Which of the following distance metrics is commonly used in hierarchical clustering?Cosine similarityEuclidean distanceJaccard indexHamming distance

1. Break Down the Problem

To identify the distance metric commonly used in hierarchical clustering, we need to analyze each option provided: Cosine similarity, Euclidean distance, Jaccard index, and Hamming distance.

2. Relevant Concepts

• Cosine Similarity: Measures the cosine of the angle between two vectors. It is more commonly used in text mining and information retrieval.
• Euclidean Distance: The straight-line distance between two points in Euclidean space. It's a widely used metric in various clustering algorithms, including hierarchical clustering.
• Jaccard Index: Used to compare the similarity and diversity of sample sets. Often applied in situations dealing with categorical data and set comparison.
• Hamming Distance: Measures the difference between two strings of equal length by counting the number of positions at which the corresponding symbols are different. It's typically used in coding theory.

3. Analysis and Detail

Among these metrics, Euclidean distance is most frequently used in hierarchical clustering. This is because hierarchical clustering creates a tree-like structure (dendrogram) based on the distances between data points, and the Euclidean distance allows for a natural geometric understanding of data separation.

4. Verify and Summarize

To recap, hierarchical clustering relies heavily on distance measures that can reflect the geometric properties of the data, making Euclidean distance an ideal choice for this purpose compared to the other options listed.

Final Answer

The distance metric commonly used in hierarchical clustering is Euclidean distance.