peak_detection_smoothed_zscore.py

import numpy as np
import matplotlib.pylab as plt

def peak_detection_smoothed_zscore_v2(x, lag, threshold, influence):
    '''
    iterative smoothed z-score algorithm
    Implementation of algorithm from https://stackoverflow.com/a/22640362/6029703
    '''

    labels = np.zeros(len(x))
    filtered_y = np.array(x)
    avg_filter = np.zeros(len(x))
    std_filter = np.zeros(len(x))
    var_filter = np.zeros(len(x))

    avg_filter[lag - 1] = np.mean(x[0:lag])
    std_filter[lag - 1] = np.std(x[0:lag])
    var_filter[lag - 1] = np.var(x[0:lag])
    for i in range(lag, len(x)):
        if abs(x[i] - avg_filter[i - 1]) > threshold * std_filter[i - 1]:
            if x[i] > avg_filter[i - 1]:
                labels[i] = 1
            else:
                labels[i] = -1
            filtered_y[i] = influence * x[i] + (1 - influence) * filtered_y[i - 1]
        else:
            labels[i] = 0
            filtered_y[i] = x[i]
        # update avg, var, std
        avg_filter[i] = avg_filter[i - 1] + 1. / lag * (filtered_y[i] - filtered_y[i - lag])
        var_filter[i] = var_filter[i - 1] + 1. / lag * ((filtered_y[i] - avg_filter[i - 1]) ** 2 - (
            filtered_y[i - lag] - avg_filter[i - 1]) ** 2 - (filtered_y[i] - filtered_y[i - lag]) ** 2 / lag)
        std_filter[i] = np.sqrt(var_filter[i])

    return dict(signals=labels,
                avgFilter=avg_filter,
                stdFilter=std_filter)


signal = [1, 1, 1.1, 1, 0.9, 1, 1, 1.1, 1, 0.9, 1, 1.1, 1, 1, 0.9, 1, 1, 1.1, 1, 1, 1, 1, 1.1, 0.9, 1, 1.1, 1, 1, 0.9, 1,
1.1, 1, 1, 1.1, 1, 0.8, 0.9, 1, 1.2, 0.9, 1, 1, 1.1, 1.2, 1, 1.5, 1, 3, 2, 5, 3, 2, 1, 1, 1, 0.9, 1, 1, 3,  
     2.6, 4, 3, 3.2, 2, 1, 1, 0.8, 4, 4, 2, 2.5, 1, 1, 1]

lag = 5          # lag 5 for the smoothing functions
threshold = 3.5  # 3.5 standard deviations for signal
influence = 0.5 

res = peak_detection_smoothed_zscore_v2(signal, lag, threshold, influence)


fig = plt.figure()
plt.ylabel('Signal') 
plt.xlabel('Time')
ax = fig.add_subplot(111)
ax.set_title("Peak detection") 
ax.plot(signal, color='r', label='Signal')
ax.plot(res['signals'], color='g', label='Peaks')
ax.plot(res['avgFilter'], color='b', label='avgFilter')
ax.plot(res['stdFilter'], color='y', label='stdFilter')
ax.legend()

plt.show()