Understanding the Achievements and Limitations of Hierarchical Clustering

Hierarchical clustering is a powerful technique in cluster analysis that is widely used in data science and machine learning. This method has two main types: divisive and agglomerative. This article will delve into these types, explore their advantages and disadvantages, and discuss how they are used in cluster analysis.

Types of Hierarchical Clustering

Just to be on the same page, there are two types of hierarchical clustering:

Agglomerative and Divisive Hierarchical Clustering

Agglomerative Clustering is the most common form of hierarchical clustering. It works by starting with each data point as its own cluster and then iteratively merging the closest clusters until a single cluster containing all the data points is formed.

Divisive Clustering is the opposite process. It begins with one big cluster containing all the data points and then recursively splits the clusters into smaller ones until each data point is in its own cluster. This is less commonly used than agglomerative clustering.

Advantages and Disadvantages of Hierarchical Clustering

Advantages

The main advantages of hierarchical clustering include:

Prominence in the algorithm: You don't need to specify the number of clusters in advance. Instead, you can use a dendrogram to determine the optimal number of clusters for your analysis. Implementation simplicity: Hierarchical clustering is relatively straightforward to implement and interpret the results. No set number of clusters: Unlike K-means clustering, where you must specify the number of clusters, hierarchical clustering can automatically determine the number of clusters based on the structure of your data.

Disadvantages

However, there are also several disadvantages to consider:

Irreversibility: The hierarchical clustering algorithm is irreversible, meaning it can never undo decisions made during the clustering process. Variability based on distance matrix: The choice of distance matrix can impact performance, leading to sensitivity to noise and outliers, breaking large clusters, difficulty handling different-sized clusters, and handling non-convex shapes. Dendrogram limitations: Identifying the correct number of clusters from a dendrogram can sometimes be challenging.

Evaluation and Further Steps

For a more in-depth understanding and practical exercises on hierarchical clustering (both agglomerative and divisive types), visit the following resource links:

How to Solve Exercises of Agglomerative and Divisive Hierarchical Clustering

Criteria for Hierarchical Clustering

Hierarchical clustering can be guided by different criteria, such as distance linkage, average linkage, minimum variance within and between variance, and centroid linkage:

Distance Linkage: This measures the distance between the closest points in two clusters. Maximum Distance Linkage: Also known as the furthest neighbor method, it uses the maximum distance between any pair of points within the two clusters. Average Linkage: The average distance between all points in one cluster and all points in the other cluster. Minimum Variance within and between Variance Maximum: A method where the variance within clusters is minimized, and the variance between clusters is maximized. Centroid Linkage: This method uses the centroid (mean) of the clusters for distance computation.

Using Dendrograms

A dendrogram is a tree-like diagram that illustrates the hierarchical clustering process. Each vertical slice in the dendrogram represents a cluster, and the distance between the merges is shown along the horizontal axis. This tool helps in visualizing the clustering process and determining the number of clusters.

By examining the dendrogram, data analysts can identify appropriate numbers of clusters and understand the hierarchical structure of their data. It is particularly useful for visual interpretation in exploratory data analysis and pre-processing steps.