Cluster Analysis

Cluster Analysis Definition

Cluster analysis is a set of statistical algorithms employed in multivariate analysis to partition a heterogeneous sample—such as individuals, groups, or entities—into a number of distinct clusters or classes based on their similarity across a specified set of attributes. The fundamental aim is to group objects such that the internal profile differences within each cluster are minimal, while the differences between the clusters themselves are maximised, relative to a chosen set of descriptive indicators. This technique seeks to identify underlying patterns and inherent structures within complex datasets by finding objects that share maximum common features with one another.

Applications

Cluster analysis is widely applied across various disciplines where classification or segmentation is required. In social sciences, it has been used to analyse census data and social indicators to create area typologies, and to identify distinct segments within labour markets. Furthermore, it serves as a powerful exploratory tool for identifying latent patterns in large datasets, measuring significant similarities and differences between entities like individuals or organisations, and developing descriptive classifications and typologies.

Methods and Techniques

There is a rich variety of methods available for performing cluster analysis, which depend on how similarity and difference are defined. These methods generally fall into two main approaches: hierarchical and non-hierarchical.

Hierarchical clustering methods proceed either from ‘bottom up’ (agglomerative) or ‘top down’ (divisive). Agglomerative clustering starts by treating every object as an individual cluster, successively merging the closest objects based on a chosen distance criterion (such as the Euclidean distance or linkage measures) until all objects are grouped into a single large cluster. Divisive clustering begins with one overarching cluster and recursively divides it into smaller subsets. The resulting hierarchical structure is often visualised using a dendrogram or tree diagram.

Other methods include linkage approaches, which define how the distance between two clusters is calculated (e.g., single link/nearest neighbour, complete linkage/furthest neighbour). Further specific algorithms include Ward’s method, which focuses on minimising the sum of squares within groups, and Wishart’s mode analysis. Recent developments include additive overlapping clustering and rectangular clustering, which allow for more complex definitions of similarity.

Practical Considerations

The successful execution of cluster analysis involves several crucial practical decisions that impact the final result. These include selecting the appropriate variables for the analysis, choosing an adequate measure for calculating similarity or distance between objects, and determining the criteria for merging cases into clusters. Because the choice of method can impose structure on the data, there is a risk of obtaining spurious clusters; therefore, employing several different methods is often recommended.

When using hierarchical algorithms, determining the optimal number of clusters remains challenging. While some rules exist—such as observing the change in error sum of squares after each fusion step—these criteria are not always unequivocal. Consequently, selecting the final cluster solution requires evaluation against various criteria, including replicability across different algorithms and samples, alongside a consideration of the interpretability and usefulness of the resulting structure.