Summary - KMeans

In this group you learned KMeans parameters and properties.

Summary: KMeans

In this group:

Lloyd's algorithm: assignment + update; inertia never rises but can get stuck in a local optimum.
k-means++ initialises with spread-out centres; n_init picks the best of several starts.
inertia_ depends on scale and always falls with k; the silhouette, Calinski-Harabasz and Davies-Bouldin complement it.
random_state gives reproducibility; ARI across seeds measures stability.
MiniBatchKMeans for large data.

Exercise KMeans and MiniBatch

Train KMeans(n_clusters=5, n_init=10, random_state=0) and MiniBatchKMeans(n_clusters=5, batch_size=100, n_init=3, random_state=0) on the same data. Print the two inertias as integers with round on one line, then the ARI of the two labellings with round(..., 3).

Show example solution

import numpy as np
from sklearn.datasets import make_blobs
from sklearn.cluster import KMeans

X, _ = make_blobs(n_samples=500, centers=5, cluster_std=1.0, random_state=3)
from sklearn.cluster import MiniBatchKMeans
from sklearn.metrics import adjusted_rand_score

km = KMeans(n_clusters=5, n_init=10, random_state=0).fit(X)
mb = MiniBatchKMeans(n_clusters=5, batch_size=100, n_init=3, random_state=0).fit(X)
print(round(km.inertia_), round(mb.inertia_))
print(round(adjusted_rand_score(km.labels_, mb.labels_), 3))

Test yourself

If KMeans results vary a lot from seed to seed, what should be tried first?
- Deleting random_state
- Increasing n_init and reviewing k
- Setting max_iter to 1
- Removing scaling
Show answer

Increasing n_init and reviewing k — More starts reduce local optima; instability can also point to a wrong k.

Use mini-batch KMeans for large data.

mb = ____(n_clusters=5, batch_size=256)

Show answer

mb = MiniBatchKMeans(n_clusters=5, batch_size=256)

Match the concepts.

Lloyd

Assignment and update
k-means++

Spread-out start
n_init

Choosing the best start
ARI across seeds

Stability

Next lesson: What is hierarchical clustering?

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