I found this wonderful graph in post here Variation on "How to plot decision boundary of a k-nearest neighbor classifier from Elements of Statistical Learning?". In this example K-NN is used to clasify data into three classes. I especially enjoy that it features the probability of class membership as a indication of the "confidence".
r
and ggplot
seem to do a great job.I wonder, whether this can be re-created in python? My initial thought tends to scikit-learn
and matplotlib
. Here is the iris example from scikit:
print(__doc__)
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.colors import ListedColormap
from sklearn import neighbors, datasets
n_neighbors = 15
# import some data to play with
iris = datasets.load_iris()
X = iris.data[:, :2] # we only take the first two features. We could
# avoid this ugly slicing by using a two-dim dataset
y = iris.target
h = .02 # step size in the mesh
# Create color maps
cmap_light = ListedColormap(['#FFAAAA', '#AAFFAA', '#AAAAFF'])
cmap_bold = ListedColormap(['#FF0000', '#00FF00', '#0000FF'])
for weights in ['uniform', 'distance']:
# we create an instance of Neighbours Classifier and fit the data.
clf = neighbors.KNeighborsClassifier(n_neighbors, weights=weights)
clf.fit(X, y)
# 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 = X[:, 0].min() - 1, X[:, 0].max() + 1
y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1
xx, yy = np.meshgrid(np.arange(x_min, x_max, h),
np.arange(y_min, y_max, h))
Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
# Put the result into a color plot
Z = Z.reshape(xx.shape)
plt.figure()
plt.pcolormesh(xx, yy, Z, cmap=cmap_light)
# Plot also the training points
plt.scatter(X[:, 0], X[:, 1], c=y, cmap=cmap_bold)
plt.xlim(xx.min(), xx.max())
plt.ylim(yy.min(), yy.max())
plt.title("3-Class classification (k = %i, weights = '%s')"
% (n_neighbors, weights))
plt.show()
This produces a graph in a sense very similar:
I have three questions:
- How can I introduce the confidence to the plot?
- How can I plot the decision-boundaries with a connected line?
- Let's say I have a new observation, how can I introduce it to the plot and plot if it is classified correctly?
I stumbled upon your question about a year ago, and loved the plot -- I just never got around to answering it, until now. Hopefully the code comments below are self-explanitory enough (I also blogged about, if you want more details). Maybe four years too late, haha.