neurokit/bio/bio_eda.py
# -*- coding: utf-8 -*-
from __future__ import division
import pandas as pd
import numpy as np
import biosppy
import cvxopt as cv
import cvxopt.solvers
from ..statistics import z_score
from ..statistics import find_closest_in_list
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def eda_process(eda, sampling_rate=1000, alpha=8e-4, gamma=1e-2, filter_type = "butter", scr_method="makowski", scr_treshold=0.1):
"""
Automated processing of EDA signal using convex optimization (CVXEDA; Greco et al., 2015).
Parameters
----------
eda : list or array
EDA signal array.
sampling_rate : int
Sampling rate (samples/second).
alpha : float
cvxEDA penalization for the sparse SMNA driver.
gamma : float
cvxEDA penalization for the tonic spline coefficients.
filter_type : str or None
Can be Butterworth filter ("butter"), Finite Impulse Response filter ("FIR"), Chebyshev filters ("cheby1" and "cheby2"), Elliptic filter ("ellip") or Bessel filter ("bessel"). Set to None to skip filtering.
scr_method : str
SCR extraction algorithm. "makowski" (default), "kim" (biosPPy's default; See Kim et al., 2004) or "gamboa" (Gamboa, 2004).
scr_treshold : float
SCR minimum treshold (in terms of signal standart deviation).
Returns
----------
processed_eda : dict
Dict containing processed EDA features.
Contains the EDA raw signal, the filtered signal, the phasic compnent (if cvxEDA is True), the SCR onsets, peak indexes and amplitudes.
This function is mainly a wrapper for the biosppy.eda.eda() and cvxEDA() functions. Credits go to their authors.
Example
----------
>>> import neurokit as nk
>>>
>>> processed_eda = nk.eda_process(eda_signal)
Notes
----------
*Details*
- **cvxEDA**: Based on a model which describes EDA as the sum of three terms: the phasic component, the tonic component, and an additive white Gaussian noise term incorporating model prediction errors as well as measurement errors and artifacts. This model is physiologically inspired and fully explains EDA through a rigorous methodology based on Bayesian statistics, mathematical convex optimization and sparsity.
*Authors*
- `Dominique Makowski <https://dominiquemakowski.github.io/>`_
*Dependencies*
- biosppy
- numpy
- pandas
- cvxopt
*See Also*
- BioSPPy: https://github.com/PIA-Group/BioSPPy
- cvxEDA: https://github.com/lciti/cvxEDA
References
-----------
- Greco, A., Valenza, G., & Scilingo, E. P. (2016). Evaluation of CDA and CvxEDA Models. In Advances in Electrodermal Activity Processing with Applications for Mental Health (pp. 35-43). Springer International Publishing.
- Greco, A., Valenza, G., Lanata, A., Scilingo, E. P., & Citi, L. (2016). cvxEDA: A convex optimization approach to electrodermal activity processing. IEEE Transactions on Biomedical Engineering, 63(4), 797-804.
- Kim, K. H., Bang, S. W., & Kim, S. R. (2004). Emotion recognition system using short-term monitoring of physiological signals. Medical and biological engineering and computing, 42(3), 419-427.
- Gamboa, H. (2008). Multi-Modal Behavioral Biometrics Based on HCI and Electrophysiology (Doctoral dissertation, PhD thesis, Universidade Técnica de Lisboa, Instituto Superior Técnico).
"""
# Initialization
eda = np.array(eda)
eda_df = pd.DataFrame({"EDA_Raw": np.array(eda)})
# Preprocessing
# ===================
# Filtering
if filter_type is not None:
filtered, _, _ = biosppy.tools.filter_signal(signal=eda,
ftype=filter_type,
band='lowpass',
order=4,
frequency=5,
sampling_rate=sampling_rate)
# Smoothing
filtered, _ = biosppy.tools.smoother(signal=filtered,
kernel='boxzen',
size=int(0.75 * sampling_rate),
mirror=True)
eda_df["EDA_Filtered"] = filtered
# Derive Phasic and Tonic
try:
tonic, phasic = cvxEDA(eda, sampling_rate=sampling_rate, alpha=alpha, gamma=gamma)
eda_df["EDA_Phasic"] = phasic
eda_df["EDA_Tonic"] = tonic
signal = phasic
except:
print("NeuroKit Warning: eda_process(): Error in cvxEDA algorithm, couldn't extract phasic and tonic components. Using raw signal.")
signal = eda
# Skin-Conductance Responses
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if scr_method == "kim":
onsets, peaks, amplitudes = biosppy.eda.kbk_scr(signal=signal, sampling_rate=sampling_rate, min_amplitude=scr_treshold)
recoveries = [np.nan]*len(onsets)
elif scr_method == "gamboa":
onsets, peaks, amplitudes = biosppy.eda.basic_scr(signal=signal, sampling_rate=sampling_rate)
recoveries = [np.nan]*len(onsets)
else: # makowski's algorithm
onsets, peaks, amplitudes, recoveries = eda_scr(signal, sampling_rate=sampling_rate, treshold=scr_treshold, method="fast")
# Store SCR onsets and recoveries positions
scr_onsets = np.array([np.nan]*len(signal))
if len(onsets) > 0:
scr_onsets[onsets] = 1
eda_df["SCR_Onsets"] = scr_onsets
scr_recoveries = np.array([np.nan]*len(signal))
if len(recoveries) > 0:
scr_recoveries[recoveries[pd.notnull(recoveries)].astype(int)] = 1
eda_df["SCR_Recoveries"] = scr_recoveries
# Store SCR peaks and amplitudes
scr_peaks = np.array([np.nan]*len(eda))
peak_index = 0
for index in range(len(scr_peaks)):
try:
if index == peaks[peak_index]:
scr_peaks[index] = amplitudes[peak_index]
peak_index += 1
except:
pass
eda_df["SCR_Peaks"] = scr_peaks
processed_eda = {"df": eda_df,
"EDA": {
"SCR_Onsets": onsets,
"SCR_Peaks_Indexes": peaks,
"SCR_Recovery_Indexes": recoveries,
"SCR_Peaks_Amplitudes": amplitudes}}
return(processed_eda)
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def cvxEDA(eda, sampling_rate=1000, tau0=2., tau1=0.7, delta_knot=10., alpha=8e-4, gamma=1e-2, solver=None, verbose=False, options={'reltol':1e-9}):
"""
A convex optimization approach to electrodermal activity processing (CVXEDA).
This function implements the cvxEDA algorithm described in "cvxEDA: a
Convex Optimization Approach to Electrodermal Activity Processing" (Greco et al., 2015).
Parameters
----------
eda : list or array
raw EDA signal array.
sampling_rate : int
Sampling rate (samples/second).
tau0 : float
Slow time constant of the Bateman function.
tau1 : float
Fast time constant of the Bateman function.
delta_knot : float
Time between knots of the tonic spline function.
alpha : float
Penalization for the sparse SMNA driver.
gamma : float
Penalization for the tonic spline coefficients.
solver : bool
Sparse QP solver to be used, see cvxopt.solvers.qp
verbose : bool
Print progress?
options : dict
Solver options, see http://cvxopt.org/userguide/coneprog.html#algorithm-parameters
Returns
----------
phasic : numpy.array
The phasic component.
Notes
----------
*Authors*
- Luca Citi (https://github.com/lciti)
- Alberto Greco
*Dependencies*
- cvxopt
- numpy
*See Also*
- cvxEDA: https://github.com/lciti/cvxEDA
References
-----------
- Greco, A., Valenza, G., & Scilingo, E. P. (2016). Evaluation of CDA and CvxEDA Models. In Advances in Electrodermal Activity Processing with Applications for Mental Health (pp. 35-43). Springer International Publishing.
- Greco, A., Valenza, G., Lanata, A., Scilingo, E. P., & Citi, L. (2016). cvxEDA: A convex optimization approach to electrodermal activity processing. IEEE Transactions on Biomedical Engineering, 63(4), 797-804.
"""
frequency = 1/sampling_rate
# Normalizing signal
eda = z_score(eda)
eda = np.array(eda)[:,0]
n = len(eda)
eda = eda.astype('double')
eda = cv.matrix(eda)
# bateman ARMA model
a1 = 1./min(tau1, tau0) # a1 > a0
a0 = 1./max(tau1, tau0)
ar = np.array([(a1*frequency + 2.) * (a0*frequency + 2.), 2.*a1*a0*frequency**2 - 8.,
(a1*frequency - 2.) * (a0*frequency - 2.)]) / ((a1 - a0) * frequency**2)
ma = np.array([1., 2., 1.])
# matrices for ARMA model
i = np.arange(2, n)
A = cv.spmatrix(np.tile(ar, (n-2,1)), np.c_[i,i,i], np.c_[i,i-1,i-2], (n,n))
M = cv.spmatrix(np.tile(ma, (n-2,1)), np.c_[i,i,i], np.c_[i,i-1,i-2], (n,n))
# spline
delta_knot_s = int(round(delta_knot / frequency))
spl = np.r_[np.arange(1.,delta_knot_s), np.arange(delta_knot_s, 0., -1.)] # order 1
spl = np.convolve(spl, spl, 'full')
spl /= max(spl)
# matrix of spline regressors
i = np.c_[np.arange(-(len(spl)//2), (len(spl)+1)//2)] + np.r_[np.arange(0, n, delta_knot_s)]
nB = i.shape[1]
j = np.tile(np.arange(nB), (len(spl),1))
p = np.tile(spl, (nB,1)).T
valid = (i >= 0) & (i < n)
B = cv.spmatrix(p[valid], i[valid], j[valid])
# trend
C = cv.matrix(np.c_[np.ones(n), np.arange(1., n+1.)/n])
nC = C.size[1]
# Solve the problem:
# .5*(M*q + B*l + C*d - eda)^2 + alpha*sum(A,1)*p + .5*gamma*l'*l
# s.t. A*q >= 0
if verbose is False:
options["show_progress"] = False
old_options = cv.solvers.options.copy()
cv.solvers.options.clear()
cv.solvers.options.update(options)
if solver == 'conelp':
# Use conelp
z = lambda m,n: cv.spmatrix([],[],[],(m,n))
G = cv.sparse([[-A,z(2,n),M,z(nB+2,n)],[z(n+2,nC),C,z(nB+2,nC)],
[z(n,1),-1,1,z(n+nB+2,1)],[z(2*n+2,1),-1,1,z(nB,1)],
[z(n+2,nB),B,z(2,nB),cv.spmatrix(1.0, range(nB), range(nB))]])
h = cv.matrix([z(n,1),.5,.5,eda,.5,.5,z(nB,1)])
c = cv.matrix([(cv.matrix(alpha, (1,n)) * A).T,z(nC,1),1,gamma,z(nB,1)])
res = cv.solvers.conelp(c, G, h, dims={'l':n,'q':[n+2,nB+2],'s':[]})
obj = res['primal objective']
else:
# Use qp
Mt, Ct, Bt = M.T, C.T, B.T
H = cv.sparse([[Mt*M, Ct*M, Bt*M], [Mt*C, Ct*C, Bt*C],
[Mt*B, Ct*B, Bt*B+gamma*cv.spmatrix(1.0, range(nB), range(nB))]])
f = cv.matrix([(cv.matrix(alpha, (1,n)) * A).T - Mt*eda, -(Ct*eda), -(Bt*eda)])
res = cv.solvers.qp(H, f, cv.spmatrix(-A.V, A.I, A.J, (n,len(f))),
cv.matrix(0., (n,1)), solver=solver)
obj = res['primal objective'] + .5 * (eda.T * eda)
cv.solvers.options.clear()
cv.solvers.options.update(old_options)
l = res['x'][-nB:]
d = res['x'][n:n+nC]
tonic = B*l + C*d
q = res['x'][:n]
p = A * q
phasic = M * q
e = eda - phasic - tonic
phasic = np.array(phasic)[:,0]
# results = (np.array(a).ravel() for a in (r, t, p, l, d, e, obj))
return(tonic, phasic)
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def eda_scr(signal, sampling_rate=1000, treshold=0.1, method="fast"):
"""
Skin-Conductance Responses extraction algorithm.
Parameters
----------
signal : list or array
EDA signal array.
sampling_rate : int
Sampling rate (samples/second).
treshold : float
SCR minimum treshold (in terms of signal standart deviation).
method : str
"fast" or "slow". Either use a gradient-based approach or a local extrema one.
Returns
----------
onsets, peaks, amplitudes, recoveries : lists
SCRs features.
Example
----------
>>> import neurokit as nk
>>>
>>> onsets, peaks, amplitudes, recoveries = nk.eda_scr(eda_signal)
Notes
----------
*Authors*
- `Dominique Makowski <https://dominiquemakowski.github.io/>`_
*Dependencies*
- biosppy
- numpy
- pandas
*See Also*
- BioSPPy: https://github.com/PIA-Group/BioSPPy
References
-----------
- Kim, K. H., Bang, S. W., & Kim, S. R. (2004). Emotion recognition system using short-term monitoring of physiological signals. Medical and biological engineering and computing, 42(3), 419-427.
- Gamboa, H. (2008). Multi-Modal Behavioral Biometrics Based on HCI and Electrophysiology (Doctoral dissertation, PhD thesis, Universidade Técnica de Lisboa, Instituto Superior Técnico).
"""
# Processing
# ===========
if method == "slow":
# Compute gradient (sort of derivative)
gradient = np.gradient(signal)
# Smoothing
size = int(0.1 * sampling_rate)
smooth, _ = biosppy.tools.smoother(signal=gradient, kernel='bartlett', size=size, mirror=True)
# Find zero-crossings
zeros, = biosppy.tools.zero_cross(signal=smooth, detrend=True)
# Separate onsets and peaks
onsets = []
peaks = []
for i in zeros:
if smooth[i+1] > smooth[i-1]:
onsets.append(i)
else:
peaks.append(i)
peaks = np.array(peaks)
onsets = np.array(onsets)
else:
# find extrema
peaks, _ = biosppy.tools.find_extrema(signal=signal, mode='max')
onsets, _ = biosppy.tools.find_extrema(signal=signal, mode='min')
# Keep only pairs
peaks = peaks[peaks > onsets[0]]
onsets = onsets[onsets < peaks[-1]]
# Artifact Treatment
# ====================
# Compute rising times
risingtimes = peaks-onsets
risingtimes = risingtimes/sampling_rate*1000
peaks = peaks[risingtimes > 100]
onsets = onsets[risingtimes > 100]
# Compute amplitudes
amplitudes = signal[peaks]-signal[onsets]
# Remove low amplitude variations
mask = amplitudes > np.std(signal)*treshold
peaks = peaks[mask]
onsets = onsets[mask]
amplitudes = amplitudes[mask]
# Recovery moments
recoveries = []
for x, peak in enumerate(peaks):
try:
window = signal[peak:onsets[x+1]]
except IndexError:
window = signal[peak:]
recovery_amp = signal[peak]-amplitudes[x]/2
try:
smaller = find_closest_in_list(recovery_amp, window, "smaller")
recovery_pos = peak + list(window).index(smaller)
recoveries.append(recovery_pos)
except ValueError:
recoveries.append(np.nan)
recoveries = np.array(recoveries)
return(onsets, peaks, amplitudes, recoveries)
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def eda_EventRelated(epoch, event_length, window_post=4):
"""
Extract event-related EDA and Skin Conductance Response (SCR).
Parameters
----------
epoch : pandas.DataFrame
An epoch contains in the epochs dict returned by :function:`neurokit.create_epochs()` on dataframe returned by :function:`neurokit.bio_process()`. Index must range from -4s to +4s (relatively to event onset and end).
event_length : int
Event's length in seconds.
window_post : float
Post-stimulus window size (in seconds) to include eventual responses (usually 3 or 4).
Returns
----------
EDA_Response : dict
Event-related EDA response features.
Example
----------
>>> import neurokit as nk
>>> bio = nk.bio_process(ecg=data["ECG"], rsp=data["RSP"], eda=data["EDA"], sampling_rate=1000, add=data["Photosensor"])
>>> df = bio["df"]
>>> events = nk.find_events(df["Photosensor"], cut="lower")
>>> epochs = nk.create_epochs(df, events["onsets"], duration=7, onset=-0.5)
>>> for epoch in epochs:
>>> bio_response = nk.bio_EventRelated(epoch, event_length=4, window_post=3)
Notes
----------
**Looking for help**: *Experimental*: respiration artifacts correction needs to be implemented.
*Details*
- **EDA_Peak**: Max of EDA (in a window starting 1s after the stim onset) minus baseline.
- **SCR_Amplitude**: Peak of SCR. If no SCR, returns NA.
- **SCR_Magnitude**: Peak of SCR. If no SCR, returns 0.
- **SCR_Amplitude_Log**: log of 1+amplitude.
- **SCR_Magnitude_Log**: log of 1+magnitude.
- **SCR_PeakTime**: Time of peak.
- **SCR_Latency**: Time between stim onset and SCR onset.
- **SCR_RiseTime**: Time between SCR onset and peak.
- **SCR_Strength**: *Experimental*: peak divided by latency. Angle of the line between peak and onset.
- **SCR_RecoveryTime**: Time between peak and recovery point (half of the amplitude).
*Authors*
- `Dominique Makowski <https://dominiquemakowski.github.io/>`_
*Dependencies*
- numpy
- pandas
*See Also*
- https://www.biopac.com/wp-content/uploads/EDA-SCR-Analysis.pdf
References
-----------
- Schneider, R., Schmidt, S., Binder, M., Schäfer, F., & Walach, H. (2003). Respiration-related artifacts in EDA recordings: introducing a standardized method to overcome multiple interpretations. Psychological reports, 93(3), 907-920.
- Leiner, D., Fahr, A., & Früh, H. (2012). EDA positive change: A simple algorithm for electrodermal activity to measure general audience arousal during media exposure. Communication Methods and Measures, 6(4), 237-250.
"""
# Initialization
EDA_Response = {}
window_end = event_length + window_post
# Sanity check
if epoch.index[-1]-event_length < 1:
print("NeuroKit Warning: eda_EventRelated(): your epoch only lasts for about %.2f s post stimulus. You might lose some SCRs." %(epoch.index[-1]-event_length))
# EDA Based
# =================
# This is a basic and bad model
if "EDA_Filtered" in epoch.columns:
baseline = epoch["EDA_Filtered"][0:1].min()
eda_peak = epoch["EDA_Filtered"][1:window_end].max()
EDA_Response["EDA_Peak"] = eda_peak - baseline
# SCR Based
# =================
if "SCR_Onsets" in epoch.columns:
# Computation
peak_onset = epoch["SCR_Onsets"][1:window_end].idxmax()
if pd.notnull(peak_onset):
amplitude = epoch["SCR_Peaks"][peak_onset:window_end].max()
peak_time = epoch["SCR_Peaks"][peak_onset:window_end].idxmax()
if pd.isnull(amplitude):
magnitude = 0
else:
magnitude = amplitude
risetime = peak_time - peak_onset
if risetime > 0:
strength = magnitude/risetime
else:
strength = np.nan
if pd.isnull(peak_time) is False:
recovery = epoch["SCR_Recoveries"][peak_time:window_end].idxmax() - peak_time
else:
recovery = np.nan
else:
amplitude = np.nan
magnitude = 0
risetime = np.nan
strength = np.nan
peak_time = np.nan
recovery = np.nan
# Storage
EDA_Response["SCR_Amplitude"] = amplitude
EDA_Response["SCR_Magnitude"] = magnitude
EDA_Response["SCR_Amplitude_Log"] = np.log(1+amplitude)
EDA_Response["SCR_Magnitude_Log"] = np.log(1+magnitude)
EDA_Response["SCR_Latency"] = peak_onset
EDA_Response["SCR_PeakTime"] = peak_time
EDA_Response["SCR_RiseTime"] = risetime
EDA_Response["SCR_Strength"] = strength # Experimental
EDA_Response["SCR_RecoveryTime"] = recovery
# Artifact Correction
# ====================
# TODO !!
# Respiration artifacts
# if "RSP_Filtered" in epoch.columns:
# pass # I Dunno, maybe with granger causality or something?
return(EDA_Response)