1、加載數據集

import numpy as np import matplotlib.pyplot as pltclass moon_data_class(object):def __init__(self,N,d,r,w):self.N=Nself.w=wself.d=dself.r=rdef 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.Nr = self.rw2 = self.w/2d = self.ddone = Truedata = np.empty(0)while done:#generate Rectangular datatmp_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 ---upperidx = 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 ----downdata_t = np.empty([N, 2])data_t[:, 0] = data[0:N, 0] + rdata_t[:, 1] = -data[0:N, 1] - ddb_moon = np.concatenate((db_moon, data_t), axis=0)return db_moonN = 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、利用最小二乘法進行計算
公式：
$$B=(X^{T}X{)}^{?1}{X}^{T}Y$$

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

3、打印運算結果

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、運行結果

總結

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