[PYTHON] Features that can be extracted from time series data

When analyzing time series data, it is sometimes necessary to extract partial time series and extract features. The following features can be extracted.

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
Wave data
        
    x : np.ndarray
Time etc.
    
    fs : int
Sample frequency
    
    order : int
Peak detection interval

    Returns
    ----------
    np.ndarray
Feature vector
    """
        
    # 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

    #Get index of peak value
    maxid = signal.argrelmax(y, order=order)  #Maximum value
    minid = signal.argrelmin(y, order=order)  #minimum value
    
    # 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)