This tutorial covers the basics of clustering. The scikit learn documentation offers a more comprehensive explantion.
import numpy as np
import matplotlib.pyplot as plt
from sklearn.cluster import KMeans
from sklearn.datasets import make_blobs
%matplotlib inline
n_samples = 1500
random_state = 170
#make up data
X, y = make_blobs(n_samples=n_samples
import numpy as np
import matplotlib.pyplot as plt
from sklearn.cluster import KMeans
from sklearn.datasets import make_blobs
%matplotlib inline
n_samples = 1500
random_state = 170
#make up data
X, y = make_blobs(n_samples=n_samples, random_state=random_state)
y_pred = KMeans(n_clusters=3, random_state=random_state).fit_predict(X)
plt.scatter(X[:, 0], X[:, 1], c=y_pred)
<matplotlib.collections.PathCollection at 0x7f8336ccc650>
plt.figure(figsize=(12, 12))
# Incorrect number of clusters
y_pred = KMeans(n_clusters=2, random_state=random_state).fit_predict(X)
plt.subplot(221)
plt.scatter(X[:, 0], X[:, 1], c=y_pred)
plt.title("Incorrect Number of Blobs")
# Anisotropicly distributed data
transformation = [[ 0.60834549, -0.63667341], [-0.40887718, 0.85253229]]
X_aniso = np.dot(X, transformation)
y_pred = KMeans(n_clusters=3, random_state=random_state).fit_predict(X_aniso)
plt.subplot(222)
plt.scatter(X_aniso[:, 0], X_aniso[:, 1], c=y_pred)
plt.title("Anisotropicly Distributed Blobs")
# Different variance
X_varied, y_varied = make_blobs(n_samples=n_samples,
cluster_std=[1.0, 2.5, 0.5],
random_state=random_state)
y_pred = KMeans(n_clusters=3, random_state=random_state).fit_predict(X_varied)
plt.subplot(223)
plt.scatter(X_varied[:, 0], X_varied[:, 1], c=y_pred)
plt.title("Unequal Variance")
# Unevenly sized blobs
X_filtered = np.vstack((X[y == 0][:500], X[y == 1][:100], X[y == 2][:10]))
y_pred = KMeans(n_clusters=3, random_state=random_state).fit_predict(X_filtered)
plt.subplot(224)
plt.scatter(X_filtered[:, 0], X_filtered[:, 1], c=y_pred)
plt.title("Unevenly Sized Blobs")
plt.show()
print(__doc__)
import time
import numpy as np
import matplotlib.pyplot as plt
from sklearn import cluster, datasets
from sklearn.neighbors import kneighbors_graph
from sklearn.preprocessing import StandardScaler
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
colors = np.array([x for x in 'bgrcmykbgrcmykbgrcmykbgrcmyk'])
colors = np.hstack([colors] * 20)
clustering_names = [
'MiniBatchKMeans', 'AffinityPropagation', 'MeanShift',
'SpectralClustering', 'Ward', 'AgglomerativeClustering',
'DBSCAN', 'Birch']
plt.figure(figsize=(len(clustering_names) * 2 + 3, 9.5))
plt.subplots_adjust(left=.02, right=.98, bottom=.001, top=.96, wspace=.05,
hspace=.01)
plot_num = 1
datasets = [noisy_circles, noisy_moons, blobs, no_structure]
for i_dataset, dataset in enumerate(datasets):
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=0.3)
# connectivity matrix for structured Ward
connectivity = kneighbors_graph(X, n_neighbors=10, include_self=False)
# make connectivity symmetric
connectivity = 0.5 * (connectivity + connectivity.T)
# create clustering estimators
ms = cluster.MeanShift(bandwidth=bandwidth, bin_seeding=True)
two_means = cluster.MiniBatchKMeans(n_clusters=2)
ward = cluster.AgglomerativeClustering(n_clusters=2, linkage='ward',
connectivity=connectivity)
spectral = cluster.SpectralClustering(n_clusters=2,
eigen_solver='arpack',
affinity="nearest_neighbors")
dbscan = cluster.DBSCAN(eps=.2)
affinity_propagation = cluster.AffinityPropagation(damping=.9,
preference=-200)
average_linkage = cluster.AgglomerativeClustering(
linkage="average", affinity="cityblock", n_clusters=2,
connectivity=connectivity)
birch = cluster.Birch(n_clusters=2)
clustering_algorithms = [
two_means, affinity_propagation, ms, spectral, ward, average_linkage,
dbscan, birch]
for name, algorithm in zip(clustering_names, clustering_algorithms):
# predict cluster memberships
t0 = time.time()
algorithm.fit(X)
t1 = time.time()
if hasattr(algorithm, 'labels_'):
y_pred = algorithm.labels_.astype(np.int)
else:
y_pred = algorithm.predict(X)
# plot
plt.subplot(4, len(clustering_algorithms), plot_num)
if i_dataset == 0:
plt.title(name, size=18)
plt.scatter(X[:, 0], X[:, 1], color=colors[y_pred].tolist(), s=10)
if hasattr(algorithm, 'cluster_centers_'):
centers = algorithm.cluster_centers_
center_colors = colors[:len(centers)]
plt.scatter(centers[:, 0], centers[:, 1], s=100, c=center_colors)
plt.xlim(-2, 2)
plt.ylim(-2, 2)
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()
/usr/local/lib/python2.7/dist-packages/sklearn/manifold/spectral_embedding_.py:217: UserWarning: Graph is not fully connected, spectral embedding may not work as expected. warnings.warn("Graph is not fully connected, spectral embedding" /usr/local/lib/python2.7/dist-packages/sklearn/cluster/hierarchical.py:207: UserWarning: the number of connected components of the connectivity matrix is 2 > 1. Completing it to avoid stopping the tree early. connectivity, n_components = _fix_connectivity(X, connectivity) /usr/local/lib/python2.7/dist-packages/sklearn/cluster/hierarchical.py:443: UserWarning: the number of connected components of the connectivity matrix is 2 > 1. Completing it to avoid stopping the tree early. connectivity, n_components = _fix_connectivity(X, connectivity) /usr/local/lib/python2.7/dist-packages/sklearn/cluster/hierarchical.py:207: UserWarning: the number of connected components of the connectivity matrix is 3 > 1. Completing it to avoid stopping the tree early. connectivity, n_components = _fix_connectivity(X, connectivity)
Automatically created module for IPython interactive environment
/usr/local/lib/python2.7/dist-packages/sklearn/cluster/hierarchical.py:443: UserWarning: the number of connected components of the connectivity matrix is 3 > 1. Completing it to avoid stopping the tree early. connectivity, n_components = _fix_connectivity(X, connectivity)
from sklearn.feature_extraction.text import TfidfVectorizer
from sklearn.cluster import KMeans
from sklearn.metrics import adjusted_rand_score
documents = ["Human machine interface for lab abc computer applications",
"A survey of user opinion of computer system response time",
"The EPS user interface management system",
"System and human system engineering testing of EPS",
"Relation of user perceived response time to error measurement",
"The generation of random binary unordered trees",
"The intersection graph of paths in trees",
"Graph minors IV Widths of trees and well quasi ordering",
"Graph minors A survey"]
true_k = 2
vectorizer = TfidfVectorizer(stop_words='english')
X = vectorizer.fit_transform(documents)
model = KMeans(n_clusters=true_k, init='k-means++', max_iter=100, n_init=1)
model.fit(X)
print("Top terms per cluster:")
order_centroids = model.cluster_centers_.argsort()[:, ::-1]
terms = vectorizer.get_feature_names()
for i in range(true_k):
print ("Cluster" + str(i))
for ind in order_centroids[i, :10]:
print (terms[ind])
Top terms per cluster: Cluster0 user eps interface human response time computer management engineering testing Cluster1 graph trees minors survey paths intersection unordered binary generation random
print(__doc__)
import numpy as np
import matplotlib.pyplot as plt
from sklearn.cluster import KMeans
from sklearn.metrics import pairwise_distances_argmin
from sklearn.datasets import load_sample_image
from sklearn.utils import shuffle
from time import time
n_colors = 64
# Load the Summer Palace photo
china = load_sample_image("china.jpg")
# Convert to floats instead of the default 8 bits integer coding. Dividing by
# 255 is important so that plt.imshow behaves works well on float data (need to
# be in the range [0-1]
china = np.array(china, dtype=np.float64) / 255
# Load Image and transform to a 2D numpy array.
w, h, d = original_shape = tuple(china.shape)
assert d == 3
image_array = np.reshape(china, (w * h, d))
print("Fitting model on a small sub-sample of the data")
t0 = time()
image_array_sample = shuffle(image_array, random_state=0)[:1000]
kmeans = KMeans(n_clusters=n_colors, random_state=0).fit(image_array_sample)
print("done in %0.3fs." % (time() - t0))
# Get labels for all points
print("Predicting color indices on the full image (k-means)")
t0 = time()
labels = kmeans.predict(image_array)
print("done in %0.3fs." % (time() - t0))
codebook_random = shuffle(image_array, random_state=0)[:n_colors + 1]
print("Predicting color indices on the full image (random)")
t0 = time()
labels_random = pairwise_distances_argmin(codebook_random,
image_array,
axis=0)
print("done in %0.3fs." % (time() - t0))
def recreate_image(codebook, labels, w, h):
"""Recreate the (compressed) image from the code book & labels"""
d = codebook.shape[1]
image = np.zeros((w, h, d))
label_idx = 0
for i in range(w):
for j in range(h):
image[i][j] = codebook[labels[label_idx]]
label_idx += 1
return image
# Display all results, alongside original image
plt.figure(1)
plt.clf()
ax = plt.axes([0, 0, 1, 1])
plt.axis('off')
plt.title('Original image (96,615 colors)')
plt.imshow(china)
plt.figure(2)
plt.clf()
ax = plt.axes([0, 0, 1, 1])
plt.axis('off')
plt.title('Quantized image (64 colors, K-Means)')
plt.imshow(recreate_image(kmeans.cluster_centers_, labels, w, h))
plt.figure(3)
plt.clf()
ax = plt.axes([0, 0, 1, 1])
plt.axis('off')
plt.title('Quantized image (64 colors, Random)')
plt.imshow(recreate_image(codebook_random, labels_random, w, h))
plt.show()
Automatically created module for IPython interactive environment Fitting model on a small sub-sample of the data done in 0.309s. Predicting color indices on the full image (k-means) done in 0.655s. Predicting color indices on the full image (random) done in 0.239s.