逻辑回归-3.决策边界

左手的ㄟ右手 2023-08-17 16:44 159阅读 0赞

# 决策边界 #

![1465169-20190902184224779-1578797120.png][]  
我们可以看出 决定y取不同值的边界为：\\\[ \\theta^T \\cdot x\_b = 0 \\\]  
上式表达式是一条直线，为决策边界，如果新来一个样本，和训练后得到的$ \\theta $相乘，根据是否大于0，决定到底属于哪一类

## 画出决策边界 ##

如果样本有两个特征\$x1,x2\$，则决策边界有：\$\\theta\_0 + \\theta\_1 \\cdot x1 +\\theta\_2 \\cdot x2 = 0\$ ，求得\$x2 = \\frac\{-\\theta\_0 - \\theta\_1 \\cdot x1\}\{\\theta\_2\}\$

# 定义x2和x1的关系表达式
    def x2(x1):
        return (-logic_reg.interception_ - logic_reg.coef_[0] * x1)/logic_reg.coef_[1]
        
    x1_plot = numpy.linspace(4,8,1000)
    x2_plot = x2(x1_plot)
    
    pyplot.scatter(X[y==0,0],X[y==0,1],color='red')
    pyplot.scatter(X[y==1,0],X[y==1,1],color='blue')
    pyplot.plot(x1_plot,x2_plot)
    pyplot.show()

![1465169-20190902184244362-1462900009.png][]

## 不规则决策边界的绘制 ##

特征域(为了可视化,特征值取2,即矩形区域)中可视化区域中所有的点，查看不规则决策边界  
定义绘制特征域中所有点的函数：

def plot_decision_boundary(model,axis):
        x0,x1 = numpy.meshgrid(
            numpy.linspace(axis[0],axis[1],int((axis[1]-axis[0])*100)),
            numpy.linspace(axis[2],axis[3],int((axis[3]-axis[2])*100))
        )
        x_new = numpy.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'])
        pyplot.contourf(x0,x1,zz,cmap=custom_cmap)

绘制逻辑回归的决策边界：

plot_decision_boundary(logic_reg,axis=[4,7.5,1.5,4.5])
    pyplot.scatter(X[y==0,0],X[y==0,1],color='blue')
    pyplot.scatter(X[y==1,0],X[y==1,1],color='red')
    pyplot.show()

![1465169-20190902184259733-1194108155.png][]

绘制K近邻算法的决策边界：

from mylib import KNN
    
    knn_clf_all = KNN.KNNClassifier(k=3)
    knn_clf_all.fit(iris.data[:,:2],iris.target)
    
    plot_decision_boundary(knn_clf_all,axis=[4,8,1.5,4.5])
    pyplot.scatter(iris.data[iris.target==0,0],iris.data[iris.target==0,1])
    pyplot.scatter(iris.data[iris.target==1,0],iris.data[iris.target==1,1])
    pyplot.scatter(iris.data[iris.target==2,0],iris.data[iris.target==2,1])
    pyplot.show()

k近邻多分类(种类为3)下的决策边界  
k取3时：  
![1465169-20190902184320415-959433069.png][]

k取50时：  
![1465169-20190902184329408-845050647.png][]

转载于:https://www.cnblogs.com/shuai-long/p/11448236.html

[1465169-20190902184224779-1578797120.png]: /images/20230809/afa219f9163e40d5ad6be3d3d695e28e.png
[1465169-20190902184244362-1462900009.png]: /images/20230809/39adc47433a7448393435cd0bf461b04.png
[1465169-20190902184259733-1194108155.png]: /images/20230809/a4fd9a3d945447559a85d8ca04b576dc.png
[1465169-20190902184320415-959433069.png]: /images/20230809/82996a6f465a4d2980f6440083ca5e54.png
[1465169-20190902184329408-845050647.png]: /images/20230809/f06e76ef82db4617af3d6e7eabe58baa.png