Hierarchical cluster analysis of features
Cluster analyses are typically used to find homogeneous groups of persons
(buyers, voters, employees etc).
A wide range of procedures exist, which can be divided into two categories: hierarchical and partitional procedures.
Partitional procedures assume a predefined number of groups and attempt to optimize the categorization of the elements (i.e. generally persons) in a step-by-step process. The criterion used for optimization is to seek to group the elements in such a way that, on the one hand, all the elements in a group are as similar as possible, and on the other hand, the resulting groups are as strongly differentiated from one another as possible.
The individual steps in the clustering process are generally not interpretable. They only serve as steps towards the final goal, but they cannot be used in their own right.
Hierarchical procedures use a different approach. These use a step-by-step process to combine two elements, or one element and an already existing group, or two already existing groups of elements. Thus the sequence of the clustering procedure produces a hierarchy of similarity of all the elements involved. With the clustering of persons, this generally delivers no additional information. Here, as in the partitional analysis, only the final groupings at different levels of cluster numbers are meaningful. Which level is the most meaningful is decided on the basis of technical and content criteria.
In contrast to the clustering of persons, the process of merging features delivers important learnings. The analysis shows us which features are combined at each step. At each level, it can thus be seen which features are perceived as similar. Existing groups of features become increasingly merged until finally they are all connected with one another.
This is how this procedure differs from factor analysis, which always delivers groupings that are independent of other solutions. It contains no structured sequential merging of all features.
Illustration 1: Dendrogram of a hierarchical clustering process with features
In the hierarchical cluster analysis, figures show at what level the merging into clear groupings occurs, i.e. which groups of features are perceived by the survey respondents as particularly differentiating. Illustration 1 shows a dendrogram that depicts the merging process. The length of the connecting lines also shows us how similar the merged groups are at each respective level.
