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Label Propagation learning a complex structure#
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: The scikit-learn developers
# SPDX-License-Identifier: BSD-3-Clause
We generate a dataset with two concentric circles. In addition, a label is associated with each sample of the dataset that is: 0 (belonging to the outer circle), 1 (belonging to the inner circle), and -1 (unknown). Here, all labels but two are tagged as unknown.
import numpy as np
from sklearn.datasets import make_circles
n_samples = 200
X, y = make_circles(n_samples=n_samples, shuffle=False)
outer, inner = 0, 1
labels = np.full(n_samples, -1.0)
labels[0] = outer
labels[-1] = inner
Plot raw data
import matplotlib.pyplot as plt
plt.figure(figsize=(4, 4))
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="center")
_ = plt.title("Raw data (2 classes=outer and inner)")
The aim of LabelSpreading
is to associate
a label to sample where the label is initially unknown.
from sklearn.semi_supervised import LabelSpreading
label_spread = LabelSpreading(kernel="knn", alpha=0.8)
label_spread.fit(X, labels)
Now, we can check which labels have been associated with each sample when the label was unknown.
output_labels = label_spread.transduction_
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.figure(figsize=(4, 4))
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="center")
plt.title("Labels learned with Label Spreading (KNN)")
plt.show()
Total running time of the script: (0 minutes 0.154 seconds)
Related examples
Demo of DBSCAN clustering algorithm
A demo of the Spectral Biclustering algorithm
Demo of affinity propagation clustering algorithm
Label Propagation digits: Demonstrating performance