數據集：
\[D=\lbrace (x_1,y_1),(x_2,y_2),...,(x_m,y_m)\rbrace \]
其中：
\[x_i = (x_{i1};x_{i2};...;x_{id}) \]
單屬性，二分類
分類面：
\[f(x)= \omega x + b \]
最小均方差求\(\omega \, b\)
\[min \sum_{i=1}^m (f(x_i)-y_i)^2 \]
解得：
\[\omega = \frac{\sum_{i=1}^m y_i(x_i- \hat x)}{\sum_{i=1}^m x^2 - \frac 1m \sum_{i=1}^m(x_i)^2} \]
\[b= \frac 1m \sum_{i=1}^m(y_i - \omega x_i) \]
python程序
import numpy as np
import matplotlib.pyplot as plt
N = 50
X = np.random.rand(N)
Y = np.random.rand(N)
#print(X)
plt.scatter(X, Y, alpha=0.6)#散點圖繪制
#求omiga
xg = 0.0 #x均值
xf = 0.0 #x平方
for i in X:
xg += i
xf += i**2
xg /= N
omiga_m = 0.0
for i in range(N):
omiga_m += Y[i]*(X[i] - xg)
omiga_d = xf - (N*xg)**2/N
omiga = omiga_m/omiga_d
#求偏移b
b_temp = 0.0
for i in range(N):
b_temp += Y[i] - omiga*X[i]
b = b_temp/N
x_linear = np.linspace(0, 1, num=50)
y_linear = [omiga*i + b for i in x_linear]
plt.plot(x_linear, y_linear, color = 'red')
plt.show()
效果
