bio_eda.py

# -*- coding: utf-8 -*-
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, 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.
    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
    filtered, _, _ = biosppy.tools.filter_signal(signal=eda,
                                 ftype='butter',
                                 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
    # ===========================
    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)
    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
            recovery = epoch["SCR_Recoveries"][peak_time:window_end].idxmax() - peak_time

        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)