Manabu Ichino

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. >

General Metrics For Mixed Features The Cartesian Space Theory For Pattern Recognition

General distance functions for mixed feature variables are defined based on the Cartesian space (U/sup (d)/, +,x) which is our new mathematical model for pattern recognition. In our metrics, a sample can be described by a d-tuple which is composed of closed intervals and/or finite sets.

The relative neighborhood graph for mixed feature variables

Abstract The rectangular influence graph (RIG) is presented as an extension of the relative neighborhood graph (RNG). The RNG is an efficient tool for analyzing the clustering of multidimensional feature vectors when all the features are quantitative. The RIG is a similar tool that can accommodate feature vectors some of whose components are qualitative. We show that the RIG is a superset of the Gabriel graph with respect to any Minkowski metric. As tools to analyze interclass structure, the interclass RIG (IRIG) and the mutual neighborhood graph (MNG) are presented. These graphs can be used to reduce the training set in the design of piecewise linear classifiers. The MNG leads also to a sufficient condition for the linear separability between classes.

A Nonparametric Multiclass Pattern Classifier

A nonparametric multiclass classifier is presented. Each pattern class is described by hyperrectangles in the measurement space. These hyperrectangles are generated by the basic event generation (BEG) algorithm which realizes set theoretical training set reduction. The classification of new patterns is performed by examining which basic event includes the patterns. The experimental results indicate that the classifier is effective.

Optimum feature selection by zero-one integer programming

An optimal method for finding a minimum feature subset based on box classifiers is described. Feature selection is represented as a problem of zero-one integer programming. An implicit enumeration method is developed in order to solve this problem. Numerical examples are presented to illustrate the effectiveness of the approach.

The quantile method for symbolic principal component analysis

In this article, we present a new quantification method to realize the principal component analysis (PCA) for symbolic data tables. We first describe the nesting property for the monotone point sequences and the correlation matrix by the rank correlation coefficient. Then, we present the object splitting method by which interval valued data table can be transformed to a usual numerical data table. We are able to apply the traditional PCA to this transformed data table. The quantile method is a generalization of the object splitting method, and can manipulate histograms, nominal multi-value types, and other types simultaneously. We present several experimental results in order to illustrate the usefulness of the quantile method.

Feature Selection for Symbolic Data Classification

This paper presents the Cartesian space model (CSM) which is a mathematical model to treat symbolic data. Then, as a similar theorem to the Theorem of the ugly duckling by Watanabe, we present the Pretended simplicity theorem based on the mutual neighborhood graph (MNG) defined on the CSM. Our feature selection method is realized in terms of the MNG. We present a parity problem in order to illustrate the effectiveness of our feature selection method.

Exploitation of Multivalued Type Proximity for Symbolic Feature Selection

In this paper, a simple and efficient feature selection scheme for symbolic data is proposed. The proposed scheme exploits the symbolic multivalued proximity measures for feature selection. The effectiveness of the proposed scheme has been demonstrated through experiments on standard symbolic data sets

Suboptimum Linear Feature Selection in Multiclass Problem

A suboptimum method of linear feature selection in multiclass problem is presented. The set of features is selected in sequential manner based on an upper bound on the probability of error. The proposed method is applied to a problem of classifying Japanese vowels. Computer simulation results are presented and discussed.

Nonparametric Feature Selection Method Based on Local Interclass Structure

A nonparametric feature selection method which can be applicable to pattern recognition problems based on mixed features is presented. In the pattern space, each pattern class is represented by multiple subregions according to local interclass structure. Then in each of the subregions, feature selection is performed in a simple nonparametric way. Our feature selection method can select a feature subset based on higher order discriminating information. Some basic properties of our approach are presented theoretically and experimentally.