"""
===============================================================================
Decision boundary of semi-supervised classifiers versus SVM on the Iris dataset
===============================================================================

This example compares decision boundaries learned by two semi-supervised
methods, namely :class:`~sklearn.semi_supervised.LabelSpreading` and
:class:`~sklearn.semi_supervised.SelfTrainingClassifier`, while varying the
proportion of labeled training data from small fractions up to the full dataset.

Both methods rely on RBF kernels: :class:`~sklearn.semi_supervised.LabelSpreading` uses
it by default, and :class:`~sklearn.semi_supervised.SelfTrainingClassifier` is paired
here with :class:`~sklearn.svm.SVC` as base estimator (also RBF-based by default) to
allow a fair comparison. With 100% labeled data,
:class:`~sklearn.semi_supervised.SelfTrainingClassifier` reduces to a fully supervised
:class:`~sklearn.svm.SVC`, since there are no unlabeled points left to pseudo-label.

In a second section, we explain how `predict_proba` is computed in
:class:`~sklearn.semi_supervised.LabelSpreading` and
:class:`~sklearn.semi_supervised.SelfTrainingClassifier`.

See
:ref:`sphx_glr_auto_examples_semi_supervised_plot_semi_supervised_newsgroups.py`
for a comparison of `LabelSpreading` and `SelfTrainingClassifier` in terms of
performance.
"""

# Authors: The scikit-learn developers
# SPDX-License-Identifier: BSD-3-Clause

# %%
import matplotlib.patches as mpatches
import matplotlib.pyplot as plt
import numpy as np

from sklearn.datasets import load_iris
from sklearn.inspection import DecisionBoundaryDisplay
from sklearn.semi_supervised import LabelSpreading, SelfTrainingClassifier
from sklearn.svm import SVC

iris = load_iris()
X = iris.data[:, :2]
y = iris.target

rng = np.random.RandomState(42)
y_rand = rng.rand(y.shape[0])
y_10 = np.copy(y)
y_10[y_rand > 0.1] = -1  # set random samples to be unlabeled
y_30 = np.copy(y)
y_30[y_rand > 0.3] = -1

ls10 = (LabelSpreading().fit(X, y_10), y_10, "LabelSpreading with 10% labeled data")
ls30 = (LabelSpreading().fit(X, y_30), y_30, "LabelSpreading with 30% labeled data")
ls100 = (LabelSpreading().fit(X, y), y, "LabelSpreading with 100% labeled data")

base_classifier = SVC(gamma=0.5, probability=True, random_state=42)
st10 = (
    SelfTrainingClassifier(base_classifier).fit(X, y_10),
    y_10,
    "Self-training with 10% labeled data",
)
st30 = (
    SelfTrainingClassifier(base_classifier).fit(X, y_30),
    y_30,
    "Self-training with 30% labeled data",
)
rbf_svc = (
    base_classifier.fit(X, y),
    y,
    "SVC with rbf kernel\n(equivalent to Self-training with 100% labeled data)",
)

tab10 = plt.get_cmap("tab10")
color_map = {cls: tab10(cls) for cls in np.unique(y)}
color_map[-1] = (1, 1, 1)
classifiers = (ls10, st10, ls30, st30, ls100, rbf_svc)

fig, axes = plt.subplots(nrows=3, ncols=2, sharex="col", sharey="row", figsize=(10, 12))
axes = axes.ravel()

handles = [
    mpatches.Patch(facecolor=tab10(i), edgecolor="black", label=iris.target_names[i])
    for i in np.unique(y)
]
handles.append(mpatches.Patch(facecolor="white", edgecolor="black", label="Unlabeled"))

for ax, (clf, y_train, title) in zip(axes, classifiers):
    DecisionBoundaryDisplay.from_estimator(
        clf,
        X,
        response_method="predict_proba",
        plot_method="contourf",
        ax=ax,
    )
    colors = [color_map[label] for label in y_train]
    ax.scatter(X[:, 0], X[:, 1], c=colors, edgecolor="black")
    ax.set_title(title)
fig.suptitle(
    "Semi-supervised decision boundaries with varying fractions of labeled data", y=1
)
fig.legend(
    handles=handles, loc="lower center", ncol=len(handles), bbox_to_anchor=(0.5, 0.0)
)
fig.tight_layout(rect=[0, 0.03, 1, 1])
plt.show()

# %%
# We observe that the decision boundaries are already quite similar to those
# using the full labeled data available for training, even when using a very
# small subset of the labels.
#
# Interpretation of `predict_proba`
# =================================
#
# `predict_proba` in `LabelSpreading`
# -----------------------------------
#
# :class:`~sklearn.semi_supervised.LabelSpreading` constructs a similarity graph
# from the data, by default using an RBF kernel. This means each sample is
# connected to every other with a weight that decays with their squared
# Euclidean distance, scaled by a parameter `gamma`.
#
# Once we have that weighted graph, labels are propagated along the graph
# edges. Each sample gradually takes on a soft label distribution that reflects
# a weighted average of the labels of its neighbors until the process converges.
# These per-sample distributions are stored in `label_distributions_`.
#
# `predict_proba` computes the class probabilities for a new point by taking a
# weighted average of the rows in `label_distributions_`, where the weights come
# from the RBF kernel similarities between the new point and the training
# samples. The averaged values are then renormalized so that they sum to one.
#
# Just keep in mind that these "probabilities" are graph-based scores, not
# calibrated posteriors. Don't over-interpret their absolute values.

from sklearn.metrics.pairwise import rbf_kernel

ls = ls100[0]  # fitted LabelSpreading instance
x_query = np.array([[3.5, 1.5]])  # point in the soft blue region

# Step 1: similarities between query and all training samples
W = rbf_kernel(x_query, X, gamma=ls.gamma)  # `gamma=20` by default

# Step 2: weighted average of label distributions
probs = np.dot(W, ls.label_distributions_)

# Step 3: normalize to sum to 1
probs /= probs.sum(axis=1, keepdims=True)

print("Manual:", probs)
print("API   :", ls.predict_proba(x_query))

# %%
# `predict_proba` in `SelfTrainingClassifier`
# ----------------------------------------------
#
# :class:`~sklearn.semi_supervised.SelfTrainingClassifier` works by repeatedly
# fitting its base estimator on the currently labeled data, then adding
# pseudo-labels for unlabeled points whose predicted probabilities exceed a
# confidence threshold. This process continues until no new points can be
# labeled, at which point the classifier has a final fitted base estimator
# stored in the attribute `estimator_`.
#
# When you call `predict_proba` on the `SelfTrainingClassifier`, it simply
# delegates to this final estimator.

st = st10[0]
print("Manual:", st.estimator_.predict_proba(x_query))
print("API   :", st.predict_proba(x_query))

# %%
# In both methods, semi-supervised learning can be understood as constructing a
# categorical distribution over classes for each sample.
# :class:`~sklearn.semi_supervised.LabelSpreading` keeps these distributions soft and
# updates them through graph-based propagation.
# Predictions (including `predict_proba`) remain tied to the training set, which
# must be stored for inference.
#
# :class:`~sklearn.semi_supervised.SelfTrainingClassifier` instead uses these
# distributions internally to decide which unlabeled points to assign pseudo-labels
# during training, but at prediction time the returned probabilities come directly from
# the final fitted estimator, and therefore the decision rule does not require storing
# the training data.