Football and the Dark Side of Cluster Analysis

In cluster analysis, decisions on data preprocessing such as how to select, transform, and standardise variables and how to aggregate information from continuous, count and categorical variables cannot be made in a supervised manner, i.e., based on prediction of a response variable. Statisticians often attempt to make such decisions in an automated way by optimising certain objective functions of the data anyway, but this usually ignores the fact that in cluster analysis these decisions determine the meaning of the resulting clustering. We argue that the decisions should be made based on the aim and intended interpretation of the clustering and the meaning of the variables. The rationale is that preprocessing should be done in such a way that the resulting distances, as used by the clustering method, match as well as possible the "interpretative distances" between objects as determined by the meaning of the variables and objects. Such "interpretative distances" are usually not precisely specified and involve a certain amount of subjectivity. We will use ongoing work on clustering football players based on performance data to illustrate how such decisions can be made, how much of an impact they can have, how the data can still help with them and to highlight some issues with the approach.