Dimension Reduction and Visualization of Symbolic Interval‐Valued Data Using Sliced Inverse Regression
Han‐Ming Wu, Chiun‐How Kao, Chun‐Houh Chen · 2020
Sliced inverse regression (SIR) is a popular slice-based sufficient dimension reduction technique for exploring the intrinsic structure of high-dimensional data. A main goal of dimension reduction is data visualization. This chapter reviews the extension of principal component analysis (PCA) to the interval-valued data, followed by a brief description of the classic SIR. It considers different families of symbolic-numerical-symbolic approaches to extend SIR to the interval-valued data. The chapter evaluates the implemented interval SIR methods and compare the results with those of interval PCA for low-dimensional discriminative and visualization purposes by means of simulation studies. The analysis of interval-valued data usually serves as the basic principle for analyzing other types of symbolic data, such as multi-valued data, modal-valued data, and modal multi-valued data. The advantage of the distributional approaches is that the resulting symbolic covariance matrix fully utilizes all the information in the data.