Unsupervised Learning:
Clustering

Learning without labels

Supervised learning, which you covered in the last two lessons, requires labelled examples. Someone has to go through the data and write down the correct answer for each row. That is expensive, slow, and sometimes impossible. You cannot label every customer, every web page, every image on the internet.

Unsupervised learning is what you turn to when you have data but no answers. When a streaming service wants to understand its user base without manually categorising millions of accounts. When a biologist wants to see which genes behave similarly without having any prior theory about the groupings. When a retailer wants to understand natural buying patterns before designing targeted promotions.

Clustering is the most widely used unsupervised technique. The goal is simple: group data points so that points in the same cluster are similar to each other and different from points in other clusters.

K-Means: the simplest clustering algorithm

K-Means is the standard starting point for clustering. It is fast, interpretable, and works surprisingly well on a huge range of problems. The name tells you two things: K is the number of clusters you specify in advance, and "Means" refers to the centroid (average position) of each cluster.

The algorithm is deceptively simple, but it makes one important assumption: clusters are roughly spherical and similarly sized. If your data has elongated, irregular, or very differently sized groups, K-Means will struggle. For those cases, alternatives like DBSCAN (which finds clusters of arbitrary shape) or Gaussian Mixture Models (which assign probabilities rather than hard labels) work better.

Choosing the right K

The biggest practical challenge with K-Means is that you have to specify K before you run the algorithm. How many clusters are there in your data? If you already knew that, you would not need clustering. You are trying to discover structure, not impose it.

The elbow method is the standard way to make this choice. You run K-Means with K ranging from 1 to 10 (or more), and for each K you record the inertia: the total squared distance from every point to its assigned centroid. As K increases, inertia always decreases. But the rate of decrease slows dramatically after the "true" number of clusters. You look for the elbow in the curve.

The elbow is often a judgment call rather than a crisp mathematical answer. If the curve is smooth with no clear bend, the silhouette score is another metric worth checking. It measures how tightly each point fits within its own cluster compared to its distance from neighbouring clusters. Values close to 1 mean good clusters; values near 0 mean overlapping clusters.

Where clustering shows up in the real world

K-Means in Scikit-learn

The Scikit-learn API for clustering is the same pattern you have seen for everything else. Create the object, fit it, get the labels out. The main difference is that fit does not need a y (target) argument, because there are no labels.

import numpy as np
import matplotlib.pyplot as plt
from sklearn.cluster import KMeans
from sklearn.preprocessing import StandardScaler

# Simulate customer data: annual spend and visit frequency
np.random.seed(42)
spend = np.random.normal(loc=[500, 2000, 8000], scale=[100, 300, 800], size=(100, 3)).flatten()
visits = np.random.normal(loc=[2, 8, 20], scale=[1, 2, 4], size=(100, 3)).flatten()
X = np.column_stack([spend, visits])

# Scale the features (important for distance-based algorithms)
scaler = StandardScaler()
X_scaled = scaler.fit_transform(X)

# Fit K-Means with 3 clusters
kmeans = KMeans(n_clusters=3, random_state=42, n_init=10)
labels = kmeans.fit_predict(X_scaled)

# Summarise each cluster
for k in range(3):
    mask = labels == k
    print(f"Cluster {k}: {mask.sum()} customers | "
          f"avg spend=${X[mask,0].mean():.0f} | "
          f"avg visits/yr={X[mask,1].mean():.1f}")

Three distinct customer segments emerge automatically: low-spend infrequent visitors, mid-range regular customers, and high-value loyal shoppers. No human had to categorise a single customer. The model found the natural groupings in the data.