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

(150, 2)

Plots.

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

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(f'KMeans 4 clusters\n{hist!r}')
ax.legend()

<matplotlib.legend.Legend object at 0x7f0676941af0>

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)

somewhere/workspace/mlinsights/mlinsights_UT_39_std/_venv/lib/python3.9/site-packages/sklearn/cluster/_kmeans.py:1316: FutureWarning: algorithm='auto' is deprecated, it will be removed in 1.3. Using 'lloyd' instead.
  warnings.warn(
somewhere/workspace/mlinsights/mlinsights_UT_39_std/_venv/lib/python3.9/site-packages/sklearn/cluster/_kmeans.py:1316: FutureWarning: algorithm='auto' is deprecated, it will be removed in 1.3. Using 'lloyd' instead.
  warnings.warn(

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

In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.

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(f'ConstraintKMeans 4 clusters (gains)\n{hist1!r}')
ax[0].legend()
ax[1].set_title(f'ConstraintKMeans 4 clusters (distances)\n{hist2!r}')
ax[1].legend()

<matplotlib.legend.Legend object at 0x7f0676804fd0>

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)

somewhere/workspace/mlinsights/mlinsights_UT_39_std/_venv/lib/python3.9/site-packages/sklearn/cluster/_kmeans.py:1316: FutureWarning: algorithm='auto' is deprecated, it will be removed in 1.3. Using 'lloyd' instead.
  warnings.warn(

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(f"ConstraintKMeans 4 clusters\nstrategy='weights'\n{hist!r}")
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()