from pylab import *
import matplotlib.cm as cm
import numpy as np
import scipy.linalg as la
from scipy.stats import chi2
from scipy.spatial import Voronoi, voronoi_plot_2d
from sklearn.datasets import make_blobs
def plot_2d_clusters(X, labels, centers):
"""
Given an observation array, a label vector, and the location of the centers
plot the clusters
"""
clabels = set(labels)
K = len(clabels)
if len(centers) != K:
raise ValueError("Expecting the number of unique labels and centres to"
" be the same!")
# Plot the true clusters
figure(figsize=(10, 10))
ax = gca()
vor = Voronoi(centers)
voronoi_plot_2d(vor, ax)
colors = cm.hsv(np.arange(K)/float(K))
for k, col in enumerate(colors):
my_members = labels == k
scatter(X[my_members, 0], X[my_members, 1], c=col, marker='o', s=20)
for k, col in enumerate(colors):
cluster_center = centers[k]
scatter(cluster_center[0], cluster_center[1], c=col, marker='o', s=200)
axis('tight')
axis('equal')
title('Clusters')
def plot_2d_GMMs(X, labels, means, covs, percentcontour=0.66, npoints=30):
"""
Given an observation array, a label vector (integer values), and GMM mean
and covariance parameters, plot the clusters and parameters.
"""
clabels = set(labels)
K = len(clabels)
if len(means) != len(covs) != K:
raise ValueError("Expecting the number of unique labels, means and"
"covariances to be the same!")
phi = np.linspace(-np.pi, np.pi, npoints)
circle = np.array([np.sin(phi), np.cos(phi)]).T
figure(figsize=(10, 10))
gca()
colors = cm.hsv(np.arange(K)/float(K))
for k, col in zip(clabels, colors):
# points
my_members = labels == k
scatter(X[my_members, 0], X[my_members, 1], c=col, marker='o', s=20)
# means
cluster_center = means[k, :]
scatter(cluster_center[0], cluster_center[1], c=col, marker='o', s=200)
# covariance
L = la.cholesky(np.array(covs[k]) * chi2.ppf(percentcontour, [3])
+ 1e-5 * np.eye(covs[k].shape[0]))
covpoints = circle.dot(L) + means[k, :]
plot(covpoints[:, 0], covpoints[:, 1], color=col, linewidth=3)
axis('tight')
axis('equal')
title('Clusters')
def load_2d_simple():
"""
Should be easily clustered with K-Means.
"""
centres = [[1, 1], [-0.5, 0], [1, -1]]
X, labels_true = make_blobs(n_samples=1000, centers=centres,
cluster_std=[[0.3, 0.3]])
return X
def load_2d_hard():
"""
Returns non-isotropoic data to motivate the use of non-euclidean norms (as
well as the ground truth).
"""
centres = np.array([[3., -1.], [-2., 1.], [2., 5.]])
covs = []
covs.append(np.array([[4., 2.], [2., 1.5]]))
covs.append(np.array([[1, -1.5], [-1.5, 3.]]))
covs.append(np.array([[1., 0.], [0., 1.]]))
N = [1000, 500, 300]
X = [np.random.randn(n, 2).dot(la.cholesky(c, lower=True)) + m
for n, m, c in zip(N, centres, covs)]
X = np.vstack(X)
labels = np.concatenate((np.zeros(N[0]), np.ones(N[1]), 2*np.ones(N[2])))
return X, labels
