[PYTHON] Merkmalsmenge, die aus Zeitreihendaten extrahiert werden kann

Bei der Analyse von Zeitreihendaten ist es manchmal erforderlich, eine Teilzeitreihe zu extrahieren und Merkmale zu extrahieren. Die folgenden Funktionen können extrahiert werden.

from scipy import fftpack, signal
import scipy
import numpy as np
import matplotlib.pyplot as plt


def pentropy(y, fs):
    f, Pxx = signal.periodogram(y, fs)
    pk = Pxx / np.mean(Pxx)
    S = scipy.stats.entropy(pk)
    return S


def generate_features(y, x, fs=1, order=5):
    """
    Parameters
    ----------
    y : np.ndarray
Wellendaten
        
    x : np.ndarray
Zeit etc.
    
    fs : int
Abtastfrequenz
    
    order : int
Spitzenerkennungsintervall

    Returns
    ----------
    np.ndarray
Merkmalsvektor
    """
        
    # norm
    L1 = np.linalg.norm(y, ord=1)
    L2 = np.linalg.norm(y, ord=2)
    
    # mean
    mean = np.mean(y)
    
    # Standard deviation
    std = np.std(y)
    
    # skewness
    skew = scipy.stats.skew(y)
    
    # kurtosis
    kurtosis = scipy.stats.kurtosis(y)
    
    # mad
    mad = np.linalg.norm(y - mean, ord=1)
    
    # percentile
    percentil_calc = np.percentile(y, [0, 1, 25, 50, 75, 99, 100])
    
    # relative_percentile
    relative_percentile = percentil_calc - mean
    
    # value range
    max_range = percentil_calc[-1] - percentil_calc[0]
    
    # asymmetry
    v_max = relative_percentile[-1]
    v_min = relative_percentile[0]
    asymmetry = v_max + v_min

    #Index des Spitzenwerts abrufen
    maxid = signal.argrelmax(y, order=order)  #Maximalwert
    minid = signal.argrelmin(y, order=order)  #Mindestwert
    
    # max height of peaks
    max_height = np.max(y[maxid])
    
    # min height of peaks
    min_height = np.min(y[minid])
    
    # peak height diff
    peak_width = max_height - min_height
    
    # mean value of peak's width
    x_p = np.append(x[maxid], x[minid])
    mean_width_all = np.mean(x_p)
    
    # number of peaks
    num_peak = len(x_p)
    
    # max, min and their diff, mean of peak's width
    diff1 = np.diff(x_p)
    width_max = np.max(diff1)
    width_min = np.min(diff1)
    width_diff = width_max - width_min
    width_mean = np.mean(diff1)
    width_median = np.median(diff1)
    
    # spectral entropy
    se = pentropy(y, fs)

    # merge to features (15features)
    features = np.concatenate([np.asarray(
        [L1, L2, mean, std, skew, kurtosis, mad, max_range,
         asymmetry, max_height, min_height, peak_width,
         mean_width_all, num_peak, width_max, width_min, width_diff,
         width_mean, width_median, se]
    ), relative_percentile])

    return features


x = np.linspace(0, 10, 100)
yorg = np.sin(x)
y = yorg + np.random.randn(100)*0.5

features = generate_features(y, x, order=5)