Introduction to Cluster Hierarchy Dendrograms

Study Notes

Introduction to Cluster Hierarchy Dendrograms

A dendrogram is a tree-like diagram representing hierarchical relationships between objects or data points.
In cluster analysis, it visually depicts how clusters are nested within each other as you move up the hierarchy.
Each branch represents the merging of two clusters at a specific distance or similarity threshold.

Construction of a Dendrogram

Dendrograms are built using algorithms measuring distances or similarities between data points.
Common methods include single linkage, complete linkage, and average linkage.
These methods compare similarities in different ways, producing unique dendrograms.

Interpreting a Dendrogram

Branch height signifies the distance at which clusters merged.
Close branches indicate higher similarity or lower distance between data points.
Horizontal distance between clusters shows their separation or overlap.
Ideal clusters are well-separated.

Types of Clustering Methods

Agglomerative Hierarchical Clustering: Common dendrogram-building method.
- Starts with individual data points as separate clusters.
- Progressively merges the closest clusters until all data points are in a single cluster.
Divisive Hierarchical Clustering:
- Starts with all data points in one cluster.
- Recursively divides clusters based on maximum distance or minimum similarity until individual data points form clusters.

Linkage Methods for Agglomerative Clustering

Single Linkage:
- Distance between two clusters is the shortest distance between any two data points, one from each cluster. Potentially prone to noise.
Complete Linkage:
- Distance between two clusters is the longest distance between any two data points, one from each cluster. Creates potentially well-defined but potentially broader clusters.
Average Linkage:
- Distance between two clusters is the average distance between all pairs of data points, one from each cluster. Provides a balanced measure, a compromise between single and complete linkage.

Different Dendrogram Representations

Horizontal dendrogram: Common layout for visualizing the tree structure.
Vertical dendrogram: Less common layout, still used to show hierarchical structure.

Applications of Cluster Hierarchy Dendrograms

Bioinformatics: Analyzing gene expression or protein structures.
Market Research: Clustering customers based on purchasing patterns or preferences.
Image Segmentation: Grouping pixels based on color or texture.
Data Compression: Hierarchically compressing data meaningfully.

Limitations of Dendrograms

Dendrogram interpretation can be subjective, heavily influenced by the chosen linkage method.
Determining the optimal number of clusters is often challenging.
Interpreting large datasets can be complex.
Dendrograms offer a hierarchical view but not necessarily all details about individual clusters.

Description

This quiz explores dendrograms and their role in cluster analysis. It covers how they are constructed using various linkage methods and how to interpret their structure. Learn about the hierarchical relationships depicted in dendrograms and their significance in data analysis.