Exploratory Projection Pursuit for Fuzzy Data

Abstract

Projection Pursuit is a computer-intensive method for multivariate statistical analysis which intends to clarify properties of multivariate data by projecting them onto lower-dimensional subspace.In practice, the projection pursuit is performed based on an algorithm to find a lower-dimensional subspace by maximizing an objective function called projection index which is a measure of interestingness of the projected data.Adapting this method for fuzzy data, it was proposed to use measures of fuzziness as projection index, and to find the subspace by minimizing the measures of fuzziness of projected data. So the subspace in which they are as crisp as possible is searched.But from the viewpoint of statistical analysis, important properties such as cluster or functional relationship are not considered.In this paper, we propose a method that includes both interestingness of data and the measures of fuzziness called hybrid index. And we confirm the efficiency of projection pursuit using this index by numerical experiments.