11-8 scikit-learn中的高斯核函数

gamma参数的意义

加载数据

import numpy as np
import matplotlib.pyplot as plt
from sklearn import datasets

X, y = datasets.make_moons()
X, y = datasets.make_moons(noise=0.15, random_state=666)

plt.scatter(X[y==0,0],X[y==0,1])
plt.scatter(X[y==1,0],X[y==1,1])
plt.show()

训练高斯核的SVM

from sklearn.preprocessing import StandardScaler
from sklearn.svm import SVC
from sklearn.pipeline import Pipeline

def RBFKernelSVC(gamma=1.0):
    return Pipeline([
        ('std_scaler', StandardScaler()),
        ('rbfSVC', SVC(kernel='rbf', gamma= gamma))
    ])

svc = PolynomialKernelSVC()
svc.fit(X, y)

绘制决策边界

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=[-1.5,2.5,-1.0,1.5])
plt.scatter(X[y==0,0],X[y==0,1])
plt.scatter(X[y==1,0],X[y==1,1])
plt.show()

gamma取不同值的效果对比

gamma=1.0	gamma=100	gamma=0.5	gamma=0.1	gamma=10

可以把训练的效果看成是俯视这些样本点。某一类的每个样本点形成了一个以它为中心的正态分布。 gamma越大，这个分布的圈就越小。