GENERALIZED MINKOWSKI METRICS FOR MIXED FEATURE-TYPE DATA-ANALYSIS

This paper presents simple and convenient generalized Minkowski metric s on the multidimensional feature space in which coordinate axes are a ssociated with not only quantitative features but also qualitative and structural features. The metrics are defined on a new mathematical mo del (U((d)), +, X) which is called simply the Cartesian space model, w here U((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((d)), and + is the Cartesian meet operator which extracts a common description from given descriptions on U((d)) . To illustrate the effectiveness of our generalized Minkowski metrics , we present an approach to the hierarchical conceptual clustering, an d a generalization of the principal component analysis for mixed featu re data.