# 11-8 scikit-learn中的高斯核函数

## gamma参数的意义

![](http://windmissing.github.io/images/2019/252.jpg)

## 加载数据

```python
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()
```

![](http://windmissing.github.io/images/2019/234.png)

## 训练高斯核的SVM

```python
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

```python
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()
```

![](http://windmissing.github.io/images/2019/253.png)

## gamma取不同值的效果对比

| ![](http://windmissing.github.io/images/2019/253.png) | ![](http://windmissing.github.io/images/2019/254.png) | ![](http://windmissing.github.io/images/2019/255.png) | ![](http://windmissing.github.io/images/2019/256.png) | ![](http://windmissing.github.io/images/2019/257.png) |
| ----------------------------------------------------- | ----------------------------------------------------- | ----------------------------------------------------- | ----------------------------------------------------- | ----------------------------------------------------- |
| 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。


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