Constraint KMeans

Simple example to show how to cluster keeping approximatively the same number of points in every cluster.

Data

from collections import Counter
import numpy
import matplotlib.pyplot as plt
from sklearn.datasets import make_blobs
from sklearn.cluster import KMeans
from mlinsights.mlmodel import ConstraintKMeans


n_samples = 100
data = make_blobs(
    n_samples=n_samples, n_features=2, centers=2, cluster_std=1.0,
    center_box=(-10.0, 0.0), shuffle=True, random_state=2)
X1 = data[0]
data = make_blobs(
    n_samples=n_samples // 2, n_features=2, centers=2, cluster_std=1.0,
    center_box=(0.0, 10.0), shuffle=True, random_state=2)
X2 = data[0]

X = numpy.vstack([X1, X2])
X.shape

Out:

(150, 2)

Plots.

fig, ax = plt.subplots(1, 1, figsize=(4, 4))
ax.plot(X[:, 0], X[:, 1], '.')
ax.set_title('4 clusters')
4 clusters

Out:

Text(0.5, 1.0, '4 clusters')

Standard KMeans

km = KMeans(n_clusters=4)
km.fit(X)
cl = km.predict(X)
hist = Counter(cl)

colors = 'brgy'
fig, ax = plt.subplots(1, 1, figsize=(4, 4))
for i in range(0, max(cl) + 1):
    ax.plot(X[cl == i, 0], X[cl == i, 1], colors[i] + '.', label='cl%d' % i)
    x = [km.cluster_centers_[i, 0], km.cluster_centers_[i, 0]]
    y = [km.cluster_centers_[i, 1], km.cluster_centers_[i, 1]]
    ax.plot(x, y, colors[i] + '+')
ax.set_title('KMeans 4 clusters\n%r' % hist)
ax.legend()
KMeans 4 clusters Counter({2: 50, 0: 50, 1: 27, 3: 23})

Out:

<matplotlib.legend.Legend object at 0x7f0fc323f100>

Constraint KMeans

km1 = ConstraintKMeans(n_clusters=4, strategy='gain',
                       balanced_predictions=True)
km1.fit(X)

km2 = ConstraintKMeans(n_clusters=4, strategy='distance',
                       balanced_predictions=True)
km2.fit(X)

Out:

ConstraintKMeans(balanced_predictions=True, n_clusters=4, strategy='distance')

This algorithm tries to exchange points between clusters.

cl1 = km1.predict(X)
hist1 = Counter(cl1)

cl2 = km2.predict(X)
hist2 = Counter(cl2)

fig, ax = plt.subplots(1, 2, figsize=(10, 4))
for i in range(0, max(cl1) + 1):
    ax[0].plot(X[cl1 == i, 0], X[cl1 == i, 1],
               colors[i] + '.', label='cl%d' % i)
    ax[1].plot(X[cl2 == i, 0], X[cl2 == i, 1],
               colors[i] + '.', label='cl%d' % i)
    x = [km1.cluster_centers_[i, 0], km1.cluster_centers_[i, 0]]
    y = [km1.cluster_centers_[i, 1], km1.cluster_centers_[i, 1]]
    ax[0].plot(x, y, colors[i] + '+')
    x = [km2.cluster_centers_[i, 0], km2.cluster_centers_[i, 0]]
    y = [km2.cluster_centers_[i, 1], km2.cluster_centers_[i, 1]]
    ax[1].plot(x, y, colors[i] + '+')
ax[0].set_title('ConstraintKMeans 4 clusters (gains)\n%r' % hist1)
ax[0].legend()
ax[1].set_title('ConstraintKMeans 4 clusters (distances)\n%r' % hist2)
ax[1].legend()
ConstraintKMeans 4 clusters (gains) Counter({0: 39, 2: 37, 1: 37, 3: 37}), ConstraintKMeans 4 clusters (distances) Counter({0: 38, 2: 38, 3: 37, 1: 37})

Out:

<matplotlib.legend.Legend object at 0x7f0fc314a280>

Another algorithm tries to extend the area of attraction of each cluster.

km = ConstraintKMeans(n_clusters=4, strategy='weights', max_iter=1000,
                      history=True)
km.fit(X)

cl = km.predict(X)
hist = Counter(cl)

Let’s plot Delaunay edges as well.

def plot_delaunay(ax, edges, points):
    for a, b in edges:
        ax.plot(points[[a, b], 0], points[[a, b], 1], '--', color="#555555")


edges = km.cluster_edges()


fig, ax = plt.subplots(1, 2, figsize=(10, 4))
for i in range(0, max(cl) + 1):
    ax[0].plot(X[cl == i, 0], X[cl == i, 1], colors[i] + '.', label='cl%d' % i)
    x = [km.cluster_centers_[i, 0], km.cluster_centers_[i, 0]]
    y = [km.cluster_centers_[i, 1], km.cluster_centers_[i, 1]]
    ax[0].plot(x, y, colors[i] + '+')
ax[0].set_title("ConstraintKMeans 4 clusters\nstrategy='weights'\n%r" % hist)
ax[0].legend()

cls = km.cluster_centers_iter_
ax[1].plot(X[:, 0], X[:, 1], '.', label='X', color='#AAAAAA', ms=3)
for i in range(0, max(cl) + 1):
    ms = numpy.arange(
        cls.shape[-1]).astype(numpy.float64) / cls.shape[-1] * 50 + 1
    ax[1].scatter(cls[i, 0, :], cls[i, 1, :],
                  color=colors[i], s=ms, label='cl%d' % i)
    plot_delaunay(ax[1], edges, km.cluster_centers_)
ax[1].set_title("Centers movement")

plt.show()
ConstraintKMeans 4 clusters strategy='weights' Counter({1: 49, 0: 49, 3: 48, 2: 4}), Centers movement

Total running time of the script: ( 0 minutes 11.076 seconds)

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