# Numerical Approximation of Andrews Plots with Optimal Spatial-Spectral Smoothing

arXiv: https://arxiv.org/abs/2304.13239 · HTML: https://mlsanity.com/paper/2304.13239/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 13 references that are in the map.
- First posted on arXiv 26 Apr 2023.

## Builds on (most cited first, 1 of 1)

- [Filament Plots for Data Visualization](https://mlsanity.com/paper/2107.10869/) (2021)

## Abstract (arXiv)

Andrews plots provide aesthetically pleasant visualizations of high-dimensional datasets. This work proves that Andrews plots (when defined in terms of the principal component scores of a dataset) are optimally ``smooth'' on average, and solve an infinite-dimensional quadratic minimization program over the set of linear isometries from the Euclidean data space to L2([0,1]). By building technical machinery that characterizes the solutions to general infinite-dimensional quadratic minimization programs over linear isometries, we further show that the solution set is (in the generic case) a manifold. To avoid the ambiguities presented by this manifold of solutions, we add ``spectral smoothing'' terms to the infinite-dimensional optimization program to induce Andrews plots with optimal spatial-spectral smoothing. We characterize the (generic) set of solutions to this program and prove that the resulting plots admit efficient numerical approximations. These spatial-spectral smooth Andrews plots tend to avoid some ``visual clutter'' that arises due to the oscillation of trigonometric polynomials.