Dual Scaling Classification and Its Application in Archaeometry

Abstract

We consider binary classification based on the dual scaling technique. In the case of more than two classes many binary classifiers can be considered. The proposed approach goes back to Mucha (An intelligent clustering technique based on dual scaling. In: S. Nishisato, Y. Baba, H. Bozdogan, K. Kanefuji (eds.) Measurement and multivariate analysis, pp. 37–46. Springer, Tokyo, 2002) and it is based on the pioneering book of Nishisato (Analysis of categorical data: Dual scaling and its applications. The University of Toronto Press, Toronto, 1980). It is applicable to mixed data the statistician is often faced with. First, numerical variables have to be discretized into bins to become ordinal variables (data preprocessing). Second, the ordinal variables are converted into categorical ones. Then the data is ready for dual scaling of each individual variable based on the given two classes: each category is transformed into a score. Then a classifier can be derived from the scores simply in an additive manner over all variables. It will be compared with the simple Bayesian classifier (SBC). Examples and applications to archaeometry (provenance studies of Roman ceramics) are presented.