How to extract the boundary values from k-nearest neighbors predict

问题

How can only the boundary values be extracted, or returned, from .predict, for sklearn.neighbors.KNeighborsClassifier()?

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()

Resulting Plot

Desired Plot

Not the colors, or styles, just that it has only the decision boundary, and the data points.

Resources

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

SO Question that doesn't answer the question

Plotting a decision boundary separating 2 classes using Matplotlib's pyplot
- This solution shows how to plot the decision boundary without filling the plot, but none of the answers show how to extract the decision boundary values.
  - plt.contour(xx, yy, Z, cmap=plt.cm.Paired)

Self Answered

I have provided a solution, but I'm not sure if it's the best solution. I'm certainly open to other options.
That said, I do not want a solution that is a colored in contourf, or pcolormesh plot.
The best solution would, succinctly, extract only the decision boundary values.

回答1:

This is one solution that I came up with, which uses np.diff along both axes of Z, the .predict result. The idea being, whenever there is a change in result, that is a decision boundary.
- Use .diff to subtract Z from itself, shifted by 1.
- Create mask, using np.diff(Z) != 0
- Use mask to select the appropriate x and y from xx and yy
Using the existing code from the OP

# 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[:, 1:][mask], 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', ax=ax, edgecolor='k')
sns.scatterplot(x=xd, y=yd, color='k', edgecolor='k', s=5, ax=ax, label='decision boundary')
lgd = plt.legend(bbox_to_anchor=(1.05, 1), loc='upper left')