kernel_smoothing.py

import numpy as np
from matplotlib import pyplot as plt

def generate_generic_kernel(bandwidth, kernel_type):
    def u(x): return x/bandwidth - 1 # u normalizes the range of the kernel supports between [-1, 1]
    kernels = {
        'epanechnikov': lambda x: 3/4 * (1 - u(x)**2),
        'triangular':   lambda x: 1 - np.abs(u(x)),
        'knn': lambda x: 1/2
        }
    if kernel_type not in kernels:
        raise ValueError(f"{kernel_type} not in {kernels.keys()}")
    return [kernels[kernel_type](x) for x in range(2 * bandwidth + 1)]

def kernel_smoothing(data: np.array, bandwidth: int = 12, kernel: str ='epanechnikov') -> np.array:
    kernels = ['epanechnikov', 'triangular', 'knn']
    if kernel not in kernels:
        raise ValueError(f"{kernel} not in {list(kernels)}")

    generated_kernel = generate_generic_kernel(bandwidth, kernel)
    return np.convolve(data, generated_kernel, mode='same') / np.sum(generated_kernel) # nadaraya-watson sum

if __name__ == "__main__":
    x = np.linspace(1,100, 1000)
    y = np.sin(x) 
    def legend(): plt.legend(('True Data', 'Filtered Data', 'Residuals'))
    y_noisy = y + np.random.randn(1000)/3

    values = {}
    values['KNN'] = kernel_smoothing(y_noisy, kernel='knn')
    values['Parabolic'] = kernel_smoothing(y_noisy)
    values['Triangular'] = kernel_smoothing(y_noisy, kernel='triangular')

    for i in values:
        plt.figure()
        plt.plot(x, y)
        plt.plot(x, values[i])
        plt.plot(x, y-values[i])
        plt.title(f'{i} Smoothing')
        legend()
    plt.show()