Bootstrap method to evaluate tightness of clusters with application to the Korean standard occlusion study

Dental arch form is an important part of dental orthodontic practice. Distance-based clustering methods are often used to find standard arch forms. In particular, S-J. Lee, S.I. Lee, J. Lim, H-J. Park, and T. Wheeler Method to classify human dental arch form, Am. J. Orthod. Dentofacial Orthop. (2010), to appear] propose a ₁-type distance which is invariant to the location-shift and the rotational transformation. Despite the popularity of the distance-based methods, little attention is given to the choice of the distance which has a great influence on final clusters. We have three goals in this paper. First, we study the properties of the ₁-type distance by Lee et al. (2010). Second, we propose a bootstrap-based procedure to evaluate quantitatively how good the clusters are. Finally, we apply the bootstrap procedure to the Korean standard occlusion study and compare the existing distance-based clustering methods in previous literature.