Introduction

Cluster analysis is an unsupervised machine learning technique that groups similar objects together. Unlike classification (supervised learning), clustering doesn't require predefined labels—the algorithm discovers natural groupings in the data.

The goal is to maximize similarity within clusters while maximizing differences between clusters. This makes cluster analysis invaluable for customer segmentation, market research, and pattern discovery.


Types of Clustering Methods

MethodApproachBest For
K-MeansPartition into K clustersLarge datasets, spherical clusters
HierarchicalBuild tree of clustersSmall-medium datasets, exploring structure
DBSCANDensity-based groupingArbitrary shapes, noise detection
Gaussian MixtureProbabilistic assignmentOverlapping clusters

K-Means Clustering

K-Means is the most widely used clustering algorithm due to its simplicity and efficiency.

Algorithm Steps

  1. Initialize: Choose K initial centroids (cluster centers)
  2. Assign: Assign each point to nearest centroid
  3. Update: Recalculate centroids as mean of assigned points
  4. Repeat: Steps 2-3 until centroids stabilize

Objective (minimize):

J = Σ Σ ||xᵢ - μₖ||²

Sum of squared distances from each point to its cluster centroid

Pros and Cons

  • Pros: Fast, scalable, easy to interpret
  • Cons: Must specify K, sensitive to initialization, assumes spherical clusters

Hierarchical Clustering

Builds a hierarchy of clusters, visualized as a dendrogram (tree diagram).

Two Approaches

  • Agglomerative (bottom-up): Start with each point as cluster, merge similar ones
  • Divisive (top-down): Start with one cluster, split recursively

Linkage Methods

MethodDistance Between Clusters
Single linkageMinimum distance between any two points
Complete linkageMaximum distance between any two points
Average linkageAverage distance between all pairs
Ward's methodMinimize within-cluster variance

Choosing Number of Clusters

Methods

  • Elbow method: Plot within-cluster variance vs K; look for "elbow"
  • Silhouette score: Measures how similar points are to own vs other clusters
  • Gap statistic: Compares clustering to random uniform distribution
  • Domain knowledge: Business context may suggest natural number
Key Insight: There's no "correct" number of clusters—it depends on how you'll use the segments. Sometimes more granular (more clusters) is better; sometimes broader is more actionable.

Business Applications

  • Customer segmentation: Group customers by behavior, demographics, value
  • Market segmentation: Identify distinct market segments
  • Product recommendation: Group similar products or users
  • Anomaly detection: Identify outliers (points in no cluster)
  • Image segmentation: Group similar pixels
  • Document clustering: Group similar documents or topics

Example: Customer Segmentation

An e-commerce company clusters customers by RFM (Recency, Frequency, Monetary) and discovers:

  • Cluster 1: High-value loyalists (recent, frequent, high spend)
  • Cluster 2: At-risk (not recent, were frequent)
  • Cluster 3: New customers (recent, low frequency)
  • Cluster 4: Bargain hunters (frequent during sales only)

Each segment gets different marketing treatment.


Conclusion

Key Takeaways

  • Cluster analysis groups similar objects without predefined labels
  • K-Means is fast and scalable; requires specifying K
  • Hierarchical clustering reveals structure via dendrogram
  • Use elbow method or silhouette score to choose K
  • Primary business use: customer and market segmentation
  • Interpret clusters after creating them—give them meaningful names
  • There's no "correct" answer—usefulness depends on application