python机器学习：SVM（7）

import numpy as np
import matplotlib.pyplot as plt
import numpy as np
import matplotlib.pyplot as plt

def plot_decision_boundary(model, axis):
    """绘制不规则决策边界"""
    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, linewidth=5, cmap=custom_cmap)

def plot_svc_decision_boundary(model, axis):
    plot_decision_boundary(model, axis)
    w = model.coef_[0]
    b = model.intercept_[0]

    # 绘制margin的直线
    # 决策边界所在直线的表达式：w0 * x0 + w1 * x1 + b = 0  -> x1 = -w0 * x0 / w1 - b / w1
    plot_x = np.linspace(axis[0], axis[1], 200)

    # w0 * x0 + w1 * x1 + b = 1  -> x1 = 1/w1 - w0 * x0 / w1 - b / w1
    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]

    # 处理超过了坐标轴范围的值
    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')

from sklearn import datasets

iris = datasets.load_iris()

X = iris.data
y = iris.target

# 为方便可视化，只取前2个特征；
# 暂时只处理2分类问题，所以只取2个类别
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()

我们只是想看分类结果的可视化，不需要对未知数据进行预测，所以就不区分训练集与测试集

from sklearn.preprocessing.data import StandardScaler

standard_scaler = StandardScaler()
standard_scaler.fit(X)
X_standard = standard_scaler.transform(X)
from sklearn.svm.classes import LinearSVC

# C取值越大，就越倾向于是一个hard margin
svc = LinearSVC(C=1e9)
svc.fit(X_standard, y)

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()

svc_2 = LinearSVC(C=0.01)
svc_2.fit(X_standard, y)
plot_decision_boundary(svc_2, 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_
svc.intercept_

可以看到系数和截距都是数组，这是因为sklearn已经预先为我们处理了使svm可以处理多分类任务，每多一个分类就等于多一条线/平面/超平面，于是系数和截距的数组就多一个元素。

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(svc_2, 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()