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12_kmeans_limitations.py
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12_kmeans_limitations.py
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'''
NOTES ON LIMITATIONS OF K-MEANS CLUSTERING
Adapted from Bart Baddely's 2014 PyData Presentation:
http://nbviewer.ipython.org/github/BartBaddeley/PyDataTalk-2014/blob/master/PyDataTalk.ipynb
Agenda:
1) K-means might not work when dimensions have different scales
2) K-means might not work for non-spherical shapes
3) K-means might not work for clusters of different sizes
'''
from sklearn.cluster import KMeans
import numpy as np
from sklearn.datasets.samples_generator import make_blobs, make_moons
import matplotlib.pyplot as plt
from sklearn.metrics.pairwise import euclidean_distances
'''
1) DIMENSIONS WITH DIFFERENT SCALES
'''
# Generate data with differing variances
np.random.seed(0)
centres = [[1, 0.75], [1, -0.75], [0, 0]]
X0, labels0_true = make_blobs(n_samples=300, centers=centres[0], cluster_std=[[0.6,0.1]])
X1, labels1_true = make_blobs(n_samples=300, centers=centres[1], cluster_std=[[0.6,0.1]])
X2, labels2_true = make_blobs(n_samples=300, centers=centres[2], cluster_std=[[0.6,0.1]])
X = np.concatenate((X0,X1,X2))
labels_true = np.concatenate((labels0_true,labels1_true+1,labels2_true+2))
colors = np.array(['#FF0054','#FBD039','#23C2BC'])
plt.figure(figsize=(12, 6))
plt.suptitle('Dimensions with Different Scales', fontsize=15)
plt.subplot(121)
for k, col in zip(range(3), colors):
my_members = labels_true == k
cluster_center = centres[k]
plt.scatter(X[my_members, 0], X[my_members, 1], c=col, marker='o',s=20)
plt.scatter(cluster_center[0], cluster_center[1], c=col, marker='o', s=200)
plt.axis('equal')
plt.title('Original data')
# Compute clustering with 3 Clusters
k_means_3 = KMeans(init='k-means++', n_clusters=3, n_init=10)
k_means_3.fit(X)
k_means_3_labels = k_means_3.labels_
k_means_3_cluster_centres = k_means_3.cluster_centers_
# Plot result
distance = euclidean_distances(k_means_3_cluster_centres,
centres,
squared=True)
order = distance.argmin(axis=0)
plt.subplot(122)
for k, col in zip(range(3), colors):
my_members = k_means_3_labels == order[k]
plt.scatter(X[my_members, 0], X[my_members, 1],c=col, marker='o', s=20)
cluster_center = k_means_3_cluster_centres[order[k]]
plt.scatter(cluster_center[0], cluster_center[1], marker = 'o', c=col, s=200, alpha=0.8)
plt.axis('equal')
plt.title('KMeans 3')
'''
#2: NON-SPHERICAL SHAPES
'''
[X, true_labels] = make_moons(n_samples=1000, noise=.05)
plt.figure(figsize=(12, 6))
plt.suptitle('Non-Spherical Shapes', fontsize=15)
plt.subplot(121)
for k, col in zip(range(2), colors):
my_members = true_labels == k
plt.scatter(X[my_members, 0], X[my_members, 1], c=col, marker='o', s=20)
plt.axis('equal')
plt.title('Original Data')
# Compute clustering with 2 Clusters
k_means_2 = KMeans(init='k-means++', n_clusters=2, n_init=10)
k_means_2.fit(X)
k_means_2_labels = k_means_2.labels_
k_means_2_cluster_centers = k_means_2.cluster_centers_
plt.subplot(122)
for k, col in zip(range(2), colors):
my_members = k_means_2_labels == k
plt.scatter(X[my_members, 0], X[my_members, 1],c=col, marker='o', s=20)
cluster_center = k_means_2_cluster_centers[k]
plt.scatter(cluster_center[0], cluster_center[1], marker = 'o', c=col, s=200, alpha=0.8)
plt.axis('equal')
plt.title('KMeans 2')
'''
#3: CLUSTERS OF DIFFERENT SIZES
'''
np.random.seed(0)
centres = [[-1, 0], [1, 0], [3, 0]]
X0, labels0_true = make_blobs(n_samples=100, centers=centres[0], cluster_std=[[0.2,0.2]])
X1, labels1_true = make_blobs(n_samples=400, centers=centres[1], cluster_std=[[0.6,0.6]])
X2, labels2_true = make_blobs(n_samples=100, centers=centres[2], cluster_std=[[0.2,0.2]])
X = np.concatenate((X0,X1,X2))
labels_true = np.concatenate((labels0_true,labels1_true+1,labels2_true+2))
plt.figure(figsize=(12, 6))
plt.suptitle('Clusters of Different Sizes', fontsize=15)
plt.subplot(121)
for k, col in zip(range(3), colors):
my_members = labels_true == k
cluster_center = centres[k]
plt.scatter(X[my_members, 0], X[my_members, 1], c=col, marker='o',s=20)
plt.scatter(cluster_center[0], cluster_center[1], c=col, marker='o', s=200)
plt.axis('equal')
plt.title('Original data')
# Compute clustering with 3 Clusters
k_means_3 = KMeans(init='k-means++', n_clusters=3, n_init=10)
k_means_3.fit(X)
k_means_3_labels = k_means_3.labels_
k_means_3_cluster_centres = k_means_3.cluster_centers_
# Plot result
distance = euclidean_distances(k_means_3_cluster_centres,
centres,
squared=True)
order = distance.argmin(axis=0)
plt.subplot(122)
for k, col in zip(range(3), colors):
my_members = k_means_3_labels == order[k]
plt.scatter(X[my_members, 0], X[my_members, 1],c=col, marker='o', s=20)
cluster_center = k_means_3_cluster_centres[order[k]]
plt.scatter(cluster_center[0], cluster_center[1], marker = 'o', c=col, s=200, alpha=0.8)
plt.axis('equal')
plt.title('KMeans 3')