Sliced Inverse Regression for Dimension Reduction and Visualization of the Interval-valued Data

Abstract

Sliced inverse regression (SIR) was introduced by Li (1991) to find the effective dimension reduction directions for exploring the intrinsic structure of high-dimensional data. For univariate response regression, SIR has been extended and applied to various types of data such as the survival data, the time series data, the functional data and the longitudinal data. This study intends to develop SIR for dimension reduction and visualization of the interval-valued symbolic data. Four families of the symbolic-numerical-symbolic approaches were considered: the quantification methods, the distributional methods, the interval arithmetic methods and the pair model methods. We compared and evaluated the proposed methods based on both simulated data and real data for lower-dimensional discriminative and visualization purposes.