基于双月数据集利用最小二乘法进行分类

1、加载数据集

import numpy as np
import matplotlib.pyplot as plt

class moon_data_class(object):
    def __init__(self,N,d,r,w):
        self.N=N
        self.w=w
      
        self.d=d
        self.r=r
    
   
    def sgn(self,x):
        if(x>0):
            return 1;
        else:
            return -1;
        
    def sig(self,x):
        return 1.0/(1+np.exp(x))
    
        
    def dbmoon(self):
        N1 = 10*self.N
        r = self.r
        w2 = self.w/2
        d = self.d
        done = True
        data = np.empty(0)
        while done:
            #generate Rectangular data
            tmp_x = 2*(r+w2)*(np.random.random([N1, 1])-0.5)
            tmp_y = (r+w2)*np.random.random([N1, 1])
            tmp = np.concatenate((tmp_x, tmp_y), axis=1)
            tmp_ds = np.sqrt(tmp_x*tmp_x + tmp_y*tmp_y)
            #generate double moon data ---upper
            idx = np.logical_and(tmp_ds > (r-w2), tmp_ds < (r+w2))
            idx = (idx.nonzero())[0]
     
            if data.shape[0] == 0:
                data = tmp.take(idx, axis=0)
            else:
                data = np.concatenate((data, tmp.take(idx, axis=0)), axis=0)
            if data.shape[0] >= N:
                done = False
        #print (data)
        db_moon = data[0:N, :]
        #print (db_moon)
        #generate double moon data ----down
        data_t = np.empty([N, 2])
        data_t[:, 0] = data[0:N, 0] + r
        data_t[:, 1] = -data[0:N, 1] - d
        db_moon = np.concatenate((db_moon, data_t), axis=0)
        return db_moon

N = 100
d = 1
r = 10
width = 6
data_source = moon_data_class(N, d, r, width)
data = data_source.dbmoon()

a = 0.001
num_MSE = []
num_step = []

x0 = [1 for x in range(1,201)]
x =  np.array([np.reshape(data[0:2*N, 0], len(data)), np.reshape(data[0:2*N, 1], len(data))]).transpose()
w = np.array([ 0, 0])

d_pre = [1 for y in range(1, 101)]
d_pos = [-1 for y in range(1, 101)]
d=d_pre+d_pos

2、利用最小二乘法进行计算
公式：
$B = (X^TX)^{-1}X^TY$

XT = x.T
B=np.dot(np.dot(np.linalg.inv(np.dot(XT,x)),XT),d)

3、打印运算结果

    x = np.array(range(-15, 25))
    y = -x*B[0]/B[1]
    
    plt.plot(x, y, 'g--')
    
    plt.plot(data[0:N, 0], data[0:N, 1], 'r*', data[N:2*N, 0], data[N:2*N, 1], 'b*')
    plt.show()

4、运行结果