Generalized Minkowski metrics for mixed feature-type data analysis

Abstract

This paper presents simple and convenient generalized Minkowski metrics on the multidimensional feature space in which coordinate axes are associated with not only quantitative features but also qualitative and structural features. The metrics are defined on a new mathematical model (U/sup (d/),[+], [X]) which is called simply the Cartesian space model, where U/sup (d/) is the feature space which permits mixed feature types, [+] is the Cartesian join operator which yields a generalized description for given descriptions on U/sup (d/), and [X] is the Cartesian meet operator which extracts a common description from given descriptions on U/sup (d/). To illustrate the effectiveness of our generalized Minkowski metrics, we present an approach to the hierarchical conceptual clustering, and a generalization of the principal component analysis for mixed feature data.>