Hierarchical clustering is a clustering method in which the data objects are represented in the form of a tree-like structure (dendrogram). It is a bottom-up approach, where each object is initially considered as a separate cluster and then, based on the similarity between objects, the clusters are merged recursively until a single cluster is formed.
Example: Suppose we have a dataset of 6 points in 2-D space as follows:
(1,2), (2,4), (2,5), (3,5), (4,6), (5,7)
We can start with each point being a cluster on its own, and then start merging the closest points into a new cluster. For example, we can merge (2,4) and (1,2) into a new cluster with an average coordinate (1.5,3), then merge that with (2,5) into a new cluster with an average coordinate (1.8,3.7).
We then proceed to form a cluster with (3,5) and the previous cluster, resulting in a new cluster with an average coordinate (2.1,4.2). Finally, we merge the last two points with the previous cluster, creating a new cluster with an average coordinate (4.5,6.5).
The dendrogram representation of the hierarchical clustering can be seen as:
(1,2)
/ \
(2,4) (2,5)
/ \ |
(3,5) (4,6) (5,7)
The resulting dendrogram shows us how the clusters were formed and at which distance level they were merged.
Hierarchical clustering is a clustering technique that identifies grouping patterns based on a hierarchical structure.
It is an unsupervised learning method used to group items based on their similarity or dissimilarity.
In hierarchical clustering, items are grouped based on the distances between them.
There are two types of hierarchical clustering methods: agglomerative and divisive.
Agglomerative clustering begins with each data point as a separate cluster and merge the most similar clusters iteratively, creating a hierarchical tree of clusters.
Divisive clustering, on the other hand, starts with all items in one cluster and successively splits them into smaller clusters based on the dissimilarity between the data points.
The result of hierarchical clustering is a dendrogram, which is a tree-like diagram that shows the hierarchies of clusters.
The dendrogram can be sliced at different levels to form clusters of different sizes and densities.
The effectiveness of hierarchical clustering depends on the choice of distance metric, linkage method, and the number of clusters.
Applications of hierarchical clustering include gene expression analysis, market segmentation, and image segmentation, among others.
What is Hierarchical Clustering?
Answer: Hierarchical Clustering is a type of clustering algorithm that groups together data points with close similarities and builds a hierarchy of clusters.
What is the difference between Agglomerative and Divisive Hierarchical Clustering?
Answer: Agglomerative Hierarchical Clustering is the bottom-up approach, where each observation starts in its cluster, and the algorithm merges the closest pairs of clusters until there is only one cluster. Divisive Hierarchical Clustering is the top-down approach, where all observations start in one cluster, and the algorithm splits the cluster recursively into smaller clusters until each observation is in its cluster.
What are the advantages of Hierarchical Clustering?
Answer: Hierarchical Clustering is simple to understand and interpret, does not require a prior assumption of the number of clusters, and provides a visual representation of the clusters’ hierarchy.
How do you determine the optimal number of clusters in Hierarchical Clustering?
Answer: There are several methods to determine the optimal number of clusters, including Elbow Method, Silhouette Score, Gap Statistic, and Dendrogram Analysis.
What are the applications of Hierarchical Clustering?
Answer: Hierarchical Clustering is used in various fields, such as biology, social sciences, marketing, and healthcare, to group similar objects or individuals, identify patterns, and make predictions.