实际使用SVM
import numpy as np
import matplotlib.pyplot as plt
from sklearn import datasets
iris = datasets.load_iris()
X = iris.data
y = iris.target
# y小于2的行
X = X[y<2,:2]
y = y[y<2]
plt.scatter(X[y==0,0],X[y==0,1],color='red')
plt.scatter(X[y==1,0],X[y==1,1],color='blue')
plt.show()
from sklearn.preprocessing import StandardScaler
standardscaler = StandardScaler()
standardscaler.fit(X)
x_standard = standardscaler.transform(X)
from sklearn.svm import LinearSVC #support vector classifier
svc = LinearSVC(C=1e9) #C的取值越大越偏向于hard SVM
svc.fit(x_standard,y)
LinearSVC(C=1000000000.0, class_weight=None, dual=True, fit_intercept=True,
intercept_scaling=1, loss='squared_hinge', max_iter=1000,
multi_class='ovr', penalty='l2', random_state=None, tol=0.0001,
verbose=0)
def plot_decision_boundary(model, axis):
x0, x1 = np.meshgrid(
np.linspace(axis[0], axis[1], int((axis[1]-axis[0])*100)).reshape(-1, 1),
np.linspace(axis[2], axis[3], int((axis[3]-axis[2])*100)).reshape(-1, 1),
)
X_new = np.c_[x0.ravel(), x1.ravel()]
y_predict = model.predict(X_new)
zz = y_predict.reshape(x0.shape)
from matplotlib.colors import ListedColormap
custom_cmap = ListedColormap(['#EF9A9A','#FFF59D','#90CAF9'])
plt.contourf(x0, x1, zz, cmap=custom_cmap)
plot_decision_boundary(svc,axis=[-3,3,-3,3])
plt.scatter(x_standard[y==0,0],x_standard[y==0,1],color='red')
plt.scatter(x_standard[y==1,0],x_standard[y==1,1],color='blue')
plt.show()
svc2 = LinearSVC(C=0.01)
svc2.fit(x_standard,y)
plot_decision_boundary(svc2,axis=[-3,3,-3,3])
plt.scatter(x_standard[y==0,0],x_standard[y==0,1],color='red')
plt.scatter(x_standard[y==1,0],x_standard[y==1,1],color='blue')
plt.show()
svc.coef_
array([[ 4.03241592, -2.49295125]])
svc.intercept_
array([0.95368349])
def plot_svc_decision_boundary(model, axis):
x0, x1 = np.meshgrid(
np.linspace(axis[0], axis[1], int((axis[1]-axis[0])*100)).reshape(-1, 1),
np.linspace(axis[2], axis[3], int((axis[3]-axis[2])*100)).reshape(-1, 1),
)
X_new = np.c_[x0.ravel(), x1.ravel()]
y_predict = model.predict(X_new)
zz = y_predict.reshape(x0.shape)
from matplotlib.colors import ListedColormap
custom_cmap = ListedColormap(['#EF9A9A','#FFF59D','#90CAF9'])
plt.contourf(x0, x1, zz, cmap=custom_cmap)
w = model.coef_[0]
b = model.intercept_[0]
# w0*x0 + w1*x1 + b = 0
# => x1 = -w0/w1 * x0 - b/w1
plot_x = np.linspace(axis[0], axis[1], 200)
up_y = -w[0]/w[1] * plot_x - b/w[1] + 1/w[1]
down_y = -w[0]/w[1] * plot_x - b/w[1] - 1/w[1]
up_index = (up_y >= axis[2]) & (up_y <= axis[3])
down_index = (down_y >= axis[2]) & (down_y <= axis[3])
plt.plot(plot_x[up_index], up_y[up_index], color='black')
plt.plot(plot_x[down_index], down_y[down_index], color='black')
plot_svc_decision_boundary(svc,axis=[-3,3,-3,3])
plt.scatter(x_standard[y==0,0],x_standard[y==0,1],color='red')
plt.scatter(x_standard[y==1,0],x_standard[y==1,1],color='blue')
plt.show()
plot_svc_decision_boundary(svc2,axis=[-3,3,-3,3])
plt.scatter(x_standard[y==0,0],x_standard[y==0,1],color='red')
plt.scatter(x_standard[y==1,0],x_standard[y==1,1],color='blue')
plt.show()
