# A slice tour for finding hollowness in high-dimensional data

arXiv: https://arxiv.org/abs/1910.10854 · HTML: https://mlsanity.com/paper/1910.10854/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Oct 2019.

## Built on by (most cited first, 3 of 3)

- [Interactive slice visualization for exploring machine learning models](https://mlsanity.com/paper/2101.06986/) (2021)
- [Computationally Efficient Learning of Statistical Manifolds](https://mlsanity.com/paper/2103.11773/) (2021)
- [Visualization of a multidimensional point cloud as a 3D swarm of avatars](https://mlsanity.com/paper/2504.06751/) (2025)

## Abstract (arXiv)

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.