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"""
================================================================
Comparing different hierarchical linkage methods on toy datasets
================================================================
This example shows characteristics of different linkage
methods for hierarchical clustering on datasets that are
"interesting" but still in 2D.
The main observations to make are:
- single linkage is fast, and can perform well on
non-globular data, but it performs poorly in the
presence of noise.
- average and complete linkage perform well on
cleanly separated globular clusters, but have mixed
results otherwise.
- Ward is the most effective method for noisy data.
While these examples give some intuition about the
algorithms, this intuition might not apply to very high
dimensional data.
"""
print(__doc__)
import time
import warnings
import numpy as np
import matplotlib.pyplot as plt
from sklearn import cluster, datasets
from sklearn.preprocessing import StandardScaler
from itertools import cycle, islice
np.random.seed(0)
######################################################################
# Generate datasets. We choose the size big enough to see the scalability
# of the algorithms, but not too big to avoid too long running times
n_samples = 1500
noisy_circles = datasets.make_circles(n_samples=n_samples, factor=.5,
noise=.05)
noisy_moons = datasets.make_moons(n_samples=n_samples, noise=.05)
blobs = datasets.make_blobs(n_samples=n_samples, random_state=8)
no_structure = np.random.rand(n_samples, 2), None
# Anisotropicly distributed data
random_state = 170
X, y = datasets.make_blobs(n_samples=n_samples, random_state=random_state)
transformation = [[0.6, -0.6], [-0.4, 0.8]]
X_aniso = np.dot(X, transformation)
aniso = (X_aniso, y)
# blobs with varied variances
varied = datasets.make_blobs(n_samples=n_samples,
cluster_std=[1.0, 2.5, 0.5],
random_state=random_state)
######################################################################
# Run the clustering and plot
# Set up cluster parameters
plt.figure(figsize=(9 * 1.3 + 2, 14.5))
plt.subplots_adjust(left=.02, right=.98, bottom=.001, top=.96, wspace=.05,
hspace=.01)
plot_num = 1
default_base = {'n_neighbors': 10,
'n_clusters': 3}
datasets = [
(noisy_circles, {'n_clusters': 2}),
(noisy_moons, {'n_clusters': 2}),
(varied, {'n_neighbors': 2}),
(aniso, {'n_neighbors': 2}),
(blobs, {}),
(no_structure, {})]
for i_dataset, (dataset, algo_params) in enumerate(datasets):
# update parameters with dataset-specific values
params = default_base.copy()
params.update(algo_params)
X, y = dataset
# normalize dataset for easier parameter selection
X = StandardScaler().fit_transform(X)
# ============
# Create cluster objects
# ============
ward = cluster.AgglomerativeClustering(
n_clusters=params['n_clusters'], linkage='ward')
complete = cluster.AgglomerativeClustering(
n_clusters=params['n_clusters'], linkage='complete')
average = cluster.AgglomerativeClustering(
n_clusters=params['n_clusters'], linkage='average')
single = cluster.AgglomerativeClustering(
n_clusters=params['n_clusters'], linkage='single')
clustering_algorithms = (
('Single Linkage', single),
('Average Linkage', average),
('Complete Linkage', complete),
('Ward Linkage', ward),
)
for name, algorithm in clustering_algorithms:
t0 = time.time()
# catch warnings related to kneighbors_graph
with warnings.catch_warnings():
warnings.filterwarnings(
"ignore",
message="the number of connected components of the " +
"connectivity matrix is [0-9]{1,2}" +
" > 1. Completing it to avoid stopping the tree early.",
category=UserWarning)
algorithm.fit(X)
t1 = time.time()
if hasattr(algorithm, 'labels_'):
y_pred = algorithm.labels_.astype(np.int)
else:
y_pred = algorithm.predict(X)
plt.subplot(len(datasets), len(clustering_algorithms), plot_num)
if i_dataset == 0:
plt.title(name, size=18)
colors = np.array(list(islice(cycle(['#377eb8', '#ff7f00', '#4daf4a',
'#f781bf', '#a65628', '#984ea3',
'#999999', '#e41a1c', '#dede00']),
int(max(y_pred) + 1))))
plt.scatter(X[:, 0], X[:, 1], s=10, color=colors[y_pred])
plt.xlim(-2.5, 2.5)
plt.ylim(-2.5, 2.5)
plt.xticks(())
plt.yticks(())
plt.text(.99, .01, ('%.2fs' % (t1 - t0)).lstrip('0'),
transform=plt.gca().transAxes, size=15,
horizontalalignment='right')
plot_num += 1
plt.show()
|
