Locally Weighted Regression

10. Implement the non-parametric Locally Weighted Regression algorithm in order to fit data points. Select appropriate data set for your experiment and draw graphs.

import matplotlib.pyplot as plt
import pandas as pd
import numpy as np

def kernel(point,xmat, k):
    m,n = np.shape(xmat)
    weights = np.mat(np.eye((m)))     # eye - identity matrix 
    for j in range(m):
        diff = point - X[j]
        weights[j,j] = np.exp(diff*diff.T/(-2.0*k**2))
    return weights

def localWeight(point,xmat,ymat,k):
    wei = kernel(point,xmat,k)
    W = (X.T*(wei*X)).I*(X.T*(wei*ymat.T))
    return W

def localWeightRegression(xmat,ymat,k):
    m,n = np.shape(xmat)
    ypred = np.zeros(m)
    for i in range(m):
        ypred[i] = xmat[i]*localWeight(xmat[i],xmat,ymat,k)
    return ypred

def graphPlot(X,ypred):
    sortindex = X[:,1].argsort(0)          #argsort - index of the smallest 
    xsort = X[sortindex][:,0]
    fig = plt.figure()
    ax = fig.add_subplot(1,1,1)
    ax.scatter(bill,tip, color='green')
    ax.plot(xsort[:,1],ypred[sortindex], color = 'red', linewidth=5)
    plt.xlabel('Total bill')
    plt.ylabel('Tip')
    plt.show();

# load data points
data = pd.read_csv('arya.csv')
bill = np.array(data.total_bill)      # We use only Bill amount and Tips data 
tip = np.array(data.tip)
mbill = np.mat(bill)          # .mat will convert nd array is converted in 2D array 
mtip = np.mat(tip)
m= np.shape(mbill)[1]
one = np.mat(np.ones(m))
X = np.hstack((one.T,mbill.T))              # 244 rows, 2 cols  # increase k to get smooth curves
ypred = localWeightRegression(X,mtip,3)
graphPlot(X,ypred)


Datasets->
total_bill,tip,sex,smoker,day,time,size
16.99,1.01,Female,No,Sun,Dinner,2
10.34,1.66,Male,No,Sun,Dinner,3
21.01,3.5,Male,No,Sun,Dinner,3
23.68,3.31,Male,No,Sun,Dinner,2
24.59,3.61,Female,No,Sun,Dinner,4
25.29,4.71,Male,No,Sun,Dinner,4
8.77,2.0,Male,No,Sun,Dinner,2
26.88,3.12,Male,No,Sun,Dinner,4
15.04,1.96,Male,No,Sun,Dinner,2
14.78,3.23,Male,No,Sun,Dinner,2
10.27,1.71,Male,No,Sun,Dinner,2
35.26,5.0,Female,No,Sun,Dinner,4
15.42,1.57,Male,No,Sun,Dinner,2
18.43,3.0,Male,No,Sun,Dinner,4
14.83,3.02,Female,No,Sun,Dinner,2
21.58,3.92,Male,No,Sun,Dinner,2
10.33,1.67,Female,No,Sun,Dinner,3
16.29,3.71,Male,No,Sun,Dinner,3
16.97,3.5,Female,No,Sun,Dinner,3
20.65,3.35,Male,No,Sat,Dinner,3
17.92,4.08,Male,No,Sat,Dinner,2
20.29,2.75,Female,No,Sat,Dinner,2
15.77,2.23,Female,No,Sat,Dinner,2
39.42,7.58,Male,No,Sat,Dinner,4
19.82,3.18,Male,No,Sat,Dinner,2
17.81,2.34,Male,No,Sat,Dinner,4
13.37,2.0,Male,No,Sat,Dinner,2
12.69,2.0,Male,No,Sat,Dinner,2
21.7,4.3,Male,No,Sat,Dinner,2
19.65,3.0,Female,No,Sat,Dinner,2
9.55,1.45,Male,No,Sat,Dinner,2
18.35,2.5,Male,No,Sat,Dinner,4
15.06,3.0,Female,No,Sat,Dinner,2
20.69,2.45,Female,No,Sat,Dinner,4
17.78,3.27,Male,No,Sat,Dinner,2
24.06,3.6,Male,No,Sat,Dinner,3
16.31,2.0,Male,No,Sat,Dinner,3
16.93,3.07,Female,No,Sat,Dinner,3
18.69,2.31,Male,No,Sat,Dinner,3
31.27,5.0,Male,No,Sat,Dinner,3
16.04,2.24,Male,No,Sat,Dinner,3
17.46,2.54,Male,No,Sun,Dinner,2
13.94,3.06,Male,No,Sun,Dinner,2
9.68,1.32,Male,No,Sun,Dinner,2
30.4,5.6,Male,No,Sun,Dinner,4
18.29,3.0,Male,No,Sun,Dinner,2
22.23,5.0,Male,No,Sun,Dinner,2
32.4,6.0,Male,No,Sun,Dinner,4
28.55,2.05,Male,No,Sun,Dinner,3
18.04,3.0,Male,No,Sun,Dinner,2
12.54,2.5,Male,No,Sun,Dinner,2
10.29,2.6,Female,No,Sun,Dinner,2
34.81,5.2,Female,No,Sun,Dinner,4
9.94,1.56,Male,No,Sun,Dinner,2
25.56,4.34,Male,No,Sun,Dinner,4
19.49,3.51,Male,No,Sun,Dinner,2
38.01,3.0,Male,Yes,Sat,Dinner,4
26.41,1.5,Female,No,Sat,Dinner,2
11.24,1.76,Male,Yes,Sat,Dinner,2
48.27,6.73,Male,No,Sat,Dinner,4
20.29,3.21,Male,Yes,Sat,Dinner,2
13.81,2.0,Male,Yes,Sat,Dinner,2
11.02,1.98,Male,Yes,Sat,Dinner,2
18.29,3.76,Male,Yes,Sat,Dinner,4
17.59,2.64,Male,No,Sat,Dinner,3
20.08,3.15,Male,No,Sat,Dinner,3
16.45,2.47,Female,No,Sat,Dinner,2
3.07,1.0,Female,Yes,Sat,Dinner,1
20.23,2.01,Male,No,Sat,Dinner,2
15.01,2.09,Male,Yes,Sat,Dinner,2
12.02,1.97,Male,No,Sat,Dinner,2
17.07,3.0,Female,No,Sat,Dinner,3
26.86,3.14,Female,Yes,Sat,Dinner,2
25.28,5.0,Female,Yes,Sat,Dinner,2
14.73,2.2,Female,No,Sat,Dinner,2
10.51,1.25,Male,No,Sat,Dinner,2
17.92,3.08,Male,Yes,Sat,Dinner,2
27.2,4.0,Male,No,Thur,Lunch,4
22.76,3.0,Male,No,Thur,Lunch,2
17.29,2.71,Male,No,Thur,Lunch,2
19.44,3.0,Male,Yes,Thur,Lunch,2
16.66,3.4,Male,No,Thur,Lunch,2
10.07,1.83,Female,No,Thur,Lunch,1
32.68,5.0,Male,Yes,Thur,Lunch,2
15.98,2.03,Male,No,Thur,Lunch,2
34.83,5.17,Female,No,Thur,Lunch,4
13.03,2.0,Male,No,Thur,Lunch,2
18.28,4.0,Male,No,Thur,Lunch,2
24.71,5.85,Male,No,Thur,Lunch,2
21.16,3.0,Male,No,Thur,Lunch,2
28.97,3.0,Male,Yes,Fri,Dinner,2
22.49,3.5,Male,No,Fri,Dinner,2
5.75,1.0,Female,Yes,Fri,Dinner,2
16.32,4.3,Female,Yes,Fri,Dinner,2
22.75,3.25,Female,No,Fri,Dinner,2
40.17,4.73,Male,Yes,Fri,Dinner,4
27.28,4.0,Male,Yes,Fri,Dinner,2
12.03,1.5,Male,Yes,Fri,Dinner,2
21.01,3.0,Male,Yes,Fri,Dinner,2
12.46,1.5,Male,No,Fri,Dinner,2
11.35,2.5,Female,Yes,Fri,Dinner,2
15.38,3.0,Female,Yes,Fri,Dinner,2
44.3,2.5,Female,Yes,Sat,Dinner,3
22.42,3.48,Female,Yes,Sat,Dinner,2
20.92,4.08,Female,No,Sat,Dinner,2
15.36,1.64,Male,Yes,Sat,Dinner,2
20.49,4.06,Male,Yes,Sat,Dinner,2
25.21,4.29,Male,Yes,Sat,Dinner,2
18.24,3.76,Male,No,Sat,Dinner,2
14.31,4.0,Female,Yes,Sat,Dinner,2
14.0,3.0,Male,No,Sat,Dinner,2
7.25,1.0,Female,No,Sat,Dinner,1
38.07,4.0,Male,No,Sun,Dinner,3
23.95,2.55,Male,No,Sun,Dinner,2
25.71,4.0,Female,No,Sun,Dinner,3
17.31,3.5,Female,No,Sun,Dinner,2
29.93,5.07,Male,No,Sun,Dinner,4
10.65,1.5,Female,No,Thur,Lunch,2
12.43,1.8,Female,No,Thur,Lunch,2
24.08,2.92,Female,No,Thur,Lunch,4
11.69,2.31,Male,No,Thur,Lunch,2
13.42,1.68,Female,No,Thur,Lunch,2
14.26,2.5,Male,No,Thur,Lunch,2
15.95,2.0,Male,No,Thur,Lunch,2
12.48,2.52,Female,No,Thur,Lunch,2
29.8,4.2,Female,No,Thur,Lunch,6
8.52,1.48,Male,No,Thur,Lunch,2
14.52,2.0,Female,No,Thur,Lunch,2
11.38,2.0,Female,No,Thur,Lunch,2
22.82,2.18,Male,No,Thur,Lunch,3
19.08,1.5,Male,No,Thur,Lunch,2
20.27,2.83,Female,No,Thur,Lunch,2
11.17,1.5,Female,No,Thur,Lunch,2
12.26,2.0,Female,No,Thur,Lunch,2
18.26,3.25,Female,No,Thur,Lunch,2
8.51,1.25,Female,No,Thur,Lunch,2
10.33,2.0,Female,No,Thur,Lunch,2
14.15,2.0,Female,No,Thur,Lunch,2
16.0,2.0,Male,Yes,Thur,Lunch,2
13.16,2.75,Female,No,Thur,Lunch,2
17.47,3.5,Female,No,Thur,Lunch,2
34.3,6.7,Male,No,Thur,Lunch,6
41.19,5.0,Male,No,Thur,Lunch,5
27.05,5.0,Female,No,Thur,Lunch,6
16.43,2.3,Female,No,Thur,Lunch,2
8.35,1.5,Female,No,Thur,Lunch,2
18.64,1.36,Female,No,Thur,Lunch,3
11.87,1.63,Female,No,Thur,Lunch,2
9.78,1.73,Male,No,Thur,Lunch,2
7.51,2.0,Male,No,Thur,Lunch,2
14.07,2.5,Male,No,Sun,Dinner,2
13.13,2.0,Male,No,Sun,Dinner,2
17.26,2.74,Male,No,Sun,Dinner,3
24.55,2.0,Male,No,Sun,Dinner,4
19.77,2.0,Male,No,Sun,Dinner,4
29.85,5.14,Female,No,Sun,Dinner,5
48.17,5.0,Male,No,Sun,Dinner,6
25.0,3.75,Female,No,Sun,Dinner,4
13.39,2.61,Female,No,Sun,Dinner,2
16.49,2.0,Male,No,Sun,Dinner,4
21.5,3.5,Male,No,Sun,Dinner,4
12.66,2.5,Male,No,Sun,Dinner,2
16.21,2.0,Female,No,Sun,Dinner,3
13.81,2.0,Male,No,Sun,Dinner,2
17.51,3.0,Female,Yes,Sun,Dinner,2
24.52,3.48,Male,No,Sun,Dinner,3
20.76,2.24,Male,No,Sun,Dinner,2
31.71,4.5,Male,No,Sun,Dinner,4
10.59,1.61,Female,Yes,Sat,Dinner,2
10.63,2.0,Female,Yes,Sat,Dinner,2
50.81,10.0,Male,Yes,Sat,Dinner,3
15.81,3.16,Male,Yes,Sat,Dinner,2
7.25,5.15,Male,Yes,Sun,Dinner,2
31.85,3.18,Male,Yes,Sun,Dinner,2
16.82,4.0,Male,Yes,Sun,Dinner,2
32.9,3.11,Male,Yes,Sun,Dinner,2
17.89,2.0,Male,Yes,Sun,Dinner,2
14.48,2.0,Male,Yes,Sun,Dinner,2
9.6,4.0,Female,Yes,Sun,Dinner,2
34.63,3.55,Male,Yes,Sun,Dinner,2
34.65,3.68,Male,Yes,Sun,Dinner,4
23.33,5.65,Male,Yes,Sun,Dinner,2
45.35,3.5,Male,Yes,Sun,Dinner,3
23.17,6.5,Male,Yes,Sun,Dinner,4
40.55,3.0,Male,Yes,Sun,Dinner,2
20.69,5.0,Male,No,Sun,Dinner,5
20.9,3.5,Female,Yes,Sun,Dinner,3
30.46,2.0,Male,Yes,Sun,Dinner,5
18.15,3.5,Female,Yes,Sun,Dinner,3
23.1,4.0,Male,Yes,Sun,Dinner,3
15.69,1.5,Male,Yes,Sun,Dinner,2
19.81,4.19,Female,Yes,Thur,Lunch,2
28.44,2.56,Male,Yes,Thur,Lunch,2
15.48,2.02,Male,Yes,Thur,Lunch,2
16.58,4.0,Male,Yes,Thur,Lunch,2
7.56,1.44,Male,No,Thur,Lunch,2
10.34,2.0,Male,Yes,Thur,Lunch,2
43.11,5.0,Female,Yes,Thur,Lunch,4
13.0,2.0,Female,Yes,Thur,Lunch,2
13.51,2.0,Male,Yes,Thur,Lunch,2
18.71,4.0,Male,Yes,Thur,Lunch,3
12.74,2.01,Female,Yes,Thur,Lunch,2
13.0,2.0,Female,Yes,Thur,Lunch,2
16.4,2.5,Female,Yes,Thur,Lunch,2
20.53,4.0,Male,Yes,Thur,Lunch,4
16.47,3.23,Female,Yes,Thur,Lunch,3
26.59,3.41,Male,Yes,Sat,Dinner,3
38.73,3.0,Male,Yes,Sat,Dinner,4
24.27,2.03,Male,Yes,Sat,Dinner,2
12.76,2.23,Female,Yes,Sat,Dinner,2
30.06,2.0,Male,Yes,Sat,Dinner,3
25.89,5.16,Male,Yes,Sat,Dinner,4
48.33,9.0,Male,No,Sat,Dinner,4
13.27,2.5,Female,Yes,Sat,Dinner,2
28.17,6.5,Female,Yes,Sat,Dinner,3
12.9,1.1,Female,Yes,Sat,Dinner,2
28.15,3.0,Male,Yes,Sat,Dinner,5
11.59,1.5,Male,Yes,Sat,Dinner,2
7.74,1.44,Male,Yes,Sat,Dinner,2
30.14,3.09,Female,Yes,Sat,Dinner,4
12.16,2.2,Male,Yes,Fri,Lunch,2
13.42,3.48,Female,Yes,Fri,Lunch,2
8.58,1.92,Male,Yes,Fri,Lunch,1
15.98,3.0,Female,No,Fri,Lunch,3
13.42,1.58,Male,Yes,Fri,Lunch,2
16.27,2.5,Female,Yes,Fri,Lunch,2
10.09,2.0,Female,Yes,Fri,Lunch,2
20.45,3.0,Male,No,Sat,Dinner,4
13.28,2.72,Male,No,Sat,Dinner,2
22.12,2.88,Female,Yes,Sat,Dinner,2
24.01,2.0,Male,Yes,Sat,Dinner,4
15.69,3.0,Male,Yes,Sat,Dinner,3
11.61,3.39,Male,No,Sat,Dinner,2
10.77,1.47,Male,No,Sat,Dinner,2
15.53,3.0,Male,Yes,Sat,Dinner,2
10.07,1.25,Male,No,Sat,Dinner,2
12.6,1.0,Male,Yes,Sat,Dinner,2
32.83,1.17,Male,Yes,Sat,Dinner,2
35.83,4.67,Female,No,Sat,Dinner,3
29.03,5.92,Male,No,Sat,Dinner,3
27.18,2.0,Female,Yes,Sat,Dinner,2
22.67,2.0,Male,Yes,Sat,Dinner,2
17.82,1.75,Male,No,Sat,Dinner,2
18.78,3.0,Female,No,Thur,Dinner,2


Output->



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