Continuous Ordinal Clustering; A Mystery Story
Résumé
Cluster analysis may be considered as an aid to decision theory because of its ability to group the various alternatives. There are often errors in the data that lead one to wish to use algorithms that are in some sense continuous or at least robust with respect to these errors. Known characterizations of continuity are order theoretic in nature even for data that has numerical significance. Reasons for this are given and arguments presented for considering an ordinal form of robustness with respect to errors in the input data. The work is preliminary and some open questions are posed.