Hierarchical Clustering

• Blockchain Council
• August 27, 2024

Hierarchical clustering is a powerful method used to organize data. This technique finds wide application across various fields, from identifying communities in social networks to arranging products in e-commerce sites. 

What Is Hierarchical Clustering? 

Hierarchical clustering is a data analysis technique used to organize data points into clusters, or groups, based on similar characteristics. This method builds a tree-like structure, known as a dendrogram, which visually represents the levels of similarity among different data clusters. 

There are two main types of hierarchical clustering: agglomerative and divisive. Agglomerative is a “bottom-up” approach where each data point starts as its own cluster, and pairs of clusters are merged as one moves up the hierarchy. Divisive is a “top-down” approach that starts with all data points in one cluster and progressively splits them into smaller clusters.

How Hierarchical Clustering Works 

Hierarchical clustering starts by treating each data point as a separate cluster. Then, it follows these steps:

• Identify the Closest Clusters: The process begins by calculating the distance between each pair of clusters. In simple terms, it looks for the two clusters that are closest to each other. This step uses specific measurements, like the Euclidean distance (straight-line distance between two points), to determine closeness.
• Merge Clusters: Once the closest pairs of clusters are identified, they are merged to form a new cluster. This new cluster represents all the data points in the merged clusters.
• Repeat the Process: This process of finding and merging the closest clusters continues iteratively until all the data points are merged into a single cluster or until the desired number of clusters is reached.
• Create a Dendrogram: The entire process can be visualized using a tree-like diagram known as a dendrogram, which shows how each cluster is related to the others. It helps in deciding where to ‘cut’ the tree to achieve a desired number of clusters.

Types Of Hierarchical Clustering

Hierarchical clustering organizes data into a tree-like structure and can be divided into two main types: 

• Agglomerative and 
• Divisive

Agglomerative Clustering

This is the more common form of hierarchical clustering. It is a bottom-up approach where each data point starts as its own cluster. The process involves repeatedly merging the closest pairs of clusters into larger clusters. This continues until all data points are merged into a single cluster or until a desired number of clusters is reached. The primary methods used in agglomerative clustering include:

• Single Linkage: Clusters are merged based on the minimum distance between data points from different clusters.
• Complete Linkage: Clusters are merged based on the maximum distance between data points from different clusters.
• Average Linkage: Clusters are merged based on the average distance between all pairs of data points in different clusters.
• Ward’s Method: This method merges clusters based on the minimum variance criterion, which minimizes the total within-cluster variance.

Divisive Clustering

This method is less common and follows a top-down approach. It starts with all data points in a single cluster. The cluster is then split into smaller, more distinct groups based on a measure of dissimilarity. This splitting continues recursively until each data point is its own cluster or a specified number of clusters is achieved. Divisive clustering is computationally intensive and not as widely used as agglomerative clustering due to its complexity and the computational resources required.

Advantages Of Hierarchical Clustering Over Other Clustering Methods

• Easy to Understand: Hierarchical clustering is straightforward to grasp and apply, even for beginners. It visualizes data in a way that is intuitive, helping to clearly see the relationships between different groups.
• No Need for Predefined Clusters: Unlike many clustering methods that require the number of clusters to be specified in advance, hierarchical clustering does not. This flexibility allows it to adapt to the data without needing prior knowledge of how many groups to expect​.
• Visual Representation: It provides a dendrogram, a tree-like diagram, which helps in understanding the clustering process and the hierarchical relationship between clusters. This visual tool is especially useful for presenting and interpreting data​​.
• Handles Non-Linear Data: Hierarchical clustering can manage non-linear data sets effectively, making it suitable for complex datasets where linear assumptions about data structure do not hold​.
• Multi-Level Clustering: It allows for viewing data at different levels of granularity. By examining the dendrogram, users can choose the level of detail that suits their needs, from broad to very specific groupings​.

Drawbacks Of Hierarchical Clustering 

• Computationally Intensive: As the dataset grows, hierarchical clustering becomes computationally expensive and slow. It’s less suitable for large datasets due to the increased time and computational resources required​.
• Sensitive to Noise and Outliers: This method is particularly sensitive to noise and outliers in the data, which can significantly affect the accuracy of the clusters formed, potentially leading to misleading results.
• Irreversible Merging: Once two clusters are merged in the process of building the hierarchy, this action cannot be undone. This irreversible process may lead to suboptimal clustering if not carefully managed​.
• Assumption of Hierarchical Structure: Hierarchical clustering assumes that data naturally forms a hierarchy. This might not be true for all types of data, limiting its applicability in scenarios where such a structure does not exist​.
• Difficulty in Determining the Optimal Number of Clusters: Despite its flexibility, determining the right number of clusters to use from the dendrogram can be challenging and subjective, often depending on the analyst’s judgment and experience.

Conclusion

Understanding hierarchical clustering opens up new possibilities for data analysis, providing a clear method for grouping and interpreting datasets. By building a dendrogram, this technique not only helps in identifying the natural groupings within data but also in understanding the relationship depth between the groups. 

FAQs

What is hierarchical clustering?

• Hierarchical clustering is a method of organizing data into clusters based on similarities.
• It creates a tree-like structure called a dendrogram to represent the clusters.

How does hierarchical clustering work?

• It starts by treating each data point as a separate cluster.
• Then, it iteratively merges or splits clusters based on their proximity to each other until the desired number of clusters is achieved.

What are the advantages of hierarchical clustering?

• It’s easy to understand and visualize, especially with dendrograms.
• There’s no need to predefine the number of clusters.
• It can handle non-linear data effectively.

What are the drawbacks of hierarchical clustering?

• It becomes computationally intensive with large datasets.
• It’s sensitive to noise and outliers in the data.
• Once clusters are merged, it’s irreversible.
• Determining the optimal number of clusters can be challenging.