Hierarchical Clustering

Hierarchical clustering is a powerful tool in data analysis. It is valuable across many fields, from market research to bioinformatics, because it helps identify underlying patterns without requiring users to specify the number of clusters beforehand. 

What Is Hierarchical Clustering? 

Hierarchical clustering is a data analysis method used to group similar objects into clusters. This technique organizes data into a hierarchical structure, which can be visualized as a tree called a dendrogram. Each level of the tree combines data points into increasingly larger clusters, starting either from individual elements and merging them into groups (agglomerative method) or by starting with one large cluster and dividing it into smaller ones (divisive method).

How Hierarchical Clustering Works 

• Initialization: In the agglomerative approach, each data point starts as its own cluster. Conversely, in divisive clustering, all points begin in a single cluster.
• Distance Calculation: The algorithm calculates the distances between data points. This can be done using various metrics, such as Euclidean distance for numerical data.
• Linkage Criteria: The method for determining the distance between clusters is chosen, such as the maximum distance (complete linkage), minimum distance (single linkage), or average distance (average linkage). The choice of linkage affects the shape and size of the resulting clusters.
• Cluster Formation: In agglomerative clustering, pairs of clusters are merged based on the linkage criteria. In divisive, a single cluster is split into two at each step.
• Repetition: The process repeats, recalculating distances and merging or splitting clusters until all data is grouped into a single cluster or until it achieves the desired number of clusters.
• Dendrogram Visualization: The results can be visualized using a dendrogram, which shows the order and distance at which points or clusters were merged. This helps to understand the data structure and to decide where to ‘cut’ the dendrogram to achieve a useful clustering.

Types Of Hierarchical Clustering

There are two main types of hierarchical clustering: agglomerative and divisive​.

Agglomerative Clustering

This is the more commonly used form of hierarchical clustering. It starts by treating each data point as a single cluster. Then, iteratively, it merges the closest pairs of clusters into larger clusters. This process continues until all points are merged into a single cluster. The primary methods of determining the “closeness” of clusters include:

• Complete Linkage: Uses the maximum distance between elements of each cluster.
• Single Linkage: Uses the minimum distance between elements of each cluster.
• Average Linkage: Takes the average distance as the basis for merging clusters.
• Ward’s Method: Minimizes the sum of squared differences within all clusters. It is a more compute-intensive method that often results in more meaningful clusters​.

Divisive Clustering

This method works in the opposite manner to agglomerative clustering. It begins with all data points in a single cluster. Then, this cluster is divided into progressively smaller clusters, usually by using a flat clustering method like K-means for splitting each cluster. This process is repeated until each data point stands alone as a cluster. Divisive clustering is less common than agglomerative due to its higher computational complexity and less stable results​.

Both methods use a dendrogram, a tree-like diagram, to illustrate the arrangement of the clusters formed. The dendrogram helps in understanding the data structure and deciding the number of clusters by cutting the dendrogram at a suitable level.

These clustering methods have broad applications, including market segmentation, image and gene expression analysis, and social network analysis. They help in identifying natural groupings in datasets without prior knowledge of the group boundaries​.

Advantages Of Hierarchical Clustering Over Other Clustering Methods

• Intuitive Results: Hierarchical clustering creates a tree-like structure, often visualized as a dendrogram, which is easy to understand. This visual helps in understanding not just where clusters split but also the relative closeness of data points in a cluster.
• No Need to Specify Cluster Numbers: Unlike K-means clustering where you need to specify the number of clusters at the start, hierarchical clustering doesn’t require this. It builds up the number of clusters step by step which can be very useful if you’re unsure how many clusters you might need.
• Flexibility in Cluster Shapes: Hierarchical clustering can form clusters of various shapes and sizes, whereas methods like K-means are usually limited to spherical clusters. This makes hierarchical clustering suitable for a wider range of data types.
• Useful in Exploratory Data Analysis: Since you can visualize the entire hierarchy of clusters, it’s a powerful tool for exploratory data analysis. You can cut the dendrogram at different heights to achieve a desired number of clusters or to explore data structure at different levels of granularity.

Drawbacks Of Hierarchical Clustering 

• Computationally Intensive: Hierarchical clustering is slower and can be computationally expensive, especially with large datasets. It needs to compute the distances between every pair of observations in your dataset, which can be inefficient for large data.
• Sensitive to Outliers: Outliers can distort the distance scale used in hierarchical clustering, leading to misleading clusters. This sensitivity can sometimes necessitate additional preprocessing steps like outlier removal.
• Irreversible Steps: Once two clusters merge in the hierarchy, they can’t be separated again in later stages of the algorithm. This “greedy” approach can sometimes lead to non-optimal clustering decisions early that affect the final results.
• Difficulty in Handling Different Data Sizes: The effectiveness of hierarchical clustering can decrease as the size and dimensionality of the dataset increase. This is because the distance metrics become less meaningful in high-dimensional spaces, often referred to as the “curse of dimensionality.”

Conclusion

Hierarchical clustering offers a unique approach to understanding complex datasets by arranging them into meaningful groups. The flexibility to study data at different levels of granularity and the intuitive presentation of results in a dendrogram make it an indispensable technique in many research areas. As data continues to grow in size and complexity, hierarchical clustering will remain a key tool for analysts seeking to extract actionable insights from vast amounts of information.

FAQs

What is hierarchical clustering?

• Hierarchical clustering is a method that groups similar objects into clusters.
• It visualizes these groups in a tree-like structure known as a dendrogram.
• It doesn’t require specifying the number of clusters in advance.

What are the types of hierarchical clustering?

• Agglomerative: Starts with each data point as a separate cluster and merges them into larger clusters.
• Divisive: Begins with all data points in one cluster and progressively splits them into smaller clusters.

How does hierarchical clustering work?

• Calculate Distances: Measure the distance between each pair of data points.
• Choose Linkage: Decide the criteria for merging (agglomerative) or splitting (divisive) clusters, like nearest or farthest points.
• Visualize: Use a dendrogram to show how clusters are merged or divided.

What are the advantages and drawbacks of hierarchical clustering?

Advantages:

• • Intuitive dendrogram visualization.
  • No need to predefine the number of clusters.
  • Can detect clusters of various shapes and sizes.

Drawbacks:

• • High computational cost, especially with large datasets.
  • Sensitive to outliers which may distort clustering.
  • Irreversible merging or splitting decisions during the process.