Using graphical techniques from discriminant analysis to understand and interpret cluster solutions

Clustering is a common form of exploratory analysis in the social and behavioural sciences and education. There are many clustering algorithms available to researchers and each algorithm assigns membership slightly different. This paper compares five classification algorithms (SPSS' TwoStep, k-means, hierarchical (nearest and furthest neighbour), and finite mixture model. The results show the highest agreement among the finite mixture model and the two-step clustering algorithm, as well as k-means and two-step. Hierarchical (nearest neighbour) does not have high agreement with k-means and the mixture model. Once a research decides on a clustering algorithm they often have a hard time interpreting clusters once a solution is reached. This study suggests using discriminant analysis as a method of interpreting cluster solutions which also allows researchers to visually see the interpretation and also provides the number of functions and which measures load on which function allowing more information about the clusters.