咱们能够看出 决定y取不一样值的边界为:\[ \theta^T \cdot x_b = 0 \]
上式表达式是一条直线,为决策边界,若是新来一个样本,和训练后获得的$ \theta $相乘,根据是否大于0,决定到底属于哪一类算法
若是样本有两个特征\(x1,x2\),则决策边界有:\(\theta_0 + \theta_1 \cdot x1 +\theta_2 \cdot x2 = 0\) ,求得\(x2 = \frac{-\theta_0 - \theta_1 \cdot x1}{\theta_2}\)函数
# 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()
特征域(为了可视化,特征值取2,即矩形区域)中可视化区域中全部的点,查看不规则决策边界
定义绘制特征域中全部点的函数:spa
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:code
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()
绘制K近邻算法的决策边界:orm
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:
blog
k取50时:
ci