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| from cvxopt import matrix, solvers
import numpy as np
import matplotlib.pyplot as plt
def split_train_test_data(mean1, mean2, sdt, n):
np.random.seed(529)
x_p1 = np.random.normal(loc=mean1, scale=sdt,size=int(n/2)).reshape(-1,1)
x_p2 = np.random.normal(loc=mean1, scale=sdt,size=int(n/2)).reshape(-1,1)
y_p = np.ones(len(x_p1))[:,np.newaxis]
X_p = np.hstack((x_p1, x_p2))
x_n1 = np.random.normal(loc=mean2, scale=sdt,size=int(n/2)).reshape(-1,1)
x_n2 = np.random.normal(loc=mean2, scale=sdt,size=int(n/2)).reshape(-1,1)
y_n = (np.ones(len(x_n1))*-1)[:,np.newaxis]
X_n = np.hstack((x_n1, x_n2))
fig = plt.figure()
ax = fig.add_subplot(111)
ax.scatter(x_p1, x_p2, color = "#ffb07c", s = 100, label = "1")
ax.scatter(x_n1, x_n2, color = "#c94cbe", s = 100, label = "-1")
plt.legend()
plt.show()
F_train = np.vstack((X_n[:int(n/2*0.8)], X_p[:int(n/2*0.8)]))
y_train = np.vstack((y_n[:int(n/2*0.8)], y_p[:int(n/2*0.8)]))
F_test = np.vstack((X_n[int(n/2*0.8):], X_p[int(n/2*0.8):]))
y_test = np.vstack((y_n[int(n/2*0.8):], y_p[int(n/2*0.8):]))
return F_train, F_test, y_train, y_test
F_train, F_test, y_train, y_test = split_train_test_data(6,1,2,50)
print("训练集规模",F_train.shape)
print("测试集规模",F_test.shape)
print("训练集标签",y_train.shape)
print("测试集标签",y_test.shape)
def train(x, y, C):
k = []
for i in range(x.shape[0]):
k.append([])
for j in range(x.shape[0]):
k[i].append(np.inner(x[i], x[j]))
k = np.array(k)
l = np.inner(y, y)
p = matrix(l * k)
q = matrix(np.ones(40)*-1)
A = matrix(y.reshape(1,-1))
b = matrix(0.)
g = matrix(np.vstack((np.eye(40)*-1, np.eye(40))))
h = matrix(np.vstack((np.zeros(len(y)).reshape(-1,1), np.ones(len(y)).reshape(-1,1)*C)))
solution = solvers.qp(p,q,g,h,A,b)
a = np.ravel(solution['x'])
w_best = np.sum(a.reshape(-1,1)*y*x, axis = 0)
b_best = 0
for j in range(x.shape[0]):
b_best += y[j] - np.sum(y * a.reshape(-1,1)* np.inner(x, x[j].T).reshape(-1,1))
b_best = b_best/x.shape[0]
return w_best, b_best
w, b = train(F_train,y_train,100)
x = np.linspace(-6, 10 , 50)
y = (-w[0]/w[1]*x - b/w[1]).ravel()
[[plt.scatter(data[0], data[1], color = "#c94cbe", s = 100)]for data in F_train[:20]]
[[plt.scatter(data[0], data[1], color = "#ffb07c", s = 100)]for data in F_train[20:]]
plt.plot(x, y, color="#087804")
def test(w, b, x):
prediction=np.sign(np.dot(x, w)+b)
return prediction
prediction = test(w, b, F_test)
num = 0
for i in range(y_test.shape[0]):
if prediction[i] == y_test[i]:
num += 1
acc = 100*num/(y_test.shape[0])
print("acc = %.2f %%"%acc)
x = np.linspace(-6, 10 , 50)
y = (-w[0]/w[1]*x - b/w[1]).ravel()
y1 = (-w[0]/w[1]*x - (b+1)/w[1]).ravel()
y2 = (-w[0]/w[1]*x - (b-1)/w[1]).ravel()
[[plt.scatter(data[0], data[1], color = "#c94cbe", s=100)]for data in F_train[:20]]
[[plt.scatter(data[0], data[1], color = "#ffb07c", s=100)]for data in F_train[20:]]
[[plt.scatter(data[0], data[1], color = "#c94cbe", marker="*", s=100)]for data in F_test[:5]]
[[plt.scatter(data[0], data[1], color = "#ffb07c", marker="*", s=100)]for data in F_test[5:]]
plt.plot(x, y, color="#087804")
plt.plot(x, y1, color="#048243", ls='--')
plt.plot(x, y2, color="#048243", ls='--')
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