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K-means Clustering

Partition data into k groups by repeatedly assigning points to the nearest center and recomputing those centers.

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The Algorithm

K-means is an unsupervised method that splits data into k clusters. It works in a loop:

  1. Place k initial centroids.
  2. Assign each point to its nearest centroid.
  3. Move each centroid to the mean of its assigned points.
  4. Repeat steps 2–3 until assignments stop changing.

You must choose k in advance. It is fast and scales well, but assumes roughly spherical, similarly-sized clusters.

Running K-means

import numpy as np
from sklearn.cluster import KMeans

x = [4, 5, 10, 4, 3, 11, 14, 6, 10, 12]
y = [21, 19, 24, 17, 16, 25, 24, 22, 21, 21]
data = np.array(list(zip(x, y)))

kmeans = KMeans(n_clusters=2, n_init=10, random_state=0)
kmeans.fit(data)

print("labels:   ", kmeans.labels_)
print("centroids:", kmeans.cluster_centers_)
print("predict new:", kmeans.predict([[5, 20]]))

n_init=10 restarts the algorithm 10 times from different seeds and keeps the best result, guarding against poor random initialization. scikit-learn uses the smart k-means++ seeding by default.

Choosing k: The Elbow Method

Plot the within-cluster sum of squares (inertia_) for a range of k. The "elbow" — where adding clusters stops helping much — is a good choice.

import matplotlib.pyplot as plt

inertias = []
for k in range(1, 8):
    km = KMeans(n_clusters=k, n_init=10, random_state=0).fit(data)
    inertias.append(km.inertia_)

plt.plot(range(1, 8), inertias, marker="o")
plt.xlabel("k")
plt.ylabel("inertia")
plt.title("Elbow Method")
plt.show()

Validating with Silhouette Score

The silhouette score (−1 to 1) measures how well each point fits its cluster versus the next-nearest one. Higher is better; pick the k that maximizes it.

from sklearn.metrics import silhouette_score

for k in range(2, 6):
    km = KMeans(n_clusters=k, n_init=10, random_state=0).fit(data)
    print(k, silhouette_score(data, km.labels_).round(3))

Limitations and Alternatives

  • Assumes spherical clusters of similar size — struggles with elongated or nested shapes.
  • Sensitive to feature scale: always standardize first.
  • Sensitive to outliers, which drag centroids. Consider KMedoids or DBSCAN.
  • For non-spherical clusters, try DBSCAN or Gaussian Mixture Models.

Best Practices

  • Scale features before clustering.
  • Use the elbow and silhouette methods together to choose k.
  • Keep n_init high (10+) for stable results.
  • Use MiniBatchKMeans for very large datasets.

Try It Yourself

Exercise 1: Cluster 6 points into 2 groups and print the centroids.

Show solution
import numpy as np
from sklearn.cluster import KMeans
data = np.array([[1, 1], [1, 2], [2, 1], [8, 8], [9, 8], [8, 9]])
km = KMeans(n_clusters=2, n_init=10, random_state=0).fit(data)
print(km.cluster_centers_.round(1))

Exercise 2: What does the "elbow" in an inertia-vs-k plot help you choose?

Show solution

A good value of k — the point where adding more clusters stops meaningfully reducing inertia.

📘 Real-World Deep Dive

Knowing <strong>ML Kmeans (scikit-learn)</strong> well is what turns scikit-learn from a curiosity into a daily tool — you'll reach for it in nearly every real project.

Real-Life Scenario

An end-to-end usage of ML Kmeans that you'd actually see in a data pipeline or analytics notebook.

Real-Life Example

import numpy as np
from sklearn.cluster import KMeans
rng = np.random.default_rng(0)
X = rng.normal(0, 1, (60, 2))
km = KMeans(n_clusters=3, n_init=10, random_state=0).fit(X)
print("inertia:", round(km.inertia_, 3))
print("labels[:10]:", km.labels_[:10])

Expected Output

(see source)

Common mistakes

  • fit expects numeric arrays; OneHotEncoder / LabelEncoder are easy to forget for categorical features.
  • Calling predict on a model trained on unscaled data and then scaling inputs at inference time silently degrades accuracy.
  • train_test_split(X, y) requires both arrays; train_test_split(X) for unsupervised learning slips past static checkers.
  • Treating ML Kmeans as a black box without reading the docs — the API has subtle defaults that bite when you scale.

🚀 Performance & Best Practices

  • Wrap preprocessing + estimator in a Pipeline so fit / predict stay reproducible.
  • Use joblib / pickle for serialising models, not the entire Python state.
  • For > 100 k rows, switch to HistGradientBoostingClassifier or cuML.
  • When working with scikit-learn, prefer vectorised / batched operations over Python loops.

🧪 Try It Yourself

  1. Reproduce the snippet on a representative slice of your own data.
  2. Profile the snippet with cProfile or timeit and find the single biggest improvement.
  3. Generalise the snippet into a small, reusable function you can drop into future projects.

FAQ: K-means Clustering

Common questions about this page.

What is K-means Clustering?

K-means Clustering is a Machine Learning lesson that explains k-means clustering in Python. Partition data into k groups by repeatedly assigning points to the nearest center and recomputing those centers. Copy the samples and run them in the... It is written for beginners who want a clear definition and working examples.

Should I run k-means clustering examples locally for better learning?

Yes. Use the browser editor on StudyGrid for a quick check, then Download the example and run it on your computer. Local runs show real errors and the real toolchain, which is one of the fastest ways to learn k-means clustering in this Machine Learning Python lesson (K-means Clustering).

How do I use k-means clustering in Python?

To use k-means clustering in Python, follow the examples on this StudyGrid page. Copy a snippet, run it in the browser, then Download and run it locally for better learning. Change the values and compare the output.

What is the syntax of k-means clustering?

This K-means Clustering tutorial shows k-means clustering syntax with short Python examples. Use the code blocks in this lesson for the exact statements, then try them in your editor.

K-means Clustering example for beginners

Yes. This page includes a beginner k-means clustering example you can copy and run. It is designed for searches such as "k-means clustering for beginners", "k-means clustering example", and "how to use k-means clustering".

What are common mistakes with k-means clustering?

Common k-means clustering mistakes include wrong syntax, mixing types, and skipping practice. Work through this Machine Learning chapter in order, run every example, and check the output before moving on.

Why should I learn k-means clustering?

K-means Clustering is used in real Python work. Learning k-means clustering helps you write clearer programs and continue the Machine Learning tutorial on StudyGrid.

Is K-means Clustering free to learn online?

Yes. You can learn k-means clustering free on StudyGrid (studygrid.in). This chapter is part of the Machine Learning path and includes examples, syntax, and next-step links.