Generalized Biplots for Multidimensional Scaled Projections

TL;DR

This paper introduces a generalized biplot method for multidimensional scaling projections, enabling meaningful attribute visualization in low-dimensional space regardless of the dissimilarity measures used.

Contribution

It proposes an iterative scheme to create attribute axes for MDS projections, extending traditional biplots beyond PCA's linear framework.

Findings

Effective visualization of attributes in MDS projections

Compatibility with arbitrary stress and dissimilarity functions

Illustrations with real data examples

Abstract

Dimension reduction and visualization is a staple of data analytics. Methods such as Principal Component Analysis (PCA) and Multidimensional Scaling (MDS) provide low dimensional (LD) projections of high dimensional (HD) data while preserving an HD relationship between observations. Traditional biplots assign meaning to the LD space of a PCA projection by displaying LD axes for the attributes. These axes, however, are specific to the linear projection used in PCA. MDS projections, which allow for arbitrary stress and dissimilarity functions, require special care when labeling the LD space. We propose an iterative scheme to plot an LD axis for each attribute based on the user-specified stress and dissimilarity metrics. We discuss the details of our general biplot methodology, its relationship with PCA-derived biplots, and provide examples using real data.