Quantité d'entités pouvant être extraite des données de séries chronologiques

Lors de l'analyse de données de séries chronologiques, il est parfois nécessaire d'extraire une série chronologique partielle et d'extraire des caractéristiques. Les caractéristiques suivantes peuvent être extraites.

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
Données de vague
        
    x : np.ndarray
Heure etc.
    
    fs : int
Fréquence d'échantillonnage
    
    order : int
Intervalle de détection de pic

    Returns
    ----------
    np.ndarray
Vecteur caractéristique
    """
        
    # 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

    #Obtenir l'indice de la valeur de pointe
    maxid = signal.argrelmax(y, order=order)  #Valeur maximum
    minid = signal.argrelmin(y, order=order)  #valeur minimum
    
    # 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)