toy数据集上不同聚类算法的比较¶
这个例子展示了不同的聚类算法在数据集上的特性，这些算法是“interesting”，但仍然是2D的。除了最后一个数据集之外，每个数据集算法都对参数进行了调整，以获得良好的聚类结果。有些算法比其他算法对参数值更敏感。
最后一个数据集是用于聚类的“NULL”情况的一个示例：数据是同构的，并且没有良好的聚类。对于此示例，空数据集使用与其上面行中的数据集相同的参数，这表示参数值和数据结构不匹配。
虽然这些例子给出了一些关于算法的直觉，但这种直觉可能不适用于非常高维的数据。
/home/circleci/project/sklearn/cluster/_affinity_propagation.py:146: FutureWarning: 'random_state' has been introduced in 0.23. It will be set to None starting from 0.25 which means that results will differ at every function call. Set 'random_state' to None to silence this warning, or to 0 to keep the behavior of versions <0.23.
warnings.warn(("'random_state' has been introduced in 0.23. "
/home/circleci/project/sklearn/cluster/_affinity_propagation.py:146: FutureWarning: 'random_state' has been introduced in 0.23. It will be set to None starting from 0.25 which means that results will differ at every function call. Set 'random_state' to None to silence this warning, or to 0 to keep the behavior of versions <0.23.
warnings.warn(("'random_state' has been introduced in 0.23. "
/home/circleci/project/sklearn/cluster/_affinity_propagation.py:146: FutureWarning: 'random_state' has been introduced in 0.23. It will be set to None starting from 0.25 which means that results will differ at every function call. Set 'random_state' to None to silence this warning, or to 0 to keep the behavior of versions <0.23.
warnings.warn(("'random_state' has been introduced in 0.23. "
/home/circleci/project/sklearn/cluster/_affinity_propagation.py:146: FutureWarning: 'random_state' has been introduced in 0.23. It will be set to None starting from 0.25 which means that results will differ at every function call. Set 'random_state' to None to silence this warning, or to 0 to keep the behavior of versions <0.23.
warnings.warn(("'random_state' has been introduced in 0.23. "
/home/circleci/project/sklearn/cluster/_affinity_propagation.py:146: FutureWarning: 'random_state' has been introduced in 0.23. It will be set to None starting from 0.25 which means that results will differ at every function call. Set 'random_state' to None to silence this warning, or to 0 to keep the behavior of versions <0.23.
warnings.warn(("'random_state' has been introduced in 0.23. "
/home/circleci/project/sklearn/cluster/_affinity_propagation.py:146: FutureWarning: 'random_state' has been introduced in 0.23. It will be set to None starting from 0.25 which means that results will differ at every function call. Set 'random_state' to None to silence this warning, or to 0 to keep the behavior of versions <0.23.
warnings.warn(("'random_state' has been introduced in 0.23. "
print(__doc__)
import time
import warnings
import numpy as np
import matplotlib.pyplot as plt
from sklearn import cluster, datasets, mixture
from sklearn.neighbors import kneighbors_graph
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)
# ============
# Set up cluster parameters
# ============
plt.figure(figsize=(9 * 2 + 3, 12.5))
plt.subplots_adjust(left=.02, right=.98, bottom=.001, top=.96, wspace=.05,
hspace=.01)
plot_num = 1
default_base = {'quantile': .3,
'eps': .3,
'damping': .9,
'preference': -200,
'n_neighbors': 10,
'n_clusters': 3,
'min_samples': 20,
'xi': 0.05,
'min_cluster_size': 0.1}
datasets = [
(noisy_circles, {'damping': .77, 'preference': -240,
'quantile': .2, 'n_clusters': 2,
'min_samples': 20, 'xi': 0.25}),
(noisy_moons, {'damping': .75, 'preference': -220, 'n_clusters': 2}),
(varied, {'eps': .18, 'n_neighbors': 2,
'min_samples': 5, 'xi': 0.035, 'min_cluster_size': .2}),
(aniso, {'eps': .15, 'n_neighbors': 2,
'min_samples': 20, 'xi': 0.1, 'min_cluster_size': .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)
# estimate bandwidth for mean shift
bandwidth = cluster.estimate_bandwidth(X, quantile=params['quantile'])
# connectivity matrix for structured Ward
connectivity = kneighbors_graph(
X, n_neighbors=params['n_neighbors'], include_self=False)
# make connectivity symmetric
connectivity = 0.5 * (connectivity + connectivity.T)
# ============
# Create cluster objects
# ============
ms = cluster.MeanShift(bandwidth=bandwidth, bin_seeding=True)
two_means = cluster.MiniBatchKMeans(n_clusters=params['n_clusters'])
ward = cluster.AgglomerativeClustering(
n_clusters=params['n_clusters'], linkage='ward',
connectivity=connectivity)
spectral = cluster.SpectralClustering(
n_clusters=params['n_clusters'], eigen_solver='arpack',
affinity="nearest_neighbors")
dbscan = cluster.DBSCAN(eps=params['eps'])
optics = cluster.OPTICS(min_samples=params['min_samples'],
xi=params['xi'],
min_cluster_size=params['min_cluster_size'])
affinity_propagation = cluster.AffinityPropagation(
damping=params['damping'], preference=params['preference'])
average_linkage = cluster.AgglomerativeClustering(
linkage="average", affinity="cityblock",
n_clusters=params['n_clusters'], connectivity=connectivity)
birch = cluster.Birch(n_clusters=params['n_clusters'])
gmm = mixture.GaussianMixture(
n_components=params['n_clusters'], covariance_type='full')
clustering_algorithms = (
('MiniBatchKMeans', two_means),
('AffinityPropagation', affinity_propagation),
('MeanShift', ms),
('SpectralClustering', spectral),
('Ward', ward),
('AgglomerativeClustering', average_linkage),
('DBSCAN', dbscan),
('OPTICS', optics),
('Birch', birch),
('GaussianMixture', gmm)
)
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)
warnings.filterwarnings(
"ignore",
message="Graph is not fully connected, spectral embedding" +
" may not work as expected.",
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))))
# add black color for outliers (if any)
colors = np.append(colors, ["#000000"])
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()
脚本的总运行时间：(0分39.499秒)