In This Article
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
| Method | Approach | Best For |
|---|---|---|
| K-Means | Partition into K clusters | Large datasets, spherical clusters |
| Hierarchical | Build tree of clusters | Small-medium datasets, exploring structure |
| DBSCAN | Density-based grouping | Arbitrary shapes, noise detection |
| Gaussian Mixture | Probabilistic assignment | Overlapping clusters |
K-Means Clustering
K-Means is the most widely used clustering algorithm due to its simplicity and efficiency.
Algorithm Steps
- Initialize: Choose K initial centroids (cluster centers)
- Assign: Assign each point to nearest centroid
- Update: Recalculate centroids as mean of assigned points
- 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
| Method | Distance Between Clusters |
|---|---|
| Single linkage | Minimum distance between any two points |
| Complete linkage | Maximum distance between any two points |
| Average linkage | Average distance between all pairs |
| Ward's method | Minimize 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
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