Comparison of the K-Means and MiniBatchKMeans clustering algorithms

We want to compare the performance of the MiniBatchKMeans and KMeans: the MiniBatchKMeans is faster, but gives slightly different results (see Mini Batch K-Means).

We will cluster a set of data, first with KMeans and then with MiniBatchKMeans, and plot the results. We will also plot the points that are labelled differently between the two algorithms.

import time

import numpy as np
import matplotlib.pyplot as plt

from sklearn.cluster import MiniBatchKMeans, KMeans
from sklearn.metrics.pairwise import pairwise_distances_argmin
from sklearn.datasets import make_blobs

# #############################################################################
# Generate sample data
np.random.seed(0)

batch_size = 45
centers = [[1, 1], [-1, -1], [1, -1]]
n_clusters = len(centers)
X, labels_true = make_blobs(n_samples=3000, centers=centers, cluster_std=0.7)

# #############################################################################
# Compute clustering with Means

k_means = KMeans(init="k-means++", n_clusters=3, n_init=10)
t0 = time.time()
k_means.fit(X)
t_batch = time.time() - t0

# #############################################################################
# Compute clustering with MiniBatchKMeans

mbk = MiniBatchKMeans(
    init="k-means++",
    n_clusters=3,
    batch_size=batch_size,
    n_init=10,
    max_no_improvement=10,
    verbose=0,
)
t0 = time.time()
mbk.fit(X)
t_mini_batch = time.time() - t0

# #############################################################################
# Plot result

fig = plt.figure(figsize=(8, 3))
fig.subplots_adjust(left=0.02, right=0.98, bottom=0.05, top=0.9)
colors = ["#4EACC5", "#FF9C34", "#4E9A06"]

# We want to have the same colors for the same cluster from the
# MiniBatchKMeans and the KMeans algorithm. Let's pair the cluster centers per
# closest one.
k_means_cluster_centers = k_means.cluster_centers_
order = pairwise_distances_argmin(k_means.cluster_centers_, mbk.cluster_centers_)
mbk_means_cluster_centers = mbk.cluster_centers_[order]

k_means_labels = pairwise_distances_argmin(X, k_means_cluster_centers)
mbk_means_labels = pairwise_distances_argmin(X, mbk_means_cluster_centers)

# KMeans
ax = fig.add_subplot(1, 3, 1)
for k, col in zip(range(n_clusters), colors):
    my_members = k_means_labels == k
    cluster_center = k_means_cluster_centers[k]
    ax.plot(X[my_members, 0], X[my_members, 1], "w", markerfacecolor=col, marker=".")
    ax.plot(
        cluster_center[0],
        cluster_center[1],
        "o",
        markerfacecolor=col,
        markeredgecolor="k",
        markersize=6,
    )
ax.set_title("KMeans")
ax.set_xticks(())
ax.set_yticks(())
plt.text(-3.5, 1.8, "train time: %.2fs\ninertia: %f" % (t_batch, k_means.inertia_))

# MiniBatchKMeans
ax = fig.add_subplot(1, 3, 2)
for k, col in zip(range(n_clusters), colors):
    my_members = mbk_means_labels == k
    cluster_center = mbk_means_cluster_centers[k]
    ax.plot(X[my_members, 0], X[my_members, 1], "w", markerfacecolor=col, marker=".")
    ax.plot(
        cluster_center[0],
        cluster_center[1],
        "o",
        markerfacecolor=col,
        markeredgecolor="k",
        markersize=6,
    )
ax.set_title("MiniBatchKMeans")
ax.set_xticks(())
ax.set_yticks(())
plt.text(-3.5, 1.8, "train time: %.2fs\ninertia: %f" % (t_mini_batch, mbk.inertia_))

# Initialise the different array to all False
different = mbk_means_labels == 4
ax = fig.add_subplot(1, 3, 3)

for k in range(n_clusters):
    different += (k_means_labels == k) != (mbk_means_labels == k)

identic = np.logical_not(different)
ax.plot(X[identic, 0], X[identic, 1], "w", markerfacecolor="#bbbbbb", marker=".")
ax.plot(X[different, 0], X[different, 1], "w", markerfacecolor="m", marker=".")
ax.set_title("Difference")
ax.set_xticks(())
ax.set_yticks(())

plt.show()