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.. "auto_examples/cluster/plot_kmeans_digits.py"
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.. rst-class:: sphx-glr-example-title
.. _sphx_glr_auto_examples_cluster_plot_kmeans_digits.py:
===========================================================
A demo of K-Means clustering on the handwritten digits data
===========================================================
In this example we compare the various initialization strategies for K-means in
terms of runtime and quality of the results.
As the ground truth is known here, we also apply different cluster quality
metrics to judge the goodness of fit of the cluster labels to the ground truth.
Cluster quality metrics evaluated (see :ref:`clustering_evaluation` for
definitions and discussions of the metrics):
=========== ========================================================
Shorthand full name
=========== ========================================================
homo homogeneity score
compl completeness score
v-meas V measure
ARI adjusted Rand index
AMI adjusted mutual information
silhouette silhouette coefficient
=========== ========================================================
.. GENERATED FROM PYTHON SOURCE LINES 29-35
Load the dataset
----------------
We will start by loading the `digits` dataset. This dataset contains
handwritten digits from 0 to 9. In the context of clustering, one would like
to group images such that the handwritten digits on the image are the same.
.. GENERATED FROM PYTHON SOURCE LINES 35-45
.. code-block:: default
import numpy as np
from sklearn.datasets import load_digits
data, labels = load_digits(return_X_y=True)
(n_samples, n_features), n_digits = data.shape, np.unique(labels).size
print(f"# digits: {n_digits}; # samples: {n_samples}; # features {n_features}")
.. rst-class:: sphx-glr-script-out
.. code-block:: none
# digits: 10; # samples: 1797; # features 64
.. GENERATED FROM PYTHON SOURCE LINES 46-56
Define our evaluation benchmark
-------------------------------
We will first our evaluation benchmark. During this benchmark, we intend to
compare different initialization methods for KMeans. Our benchmark will:
* create a pipeline which will scale the data using a
:class:`~sklearn.preprocessing.StandardScaler`;
* train and time the pipeline fitting;
* measure the performance of the clustering obtained via different metrics.
.. GENERATED FROM PYTHON SOURCE LINES 56-113
.. code-block:: default
from time import time
from sklearn import metrics
from sklearn.pipeline import make_pipeline
from sklearn.preprocessing import StandardScaler
def bench_k_means(kmeans, name, data, labels):
"""Benchmark to evaluate the KMeans initialization methods.
Parameters
----------
kmeans : KMeans instance
A :class:`~sklearn.cluster.KMeans` instance with the initialization
already set.
name : str
Name given to the strategy. It will be used to show the results in a
table.
data : ndarray of shape (n_samples, n_features)
The data to cluster.
labels : ndarray of shape (n_samples,)
The labels used to compute the clustering metrics which requires some
supervision.
"""
t0 = time()
estimator = make_pipeline(StandardScaler(), kmeans).fit(data)
fit_time = time() - t0
results = [name, fit_time, estimator[-1].inertia_]
# Define the metrics which require only the true labels and estimator
# labels
clustering_metrics = [
metrics.homogeneity_score,
metrics.completeness_score,
metrics.v_measure_score,
metrics.adjusted_rand_score,
metrics.adjusted_mutual_info_score,
]
results += [m(labels, estimator[-1].labels_) for m in clustering_metrics]
# The silhouette score requires the full dataset
results += [
metrics.silhouette_score(
data,
estimator[-1].labels_,
metric="euclidean",
sample_size=300,
)
]
# Show the results
formatter_result = (
"{:9s}\t{:.3f}s\t{:.0f}\t{:.3f}\t{:.3f}\t{:.3f}\t{:.3f}\t{:.3f}\t{:.3f}"
)
print(formatter_result.format(*results))
.. GENERATED FROM PYTHON SOURCE LINES 114-127
Run the benchmark
-----------------
We will compare three approaches:
* an initialization using `k-means++`. This method is stochastic and we will
run the initialization 4 times;
* a random initialization. This method is stochastic as well and we will run
the initialization 4 times;
* an initialization based on a :class:`~sklearn.decomposition.PCA`
projection. Indeed, we will use the components of the
:class:`~sklearn.decomposition.PCA` to initialize KMeans. This method is
deterministic and a single initialization suffice.
.. GENERATED FROM PYTHON SOURCE LINES 127-145
.. code-block:: default
from sklearn.cluster import KMeans
from sklearn.decomposition import PCA
print(82 * "_")
print("init\t\ttime\tinertia\thomo\tcompl\tv-meas\tARI\tAMI\tsilhouette")
kmeans = KMeans(init="k-means++", n_clusters=n_digits, n_init=4, random_state=0)
bench_k_means(kmeans=kmeans, name="k-means++", data=data, labels=labels)
kmeans = KMeans(init="random", n_clusters=n_digits, n_init=4, random_state=0)
bench_k_means(kmeans=kmeans, name="random", data=data, labels=labels)
pca = PCA(n_components=n_digits).fit(data)
kmeans = KMeans(init=pca.components_, n_clusters=n_digits, n_init=1)
bench_k_means(kmeans=kmeans, name="PCA-based", data=data, labels=labels)
print(82 * "_")
.. rst-class:: sphx-glr-script-out
.. code-block:: none
__________________________________________________________________________________
init time inertia homo compl v-meas ARI AMI silhouette
k-means++ 0.037s 69545 0.598 0.645 0.621 0.469 0.617 0.152
random 0.044s 69735 0.681 0.723 0.701 0.574 0.698 0.170
PCA-based 0.014s 72686 0.636 0.658 0.647 0.521 0.643 0.142
__________________________________________________________________________________
.. GENERATED FROM PYTHON SOURCE LINES 146-153
Visualize the results on PCA-reduced data
-----------------------------------------
:class:`~sklearn.decomposition.PCA` allows to project the data from the
original 64-dimensional space into a lower dimensional space. Subsequently,
we can use :class:`~sklearn.decomposition.PCA` to project into a
2-dimensional space and plot the data and the clusters in this new space.
.. GENERATED FROM PYTHON SOURCE LINES 153-204
.. code-block:: default
import matplotlib.pyplot as plt
reduced_data = PCA(n_components=2).fit_transform(data)
kmeans = KMeans(init="k-means++", n_clusters=n_digits, n_init=4)
kmeans.fit(reduced_data)
# Step size of the mesh. Decrease to increase the quality of the VQ.
h = 0.02 # point in the mesh [x_min, x_max]x[y_min, y_max].
# Plot the decision boundary. For that, we will assign a color to each
x_min, x_max = reduced_data[:, 0].min() - 1, reduced_data[:, 0].max() + 1
y_min, y_max = reduced_data[:, 1].min() - 1, reduced_data[:, 1].max() + 1
xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))
# Obtain labels for each point in mesh. Use last trained model.
Z = kmeans.predict(np.c_[xx.ravel(), yy.ravel()])
# Put the result into a color plot
Z = Z.reshape(xx.shape)
plt.figure(1)
plt.clf()
plt.imshow(
Z,
interpolation="nearest",
extent=(xx.min(), xx.max(), yy.min(), yy.max()),
cmap=plt.cm.Paired,
aspect="auto",
origin="lower",
)
plt.plot(reduced_data[:, 0], reduced_data[:, 1], "k.", markersize=2)
# Plot the centroids as a white X
centroids = kmeans.cluster_centers_
plt.scatter(
centroids[:, 0],
centroids[:, 1],
marker="x",
s=169,
linewidths=3,
color="w",
zorder=10,
)
plt.title(
"K-means clustering on the digits dataset (PCA-reduced data)\n"
"Centroids are marked with white cross"
)
plt.xlim(x_min, x_max)
plt.ylim(y_min, y_max)
plt.xticks(())
plt.yticks(())
plt.show()
.. image-sg:: /auto_examples/cluster/images/sphx_glr_plot_kmeans_digits_001.png
:alt: K-means clustering on the digits dataset (PCA-reduced data) Centroids are marked with white cross
:srcset: /auto_examples/cluster/images/sphx_glr_plot_kmeans_digits_001.png
:class: sphx-glr-single-img
.. rst-class:: sphx-glr-timing
**Total running time of the script:** (0 minutes 0.753 seconds)
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