（斯坦福机器学习课程笔记）局部加权线性回归练习

本文链接：https://blog.youkuaiyun.com/qq_32231743/article/details/53639904

代码使用PTHON3.x

题目如下

import numpy as np
import random
import matplotlib.pyplot as plt
F64='float64'
def gen_sin_dot_sample(num_point):
    x=np.linspace(0,10,num_point)
    y=np.sin(x)+np.random.random(num_point)*0.05
    return [x.tolist(),y.tolist()]

def show_point(p_x,p_y):
    plt.figure(1)
    plt.plot(p_x,p_y,'ob')
    plt.xlim(-5.2,15.2)
    plt.ylim(-1.8,1.8)
    plt.xlabel('x')
    plt.ylabel('y')
    plt.show()
[x,y]=gen_sin_dot_sample(100)
show_point(x,y)

得到下图样本点
这里写图片描述
要求用局部加权线性回归拟合该曲线

======================================================
代码如下

import numpy as np
import random
import matplotlib.pyplot as plt

F64='float64'

def gen_sin_dot_sample(num_point):
    x = np.linspace(0,10,num_point)
    y = np.sin(x)+np.random.random(num_point)*0.5
    return [x.tolist(),y.tolist()]

def draw_point(p_x,p_y):
    plt.figure(1)
    plt.plot(p_x,p_y,'ob')
    plt.xlim(-5.2,15.2)
    plt.ylim(-2.2,2.2)
    plt.xlabel('x')
    plt.ylabel('y')
    plt.show()

def draw_point_and_line(p_x,p_y,l_x,l_y):
    plt.figure(1)
    plt.plot(p_x,p_y,'ob')
    plt.plot(l_x,l_y,'r')
    plt.xlim(-5.2,15.2)
    plt.ylim(-2.2,2.2)
    plt.xlabel('x')
    plt.ylabel('y')
    plt.show()

def lwr(x,y,x_calculate,times_iteration,k,study_rate):# x,y,x_calculate is list
    num_sample = len(x)
    x = np.asarray(x,dtype=F64).reshape((num_sample,1))
    y = np.asarray(y,dtype=F64).reshape((num_sample,1))
    one_mat = np.ones((num_sample,1),dtype=F64)
    x_add_one = np.hstack((one_mat,x))
    theta = np.random.random((2))
    theta = theta.astype(F64).reshape(2,1)
    for i in xrange(times_iteration):
        weight = np.exp(-np.square(np.hstack((x,x))-x_calculate)/(k**2))
        diff_theta = ((np.dot(x_add_one,theta)-y)*x_add_one*weight).mean(0,dtype=F64,keepdims=True)
        theta = theta-diff_theta.transpose()*study_rate
    return theta.reshape((2)).tolist()


[x,y] = gen_sin_dot_sample(100)
x_calculate = np.linspace(0,10,50).tolist()
point_list=[]
for i in x_calculate:
    theta = lwr(x,y,i,1000,0.3,0.1)
    point_y = theta[0]+theta[1]*i
    point_list.append(point_y)

draw_point_and_line(x,y,x_calculate,point_list)