ML 10 - LOCALLY WEIGHTED REGRESSION ALGORITHM

10. IMPLEMENT THE NON-PARAMETRIC LOCALLY WEIGHTED REGRESSIONALGORITHM IN ORDER TO FIT DATA POINTS. SELECT APPROPRIATE DATA SET FOR YOUR EXPERIMENT AND DRAW GRAPHS.

 SOLUTION 

NO DATASET

lab10.py

from math import ceil
import numpy as np
from scipy import linalg

def lowess(x, y, f, iterations):
    n = len(x)
    r = int(ceil(f * n))
    h = [np.sort(np.abs(x - x[i]))[r] for i in range(n)]
    w = np.clip(np.abs((x[:, None] - x[None, :]) / h), 0.0, 1.0)
    w = (1 - w ** 3) ** 3
    yest = np.zeros(n)
    delta = np.ones(n)
    for iteration in range(iterations):
        for i in range(n):
            weights = delta * w[:, i]
            b = np.array([np.sum(weights * y), np.sum(weights * y * x)])
            A = np.array([[np.sum(weights), np.sum(weights * x)],[np.sum(weights * x), np.sum(weights * x * x)]])
            beta = linalg.solve(A, b)
            yest[i] = beta[0] + beta[1] * x[i]

        residuals = y - yest
        s = np.median(np.abs(residuals))
        delta = np.clip(residuals / (6.0 * s), -1, 1)
        delta = (1 - delta ** 2) ** 2

    return yest

import math
n = 100
x = np.linspace(0, 2 * math.pi, n)
y = np.sin(x) + 0.3 * np.random.randn(n)
f =0.25
iterations=3
yest = lowess(x, y, f, iterations)
    
import matplotlib.pyplot as plt
plt.plot(x,y,"r.")

plt.plot(x,yest,"b-")

STEPS & OUTPUT:

to view steps & output click HERE