Introduction to Cluster Hierarchy Dendrograms

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.