In [1]:
import numpy as np
from scipy import ndimage
from time import time
from sklearn import datasets, manifold
from sklearn.cluster import KMeans, AgglomerativeClustering
from sklearn.mixture import GMM
from sklearn.cross_validation import StratifiedKFold
import matplotlib.pyplot as plt
import matplotlib as mpl
%matplotlib inline
Example adapted from here.
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iris = datasets.load_iris()
X,y = iris.data[:,:2], iris.target
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num_clusters = 8
model = KMeans(n_clusters=num_clusters)
model.fit(X)
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In [7]:
labels = model.labels_
cluster_centers = model.cluster_centers_
print cluster_centers
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plt.scatter(X[:,0], X[:,1],c=labels.astype(np.float))
plt.hold(True)
plt.scatter(cluster_centers[:,0], cluster_centers[:,1], c = np.arange(num_clusters), marker = '^', s = 150)
plt.show()
plt.scatter(X[:,0], X[:,1],c=np.choose(y,[0,2,1]).astype(np.float))
plt.show()
Example taken from here.
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def make_ellipses(gmm, ax):
"""
Visualize the gaussians in a GMM as ellipses
"""
for n, color in enumerate('rgb'):
v, w = np.linalg.eigh(gmm._get_covars()[n][:2, :2])
u = w[0] / np.linalg.norm(w[0])
angle = np.arctan2(u[1], u[0])
angle = 180 * angle / np.pi # convert to degrees
v *= 9
ell = mpl.patches.Ellipse(gmm.means_[n, :2], v[0], v[1],
180 + angle, color=color)
ell.set_clip_box(ax.bbox)
ell.set_alpha(0.5)
ax.add_artist(ell)
In [10]:
iris = datasets.load_iris()
# Break up the dataset into non-overlapping training (75%) and testing
# (25%) sets.
skf = StratifiedKFold(iris.target, n_folds=4)
# Only take the first fold.
train_index, test_index = next(iter(skf))
X_train = iris.data[train_index]
y_train = iris.target[train_index]
X_test = iris.data[test_index]
y_test = iris.target[test_index]
n_classes = len(np.unique(y_train))
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# Try GMMs using different types of covariances.
classifiers = dict((covar_type, GMM(n_components=n_classes,
covariance_type=covar_type, init_params='wc', n_iter=20))
for covar_type in ['spherical', 'diag', 'tied', 'full'])
n_classifiers = len(classifiers)
plt.figure(figsize=(2*3 * n_classifiers / 2, 2*6))
plt.subplots_adjust(bottom=.01, top=0.95, hspace=.15, wspace=.05,
left=.01, right=.99)
for index, (name, classifier) in enumerate(classifiers.items()):
# Since we have class labels for the training data, we can
# initialize the GMM parameters in a supervised manner.
classifier.means_ = np.array([X_train[y_train == i].mean(axis=0)
for i in xrange(n_classes)])
# Train the other parameters using the EM algorithm.
classifier.fit(X_train)
h = plt.subplot(2, n_classifiers / 2, index + 1)
make_ellipses(classifier, h)
for n, color in enumerate('rgb'):
data = iris.data[iris.target == n]
plt.scatter(data[:, 0], data[:, 1], 0.8, color=color,
label=iris.target_names[n])
# Plot the test data with crosses
for n, color in enumerate('rgb'):
data = X_test[y_test == n]
plt.plot(data[:, 0], data[:, 1], 'x', color=color)
y_train_pred = classifier.predict(X_train)
train_accuracy = np.mean(y_train_pred.ravel() == y_train.ravel()) * 100
plt.text(0.05, 0.9, 'Train accuracy: %.1f' % train_accuracy,
transform=h.transAxes)
y_test_pred = classifier.predict(X_test)
test_accuracy = np.mean(y_test_pred.ravel() == y_test.ravel()) * 100
plt.text(0.05, 0.8, 'Test accuracy: %.1f' % test_accuracy,
transform=h.transAxes)
plt.xticks(())
plt.yticks(())
plt.title(name)
plt.legend(loc='lower right', prop=dict(size=12))
plt.show()
Example taken from here.
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digits = datasets.load_digits(n_class=10)
X = digits.data
y = digits.target
n_samples, n_features = X.shape
np.random.seed(0)
def nudge_images(X, y):
# Having a larger dataset shows more clearly the behavior of the
# methods, but we multiply the size of the dataset only by 2, as the
# cost of the hierarchical clustering methods are strongly
# super-linear in n_samples
shift = lambda x: ndimage.shift(x.reshape((8, 8)),
.3 * np.random.normal(size=2),
mode='constant',
).ravel()
X = np.concatenate([X, np.apply_along_axis(shift, 1, X)])
Y = np.concatenate([y, y], axis=0)
return X, Y
X, y = nudge_images(X, y)
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def plot_clustering(X_red, X, labels, title=None):
x_min, x_max = np.min(X_red, axis=0), np.max(X_red, axis=0)
X_red = (X_red - x_min) / (x_max - x_min)
plt.figure(figsize=(2*6, 2*4))
for i in range(X_red.shape[0]):
plt.text(X_red[i, 0], X_red[i, 1], str(y[i]),
color=plt.cm.spectral(labels[i] / 10.),
fontdict={'weight': 'bold', 'size': 9})
plt.xticks([])
plt.yticks([])
if title is not None:
plt.title(title, size=17)
plt.axis('off')
plt.tight_layout()
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print("Computing embedding")
X_red = manifold.SpectralEmbedding(n_components=2).fit_transform(X)
print("Done.")
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from sklearn.cluster import AgglomerativeClustering
for linkage in ('ward', 'average', 'complete'):
clustering = AgglomerativeClustering(linkage=linkage, n_clusters=10)
t0 = time()
clustering.fit(X_red)
print("%s : %.2fs" % (linkage, time() - t0))
plot_clustering(X_red, X, clustering.labels_, "%s linkage" % linkage)
plt.show()