Hierarchical clustering is one of the most intuitive and widely used methods in unsupervised learning. Unlike partition-based clustering methods such as k-means, hierarchical clustering builds a tree-like structure of nested clusters that helps analysts explore relationships at multiple levels. Whether the goal is to understand patterns in financial risk, classify genomic sequences, segment customers, or analyze social behavior, hierarchical clustering provides a powerful way to group data based on similarity.
This article expands on the standard implementation approach by discussing the origins of hierarchical clustering, real-world applications, and case studies—and then walks through a complete example of how to implement hierarchical clustering in R.
Origins of Hierarchical Clustering
Hierarchical clustering has its foundations in early statistical taxonomy, psychology, and biology. Its roots can be traced back to the 1950s and 1960s, when researchers sought systematic approaches to classify organisms and understand relationships among psychological traits.
Key developments include:
Early Biological Taxonomy
Biologists needed methods to classify species into nested groups such as kingdom, phylum, class, order, and so on. This natural hierarchy inspired early clustering techniques aimed at creating tree-like structures (now called dendrograms).
Work by Johnson (1967)
W. Johnson formalized the process of hierarchical clustering by presenting an algorithm that builds nested groups by iteratively merging or splitting clusters based on distances between observations. His seminal work laid the foundation for the agglomerative and divisive clustering methods widely used today.
Adoption in Social Sciences
In the 1970s and 1980s, psychologists began using hierarchical clustering to understand behavioral patterns and personality attributes. The need to visualize relationships between variables led to the popularization of dendrograms.
Integration into Computer Science & Data Mining
By the 1990s, hierarchical clustering became standard in data mining, gene expression analysis, marketing segmentation, and pattern recognition, thanks to increased computational power.
Today, hierarchical clustering remains a fundamental technique in machine learning and data exploration due to its interpretability, flexibility, and visual appeal.
What Is Hierarchical Clustering?
Hierarchical clustering groups similar data points into clusters while forming a hierarchical structure of nested groupings. Unlike k-means, it does not require specifying the number of clusters beforehand.
There are two main types:
1. Divisive Clustering (Top-Down)
Also known as DIANA (Divisive Analysis), this method:
- Starts with all data points in a single cluster
- Recursively divides clusters into smaller ones
- Continues until every point becomes its own cluster
Divisive clustering works well for identifying large, broad clusters.
2. Agglomerative Clustering (Bottom-Up)
Also known as HAC (Hierarchical Agglomerative Clustering) or AGNES, this method:
- Assigns each data point to its own cluster
- Merges the two closest clusters
- Repeats until only one cluster remains
Agglomerative clustering is highly popular due to its simplicity and strong performance on varied datasets.
Distance and Linkage Methods
To build the cluster hierarchy, we need a way to measure distance between data points and distance between clusters.
Common Linkage Methods:
1. Single Linkage
- Distance = shortest distance between any two points in the two clusters
- Produces long, loose, chain-like clusters
2. Complete Linkage
- Distance = farthest distance between points in the two clusters
- Produces compact, tight clusters
3. Average Linkage
- Distance = average pairwise distance
- Balanced and stable
4. Ward’s Method
- Minimizes within-cluster variance
- Often produces the most meaningful clusters in practice
Real-World Applications of Hierarchical Clustering
1. Customer Segmentation in Marketing
Businesses use hierarchical clustering to analyze customer purchasing behavior, spending patterns, or digital footprints. For example, e-commerce platforms classify customers based on order frequency, product preferences, and browsing habits.
Impact:
- Tailored promotions
- Improved customer lifetime value predictions
- Behavior-based product recommendations
2. Healthcare & Genomics
Hierarchical clustering is essential for grouping genes with similar expression profiles. Researchers use it to:
- Identify disease subtypes
- Study protein functions
- Analyze patient health patterns
Example: Clustering genome sequences to identify clusters of viral mutations.
3. Document and Text Clustering
Hierarchical clustering helps group documents based on similarity metrics like cosine distance or TF-IDF scores.
Use cases:
- Topic discovery
- Organizing knowledge bases
- Legal document classification
4. Image Segmentation
Computer vision tasks use hierarchical clustering to:
- Cluster pixels with similar color intensities
- Detect regions of interest
- Group similar shapes
5. Financial Risk Analysis
Banks cluster customers based on:
- Credit score
- Loan repayment history
- Spending behavior
This helps identify high-risk and low-risk borrower segments.
Case Studies Using Hierarchical Clustering
Case Study 1: Social Media User Behavior Analysis
A social media platform wanted to categorize users based on engagement patterns (likes, comments, shares, posting frequency, etc.). Such behavior naturally follows hierarchical patterns.
Process:
- Data scaled and clustered using Ward’s method
- Resulting dendrogram helped identify natural breakpoints
- Users segmented into “silent observers,” “active contributors,” and “viral amplifiers”
Outcome: Higher engagement rates after targeted content strategy.
Case Study 2: Crime Pattern Detection in Metropolitan Regions
A city government analyzed crime metrics such as thefts, assaults, and burglaries across districts.
- Method: Hierarchical clustering using complete linkage identified regional clusters with similar crime intensities.
- Outcome: Enabled better police resource allocation and hotspot prediction.
Case Study 3: Retail Store Performance Classification
A retail chain analyzed sales, footfalls, inventory turnover, and profit metrics across its locations.
Results: Hierarchical clustering helped classify stores into:
- High-performing stores
- Growth-potential stores
- Underperforming stores
Outcome: Custom strategies were developed for each group, improving overall efficiency.
Implementing Hierarchical Clustering in R
Below is the streamlined process for performing hierarchical clustering on a numerical dataset such as Freedman from the car package.
1. Data Preparation
- Remove missing values
- Standardize variables (important for distance-based algorithms)
data <- car::Freedman data <- na.omit(data) data <- scale(data)
2. Compute Distance Matrix
d <- dist(data, method = "euclidean")
3. Perform Agglomerative Clustering
hc1 <- hclust(d, method = "complete") plot(hc1, cex = 0.6, hang = -1)
4. Using AGNES to Compare Linkage Methods
hc2 <- agnes(data, method = "complete") hc2$ac
To compare multiple linkage methods:
m <- c("average", "single", "complete", "ward") ac <- function(x) agnes(data, method = x)$ac purrr::map_dbl(m, ac)
Ward’s method often yields the strongest clustering structure.
5. Divisive Clustering with DIANA
hc4 <- diana(data) pltree(hc4, cex = 0.6, hang = -1)
6. Cutting the Dendrogram into Clusters
clust <- cutree(hc4, k = 5)
7. Visualizing Clusters
Using factoextra:
fviz_cluster(list(data = data, cluster = clust))
8. Comparing Methods Using Tanglegram
library(dendextend) tanglegram(as.dendrogram(agnes(data, method="single")), as.dendrogram(agnes(data, method="complete")))
This visually compares clustering approaches.
Conclusion
Hierarchical clustering remains one of the most powerful and intuitive tools in unsupervised machine learning. Its ability to reveal natural data groupings, visualize nested structures, and provide flexibility through multiple linkage methods makes it invaluable across industries.
In this article, we explored:
- The origins of hierarchical clustering
- Divisive and agglomerative methods
- Linkage techniques and cluster distance calculations
- Real-life applications and case studies
- A complete R-based implementation guide
Whether used for customer segmentation, genomic analysis, social behavior modeling, or operational decision-making, hierarchical clustering provides deep, actionable insights when applied correctly.
This article was originally published on Perceptive Analytics.
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