Unlike **K-means**, hierarchical clustering doesn't produce a fixed number of clusters directly. Instead, it produces a hierarchy. You need a method to decide where to **cut the dendrogram** to obtain the desired number of clusters. 

## Methods for Determining the Number of Clusters

To determine the optimal number of clusters, several methods are commonly used, including dendrogram visualization, the elbow method, and the silhouette method.

### Dendrogram Visualization

This method involves visually inspecting the dendrogram for the **largest vertical gaps** that are **not intersected by horizontal lines**. The number of clusters can be deduced from the number of vertical lines these gaps encompass. However, this method is **subjective** and relies heavily on visual interpretation.

### Elbow Method (using within-cluster sum of squares - WCSS)

In this approach, you perform hierarchical clustering for a range of cluster numbers and calculate the WCSS for each. By plotting the **WCSS values against the number of clusters**, you can identify an **"elbow" point** in the plot. This point indicates a good balance between minimizing WCSS and avoiding an excessive number of clusters, similar to the elbow method in K-means.

### Silhouette Method

This method involves calculating **silhouette scores** for different numbers of clusters by cutting the dendrogram at various heights. The optimal number of clusters is the one that corresponds to the **highest average silhouette score**.

Which of the following is a commonly used method to determine the number of clusters in hierarchical clustering?

Gain a solid understanding of cluster analysis, a key unsupervised learning technique for uncovering patterns in unlabeled data. Explore the essentials of K-Means, Hierarchical Clustering, DBSCAN, and GMMs, and get hands-on experience with real datasets to build confidence in applying clustering to real-world problems.

Dive into the fundamentals of clustering and discover how it differs from classification. Explore essential algorithms, tools, and libraries that power this unsupervised learning technique to uncover hidden patterns in data.

Gain a solid understanding of key preprocessing techniques that ensure effective clustering. Learn how to handle missing values, encode categorical features, normalize data, and choose appropriate distance measures and linkages to boost clustering accuracy.

Master the skills needed to apply K-Means clustering effectively. Learn how the algorithm works, determine the optimal number of clusters, and gain hands-on experience by implementing K-Means on both synthetic and real-world datasets.

Explore the essentials of hierarchical clustering and learn how to group data into meaningful clusters using dendrograms. Build confidence in identifying the optimal number of clusters and implementing the technique on both synthetic and real-world datasets.

Discover how DBSCAN excels at detecting clusters of varying shapes and handling noise in data. Learn the mechanics behind this density-based algorithm, how to assign points to clusters, and apply it to both synthetic and real datasets with confidence.

Gain a solid understanding of Gaussian Mixture Models and how they use probability to model complex cluster shapes. Learn the principles of Gaussian distribution, explore how GMMs work, and build confidence by applying them to both dummy and real-world data.

Cluster Analysis

Optimal Number of Clusters

Methods for Determining the Number of Clusters

Dendrogram Visualization

Elbow Method (using within-cluster sum of squares - WCSS)

Silhouette Method