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

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(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 0x7f84b42a3520>

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)

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

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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(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 0x7f847410a8c0>

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(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(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")

Text(0.5, 1.0, 'Centers movement')