Label Propagation learning a complex structureΒΆ

Example of LabelPropagation learning a complex internal structure to demonstrate “manifold learning”. The outer circle should be labeled “red” and the inner circle “blue”. Because both label groups lie inside their own distinct shape, we can see that the labels propagate correctly around the circle.


# Authors: Clay Woolam <>
#          Andreas Mueller <>
# License: BSD

import numpy as np
import matplotlib.pyplot as plt
from sklearn.semi_supervised import label_propagation
from sklearn.datasets import make_circles

# generate ring with inner box
n_samples = 200
X, y = make_circles(n_samples=n_samples, shuffle=False)
outer, inner = 0, 1
labels = -np.ones(n_samples)
labels[0] = outer
labels[-1] = inner

Learn with LabelSpreading

label_spread = label_propagation.LabelSpreading(kernel='knn', alpha=1.0), labels)

Plot output labels

output_labels = label_spread.transduction_
plt.figure(figsize=(8.5, 4))
plt.subplot(1, 2, 1)
plt.scatter(X[labels == outer, 0], X[labels == outer, 1], color='navy',
            marker='s', lw=0, label="outer labeled", s=10)
plt.scatter(X[labels == inner, 0], X[labels == inner, 1], color='c',
            marker='s', lw=0, label='inner labeled', s=10)
plt.scatter(X[labels == -1, 0], X[labels == -1, 1], color='darkorange',
            marker='.', label='unlabeled')
plt.legend(scatterpoints=1, shadow=False, loc='upper right')
plt.title("Raw data (2 classes=outer and inner)")

plt.subplot(1, 2, 2)
output_label_array = np.asarray(output_labels)
outer_numbers = np.where(output_label_array == outer)[0]
inner_numbers = np.where(output_label_array == inner)[0]
plt.scatter(X[outer_numbers, 0], X[outer_numbers, 1], color='navy',
            marker='s', lw=0, s=10, label="outer learned")
plt.scatter(X[inner_numbers, 0], X[inner_numbers, 1], color='c',
            marker='s', lw=0, s=10, label="inner learned")
plt.legend(scatterpoints=1, shadow=False, loc='upper right')
plt.title("Labels learned with Label Spreading (KNN)")

plt.subplots_adjust(left=0.07, bottom=0.07, right=0.93, top=0.92)

Total running time of the script: (0 minutes 0.122 seconds)

Download Python source code:
Download IPython notebook: plot_label_propagation_structure.ipynb