
return nolds.dfa(y)
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)
0.0001, 0.02, 1.3, 1.6)
apq11Shimmer = call([sound, pointProcess], "Get shimmer (apq11)", 0, 0,
0.0001, 0.02, 1.3, 1.6)
ddaShimmer = call([sound, pointProcess], "Get shimmer (dda)", 0, 0, 0.0001,
0.02, 1.3, 1.6)
voice_report = call([sound, pitch, pointProcess], "Voice report", 0.0, 0.0,
f0min, f0max, 1.3, 1.6, 0.03, 0.45)
return meanF0, stdevF0, localJitter, localabsoluteJitter, rapJitter, ppq5Jitter, ddpJitter, localShimmer, localdbShimmer, apq3Shimmer, aqpq5Shimmer, apq11Shimmer, ddaShimmer, voice_report
AudioFile_path = sys.argv[1]
sample_rate, samples = wavfile.read(AudioFile_path)
frequencies, times, spectogram = signal.spectrogram(samples, sample_rate)
sound = parselmouth.Sound(AudioFile_path)
DFA = nolds.dfa(times)
PPE = entropy.shannon_entropy(times)
(meanF0, stdevF0, localJitter, localabsoluteJitter, rapJitter, ppq5Jitter,
ddpJitter, localShimmer, localdbShimmer, apq3Shimmer, aqpq5Shimmer,
apq11Shimmer, ddaShimmer,
voice_report) = measurePitch(sound, 75, 500, "Hertz")
voice_report = voice_report.strip()
hnr = voice_report[984:989]
nhr = voice_report[941:953]
# from sklearn.preprocessing import MinMaxScaler
# sc = MinMaxScaler()
# DFA = sc.fit_transform(DFA)
# PPE = sc.fit_transform(PPE)
import nolds
import numpy as np
rwalk = np.cumsum(np.random.random(1000))
print("fractal {}".format(nolds.dfa(rwalk)))
print("Lup {}".format(nolds.lyap_e(rwalk)))
print("Lup {}".format(nolds.lyap_r(rwalk)))
print("Hurst {}".format(nolds.hurst_rs(rwalk)))
