Advances in Data Science

3Dimension Reduction and Visualization of Symbolic Interval-Valued Data Using Sliced Inverse Regression

Dimension reduction of interval-valued data is an active research topic in symbolic data analysis (SDA). The main thread has focused on the extension of principal component analysis (PCA). In this study, we extend classic sliced inverse regression (SIR), an alternative dimension reduction method, to interval-valued data to create a method we call interval SIR (iSIR). SIR is a popular slice-based sufficient dimension reduction technique for exploring the intrinsic structure of high-dimensional data. It has been extended and applied to different data types, such as survival data, time-series data, functional data, and longitudinal data. This study considered three families of symbolic-numerical-symbolic approaches to implement iSIR: quantification approaches, distributional approaches, and interval arithmetic approaches. Each family consists of several methods. We evaluated the methods for low-dimensional discriminative and visualization purposes by means of simulation studies and through application to an empirical dataset. Comparison with results obtained via symbolic principal component analysis was also reported. The results provided clues for selecting an appropriate extension of iSIR to analyze the interval-valued data.

3.1. Introduction

In contrast with conventional numerical data tables where an observation on p random variables is realized by a single point in , an ...