K-Means Clustering Notes & Questions | Class 12 Future Skills & AI | Drishti OS

What you'll learn

The difference between supervised and unsupervised learning
The four steps of the K-Means algorithm
How to choose the right number of clusters K using the elbow method
Limitations of K-Means (sensitivity to initialisation, non-convex shapes)
Real-world applications of clustering

Key concepts

Unsupervised Learning

In unsupervised learning, data has no labels. The algorithm finds hidden structure — natural groupings — in the data on its own.

Learning Type	Labels?	Goal	Example
Supervised	Yes	Predict a label	Spam detection
Unsupervised	No	Discover structure	Customer segmentation

The K-Means Algorithm

Goal: Partition n data points into K clusters such that each point belongs to the cluster with the nearest centroid.

Step-by-step:

Step	Action
1. Initialise	Randomly place K centroids in the data space
2. Assign	Assign each data point to the nearest centroid
3. Update	Recalculate each centroid as the mean of all points assigned to it
4. Repeat	Repeat steps 2–3 until centroids stop moving (convergence)

Distance metric (Euclidean):

d(x, c) = √[(x₁ − c₁)² + (x₂ − c₂)²]

Convergence: The algorithm converges when no data point changes its cluster assignment between iterations.

Worked Example (2D)

Data: students clustered by (study hours, exam score).

Iteration 1: Centroids placed randomly
Iteration 2: Points assigned to nearest centroid
Iteration 3: Centroids shift to group means
Iteration 4: Converged — cluster centres stable

Result: Three natural groups — high-study/high-score, low-study/low-score, mid-range.

Choosing K: The Elbow Method

Run K-Means for K = 1, 2, 3, … and record the Within-Cluster Sum of Squares (WCSS) — total squared distance from each point to its centroid.

K	WCSS
1	5000
2	2000
3	800
4	750
5	740

Plot K vs WCSS. The "elbow" — where the drop in WCSS significantly slows — suggests the optimal K. Here: K = 3.

Limitations of K-Means

Limitation	Description
Sensitive to initialisation	Different starting centroids can produce different final clusters
Requires K upfront	K must be chosen before running — often not obvious
Assumes spherical clusters	Performs poorly on elongated or non-convex cluster shapes
Sensitive to outliers	Outliers pull centroids away from true cluster centres
Not suitable for categorical data	Euclidean distance is not meaningful for non-numeric features

Fix for initialisation sensitivity: Use K-Means++ initialisation — centroids are chosen with probability proportional to distance from already-chosen centroids, spreading them out intelligently.

Applications of K-Means

Domain	Application
Business	Customer segmentation by purchasing behaviour
Healthcare	Grouping patients by symptoms for diagnosis
Image processing	Colour quantisation (reducing colours in an image)
Geography	Identifying urban zones, traffic clustering
Biology	Grouping genes with similar expression patterns

Quick check

K-Means is an unsupervised algorithm. What does this mean, and how does it differ from a supervised algorithm like logistic regression?
Describe the four steps of the K-Means algorithm in your own words. What is the termination condition?
A student runs K-Means with K = 3 twice and gets different cluster assignments each time. What causes this, and how can it be fixed?
The elbow method gives a WCSS plot that shows a sharp drop from K=1 to K=4, then a very gradual decrease for K=5, 6, 7. What value of K should be chosen?
K-Means performs poorly on a dataset where two clusters form crescent (moon) shapes. Explain why, and name a clustering algorithm better suited to non-convex shapes.

K-Means Clustering