Hiroyuki Yaguchi

Generalized Minkowski metrics for mixed feature-type data analysis

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. >

An apparent simplicity appearing in pattern classification problems

Abstract An apparent simplicity appearing in the classification problems is described in order to assert the importance of the feature selection. If we assume that the sample size is finite, then, by increasing the number of features used to describe each sample pattern, we can improve the interclass distinguishability. On the other hand, increasing the number of features reduces the generality of class descriptions. Therefore, the enhanced distinguishability may be an apparent simplicity appearing in the interclass structure. We illustrate theoretically and experimentally the existence of the trade-off between the interclass distinguishability and the generality of class descriptions.

The New Feature Selection Method Based on the Interclass Distinguishibility and the Generality of Class Description

Abstract In many actual pattern classification problems, feature selection is an important design process. Assume that the sample size is finite. Then, by increasing the number of features used to describe each sample pattern, the interclass distinguishability is improved on one side but the generality of class description is deteriorated on the other side. This paper presents a new feature selection method which takes into account both of the interclass distinguishability and the generality of class description. In our new method, we used the Interclass Mutual Neighbor IMN as an index of the distinguishability and the generality. We defined IMN as the number of samples included in a particular region made from a pair of samples which come from opposed pattern class. We applied the proposed method to some data sets As the results we illustrate the effectiveness of our feature selection method by applying it to several artificial and actual data sets.