如何从k最近邻预测中提取边界值

问题描述

• 对于sklearn.neighbors.KNeighborsClassifier()，如何仅从.predict提取或返回边界值？

MRE

import pandas as pd
import numpy as np
from sklearn.datasets import load_iris
from sklearn.neighbors import KNeighborsClassifier
import seaborn as sns
import matplotlib.pyplot as plt
from matplotlib.colors import ListedColormap

# prepare data
iris = load_iris()
X = iris.data
y = iris.target
df = pd.DataFrame(X,columns=iris.feature_names)
df['label'] = y
species_map = dict(zip(range(3),iris.target_names))
df['species'] = df.label.map(species_map)
df = df.reindex(['sepal length (cm)','sepal width (cm)','petal length (cm)','petal width (cm)','species','label'],axis=1)

# instantiate model
knn = KNeighborsClassifier(n_neighbors=6)

# predict for 'petal length (cm)' and 'petal width (cm)'
knn.fit(df.iloc[:,2:4],df.label)

h = .02  # step size in the mesh

# create colormap for the contour plot
cmap_light = ListedColormap(list(sns.color_palette('pastel',n_colors=3)))

# Plot the decision boundary.
# For that,we will assign a color to each point in the mesh [x_min,x_max]x[y_min,y_max].
x_min,x_max = df['petal length (cm)'].min() - 1,df['petal length (cm)'].max() + 1
y_min,y_max = df['petal width (cm)'].min() - 1,df['petal width (cm)'].max() + 1
xx,yy = np.meshgrid(np.arange(x_min,x_max,h),np.arange(y_min,y_max,h))
Z = knn.predict(np.c_[xx.ravel(),yy.ravel()]).reshape(xx.shape)

# create plot
fig,ax = plt.subplots()

# add data points
sns.scatterplot(data=df,x='petal length (cm)',y='petal width (cm)',hue='species',ax=ax,edgecolor='k')

# add decision boundary countour map
ax.contourf(xx,yy,Z,cmap=cmap_light,alpha=0.4)

# legend
lgd = plt.legend(bBox_to_anchor=(1.05,1),loc='upper left')

plt.show()

结果图

所需图

• 没有颜色或样式，只是具有决策边界和数据点。

资源

• scikit-learn: Nearest Neighbors Classification
• scikit-learn: Plot the decision boundaries of a VotingClassifier
• scikit-learn: Comparing Nearest Neighbors with and without Neighborhood Components Analysis

无法回答问题的问题

• Plotting a decision boundary separating 2 classes using Matplotlib's pyplot
  • 此solution显示了如何在不填充图的情况下绘制决策边界，但是没有答案显示如何提取决策边界值。
    • plt.contour(xx,cmap=plt.cm.Paired)

自我回答

• 我提供了 a 解决方案，但是我不确定这是否是最好的解决方案。我当然愿意接受其他选择。
• 也就是说，我不希望在contourf或pcolormesh情节中着色的解决方案。
• 最好的解决方案是简洁地仅提取决策边界值。

解决方法

• 这是我想到的一种解决方案，它在Z的两个轴上使用np.diff，得到.predict的结果。这个想法是，只要结果发生变化，这就是决策边界。
  • 使用.diff从自身中减去Z，移位1。
  • 使用mask创建np.diff(Z) != 0
  • 使用mask从x和y中选择适当的xx和yy
• 使用OP中的现有代码

# use diff to create a mask
mask = np.diff(Z,axis=1) != 0
mask2 = np.diff(Z,axis=0) != 0

# apply mask against xx and yy
xd = np.concatenate((xx[:,1:][mask],xx[1:,:][mask2]))
yd = np.concatenate((yy[:,yy[1:,:][mask2]))

# plot just the decision boundary
fig,ax = plt.subplots()
sns.scatterplot(x=xd,y=yd,color='k',edgecolor='k',s=5,ax=ax,label='decision boundary')
plt.show()

fig,ax = plt.subplots()
sns.scatterplot(data=df,x='petal length (cm)',y='petal width (cm)',hue='species',edgecolor='k')
sns.scatterplot(x=xd,label='decision boundary')
lgd = plt.legend(bbox_to_anchor=(1.05,1),loc='upper left')

xd和yd正确覆盖plt.contourf