"""
==================================================
Principal Component Analysis (PCA) on Iris Dataset
==================================================

This example shows a well known decomposition technique known as Principal Component
Analysis (PCA) on the
`Iris dataset <https://en.wikipedia.org/wiki/Iris_flower_data_set>`_.

This dataset is made of 4 features: sepal length, sepal width, petal length, petal
width. We use PCA to project this 4 feature space into a 3-dimensional space.
"""

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

# %%
# Loading the Iris dataset
# ------------------------
#
# The Iris dataset is directly available as part of scikit-learn. It can be loaded
# using the :func:`~sklearn.datasets.load_iris` function. With the default parameters,
# a :class:`~sklearn.utils.Bunch` object is returned, containing the data, the
# target values, the feature names, and the target names.
from sklearn.datasets import load_iris

iris = load_iris(as_frame=True)
print(iris.keys())

# %%
# Plot of pairs of features of the Iris dataset
# ---------------------------------------------
#
# Let's first plot the pairs of features of the Iris dataset.
import seaborn as sns

# Rename classes using the iris target names
iris.frame["target"] = iris.target_names[iris.target]
_ = sns.pairplot(iris.frame, hue="target")

# %%
# Each data point on each scatter plot refers to one of the 150 iris flowers
# in the dataset, with the color indicating their respective type
# (Setosa, Versicolor, and Virginica).
#
# You can already see a pattern regarding the Setosa type, which is
# easily identifiable based on its short and wide sepal. Only
# considering these two dimensions, sepal width and length, there's still
# overlap between the Versicolor and Virginica types.
#
# The diagonal of the plot shows the distribution of each feature. We observe
# that the petal width and the petal length are the most discriminant features
# for the three types.
#
# Plot a PCA representation
# -------------------------
# Let's apply a Principal Component Analysis (PCA) to the iris dataset
# and then plot the irises across the first three PCA dimensions.
# This will allow us to better differentiate among the three types!

import matplotlib.pyplot as plt

# unused but required import for doing 3d projections with matplotlib < 3.2
import mpl_toolkits.mplot3d  # noqa: F401

from sklearn.decomposition import PCA

fig = plt.figure(1, figsize=(8, 6))
ax = fig.add_subplot(111, projection="3d", elev=-150, azim=110)

X_reduced = PCA(n_components=3).fit_transform(iris.data)
scatter = ax.scatter(
    X_reduced[:, 0],
    X_reduced[:, 1],
    X_reduced[:, 2],
    c=iris.target,
    s=40,
)

ax.set(
    title="First three PCA dimensions",
    xlabel="1st Eigenvector",
    ylabel="2nd Eigenvector",
    zlabel="3rd Eigenvector",
)
ax.xaxis.set_ticklabels([])
ax.yaxis.set_ticklabels([])
ax.zaxis.set_ticklabels([])

# Add a legend
legend1 = ax.legend(
    scatter.legend_elements()[0],
    iris.target_names.tolist(),
    loc="upper right",
    title="Classes",
)
ax.add_artist(legend1)

plt.show()

# %%
# PCA will create 3 new features that are a linear combination of the 4 original
# features. In addition, this transformation maximizes the variance. With this
# transformation, we see that we can identify each species using only the first feature
# (i.e., first eigenvector).