Measuring similarity is key to cluster analysis. ‘Similarity’ quantifies how alike or different objects or datapoints are. This is crucial for tasks like recommendations, image recognition, and document clustering. The method we use for measuring similarity depends on our data and the intended application.

Here is an (artificial) example of a cluster analysis which minimises intra-cluster distance, and maximises inter-cluster distance:

There are two main types of measurement:

• distance-based measures (measuring how far apart items are); and
• correlation-based measures (evaluating relationships between variables).

graph TB
    A["Similarity Measures"] --> B["Distance-Based"]
    A --> C["Correlation-Based"]
    
    B --> D["Euclidean Distance"]
    B --> E["Manhattan Distance"]
    
    C --> F["Cosine Similarity"]
    C --> G["Pearson Correlation"]
    
    D --> H["Straight line distance<br/>between points"]
    E --> I["Sum of absolute<br/>differences along axes"]
    F --> J["Angle between<br/>vectors"]
    G --> K["Linear relationship<br/>between variables"]

    %% Add descriptions
    style D fill:#e1f5fe
    style E fill:#e1f5fe
    style F fill:#f3e5f5
    style G fill:#f3e5f5

Content map

To learn more about probability spaces, read each of the following sections:

Euclidean Distance

Manhattan Distance

Cosine Similarity

Jaccard Index

Next element

Clustering algorithms