A slice tour for finding hollowness in high-dimensional data

TL;DR

This paper introduces a simple slicing technique in high-dimensional data visualization, enabling better detection of non-linear and concave structures through interpolated projections during data tours.

Contribution

It presents a novel slicing method in the orthogonal space of projections, implemented as an R extension to enhance high-dimensional data exploration.

Findings

Enables visualization of concavities and non-linear structures

Implemented as an R package extension

Facilitates exploration of complex multivariate distributions

Abstract

Taking projections of high-dimensional data is a common analytical and visualisation technique in statistics for working with high-dimensional problems. Sectioning, or slicing, through high dimensions is less common, but can be useful for visualising data with concavities, or non-linear structure. It is associated with conditional distributions in statistics, and also linked brushing between plots in interactive data visualisation. This short technical note describes a simple approach for slicing in the orthogonal space of projections obtained when running a tour, thus presenting the viewer with an interpolated sequence of sliced projections. The method has been implemented in R as an extension to the tourr package, and can be used to explore for concave and non-linear structures in multivariate distributions.