Hierarchical Cluster Analysis [Simply explained]

Summary

Hierarchical Cluster Analysis (HCA) is a clustering method that groups objects into hierarchical structures based on their similarities. The video explains the key concepts of HCA, including calculating distances between data points using methods like Euclidean, Manhattan, and Maximum Distance. It also covers different linkage methods—Single, Complete, and Average Linkage—and how clusters are formed step-by-step. The process involves calculating a distance matrix and progressively merging clusters. The video provides a practical example of HCA and demonstrates how to use an online tool to calculate and visualize clusters, making HCA more accessible for users.

Takeaways

• 😀 Hierarchical cluster analysis is a clustering method that creates a hierarchical tree (dendrogram) representing the relationships between data points and how they are grouped at various levels.
• 😀 The first step in hierarchical clustering is to plot the data points on a scatter plot and assign each point to its own cluster.
• 😀 Clusters are progressively merged, with the closest clusters being joined first. This merging continues until all points are in a single cluster.
• 😀 To calculate the distance between two points, you can use different distance metrics like Euclidean distance, Manhattan distance, and maximum distance.
• 😀 Euclidean distance is calculated as the square root of the sum of the squared differences between corresponding coordinates of two points.
• 😀 Manhattan distance is the sum of the absolute differences between the corresponding coordinates of two points.
• 😀 Maximum distance is the largest absolute difference between corresponding coordinates of two points.
• 😀 In hierarchical clustering, different linkage methods determine how clusters are connected, including single linkage, complete linkage, and average linkage.
• 😀 Single linkage merges clusters based on the closest elements between them, while complete linkage merges based on the furthest elements.
• 😀 Average linkage merges clusters based on the average of all pairwise distances between their elements.
• 😀 The distance matrix is a key tool in hierarchical clustering, helping to calculate and visualize the distance between all pairs of clusters as the merging process progresses.

Q & A

What is hierarchical cluster analysis?

Hierarchical cluster analysis is a clustering method that creates a hierarchical tree of objects to be clustered. The tree shows the relationships between the objects and how they are grouped at various levels.

How is hierarchical cluster analysis calculated?

The calculation starts by plotting the data points on a scatter plot and assigning each point its own class. Clusters are then progressively merged based on their proximity, using a distance metric like Euclidean, Manhattan, or Maximum distance.

What is the role of the distance matrix in hierarchical clustering?

The distance matrix shows the distances between every pair of clusters. It helps to determine which clusters are closest and should be merged first in the hierarchical process.

What are the most common methods for calculating the distance between points?

The most common methods for calculating the distance between points are Euclidean distance, Manhattan distance, and Maximum distance.

How is Euclidean distance calculated?

Euclidean distance is calculated as the square root of the sum of the squared differences between corresponding coordinates of two points.

What is the difference between single linkage, complete linkage, and average linkage?

Single linkage uses the shortest distance between elements of two clusters, complete linkage uses the longest distance, and average linkage uses the average of all pairwise distances between the clusters.

What happens after the first cluster merger in hierarchical clustering?

After the first cluster merger, the distance matrix is updated to reflect the new distances between the merged clusters and the remaining clusters, and the process continues with merging the next closest clusters.

What is a dendrogram and how is it used in hierarchical clustering?

A dendrogram is a tree-like diagram used to visualize the sequence of cluster mergers. It helps in determining the number of clusters by examining the 'elbow' of the tree, where the rate of merger decreases.

How does the elbow method help in determining the optimal number of clusters?

The elbow method helps determine the optimal number of clusters by identifying the point in the dendrogram where adding more clusters results in minimal improvement, indicating the ideal number of clusters.

Can hierarchical clustering be performed online, and if so, how?

Yes, hierarchical clustering can be performed online using tools like datadeep.net, where users can upload their dataset, choose clustering parameters (distance and linkage methods), and view the results in tree and scatter plots.