Plot Label Propagation Digits¶
=================================================== Label Propagation digits: Demonstrating performance¶
This example demonstrates the power of semisupervised learning by training a Label Spreading model to classify handwritten digits with sets of very few labels.
The handwritten digit dataset has 1797 total points. The model will be trained using all points, but only 30 will be labeled. Results in the form of a confusion matrix and a series of metrics over each class will be very good.
At the end, the top 10 most uncertain predictions will be shown.
Imports for Label Spreading on Handwritten Digits with Few Labels¶
LabelSpreading propagates known labels through a similarity graph to classify unlabeled samples: Given 340 digit samples where only 40 have labels (the remaining 300 are marked as -1), the algorithm constructs a graph where edge weights reflect pairwise similarity (controlled by gamma=0.25), then iteratively spreads label information from labeled nodes to their neighbors until convergence. Each unlabeled sample receives a soft label distribution (label_distributions_) representing its estimated probability of belonging to each class, and the final hard prediction (transduction_) is the argmax of this distribution. The key insight is that samples connected by high-similarity paths in the feature space tend to share the same label, even when only a tiny fraction of labels are known.
Prediction uncertainty via entropy identifies samples the model is least confident about: Computing the Shannon entropy of each sample’s label distribution using scipy.stats.distributions.entropy produces a scalar measure of prediction uncertainty – high entropy means the model spreads probability mass across multiple classes, indicating confusion. Displaying the 10 most uncertain predictions alongside their true labels reveals where the model struggles, often at digit boundaries (e.g., confusing 3s and 8s, or 4s and 9s). This uncertainty quantification is a natural byproduct of the graph-based approach and is valuable for active learning, where a human annotator would prioritize labeling the most uncertain samples to maximally improve the model.
# Authors: The scikit-learn developers
# SPDX-License-Identifier: BSD-3-Clause
# %%
# Data generation
# ---------------
#
# We use the digits dataset. We only use a subset of randomly selected samples.
import numpy as np
from sklearn import datasets
digits = datasets.load_digits()
rng = np.random.RandomState(2)
indices = np.arange(len(digits.data))
rng.shuffle(indices)
# %%
#
# We selected 340 samples of which only 40 will be associated with a known label.
# Therefore, we store the indices of the 300 other samples for which we are not
# supposed to know their labels.
X = digits.data[indices[:340]]
y = digits.target[indices[:340]]
images = digits.images[indices[:340]]
n_total_samples = len(y)
n_labeled_points = 40
indices = np.arange(n_total_samples)
unlabeled_set = indices[n_labeled_points:]
# %%
# Shuffle everything around
y_train = np.copy(y)
y_train[unlabeled_set] = -1
# %%
# Semi-supervised learning
# ------------------------
#
# We fit a :class:`~sklearn.semi_supervised.LabelSpreading` and use it to predict
# the unknown labels.
from sklearn.metrics import classification_report
from sklearn.semi_supervised import LabelSpreading
lp_model = LabelSpreading(gamma=0.25, max_iter=20)
lp_model.fit(X, y_train)
predicted_labels = lp_model.transduction_[unlabeled_set]
true_labels = y[unlabeled_set]
print(
"Label Spreading model: %d labeled & %d unlabeled points (%d total)"
% (n_labeled_points, n_total_samples - n_labeled_points, n_total_samples)
)
# %%
# Classification report
print(classification_report(true_labels, predicted_labels))
# %%
# Confusion matrix
from sklearn.metrics import ConfusionMatrixDisplay
ConfusionMatrixDisplay.from_predictions(
true_labels, predicted_labels, labels=lp_model.classes_
)
# %%
# Plot the most uncertain predictions
# -----------------------------------
#
# Here, we will pick and show the 10 most uncertain predictions.
from scipy import stats
pred_entropies = stats.distributions.entropy(lp_model.label_distributions_.T)
# %%
# Pick the top 10 most uncertain labels
uncertainty_index = np.argsort(pred_entropies)[-10:]
# %%
# Plot
import matplotlib.pyplot as plt
f = plt.figure(figsize=(7, 5))
for index, image_index in enumerate(uncertainty_index):
image = images[image_index]
sub = f.add_subplot(2, 5, index + 1)
sub.imshow(image, cmap=plt.cm.gray_r)
plt.xticks([])
plt.yticks([])
sub.set_title(
"predict: %i\ntrue: %i" % (lp_model.transduction_[image_index], y[image_index])
)
f.suptitle("Learning with small amount of labeled data")
plt.show()