# On the Selection of Tuning Parameters for Patch-Stitching Embedding Methods

arXiv: https://arxiv.org/abs/2207.07218 · HTML: https://mlsanity.com/paper/2207.07218/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 85 references that are in the map.
- First posted on arXiv 14 Jul 2022.

## Builds on (most cited first, 5 of 5)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Attraction-Repulsion Spectrum in Neighbor Embeddings](https://mlsanity.com/paper/2007.08902/) (2020)
- [On UMAP's true loss function](https://mlsanity.com/paper/2103.14608/) (2021)
- [Intrinsic Isometric Manifold Learning with Application to Localization](https://mlsanity.com/paper/1806.00556/) (2018)
- [Unconstrained and Curvature-Constrained Shortest-Path Distances and their Approximation](https://mlsanity.com/paper/1706.09441/) (2017)

## Abstract (arXiv)

While classical scaling, just like principal component analysis, is parameter-free, other methods for embedding multivariate data require the selection of one or several tuning parameters. This tuning can be difficult due to the unsupervised nature of the situation. We propose a simple, almost obvious, approach to supervise the choice of tuning parameter(s): minimize a notion of stress. We apply this approach to the selection of the patch size in a prototypical patch-stitching embedding method, both in the multidimensional scaling (aka network localization) setting and in the dimensionality reduction (aka manifold learning) setting. In our study, we uncover a new bias--variance tradeoff phenomenon.