# No Pressure! Addressing the Problem of Local Minima in Manifold Learning Algorithms

arXiv: https://arxiv.org/abs/1906.11389 · HTML: https://mlsanity.com/paper/1906.11389/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jun 2019.

## Built on by (most cited first, 1 of 1)

- [GradMax: Growing Neural Networks using Gradient Information](https://mlsanity.com/paper/2201.05125/) (2022)

## Abstract (arXiv)

Nonlinear embedding manifold learning methods provide invaluable visual insights into the structure of high-dimensional data. However, due to a complicated nonconvex objective function, these methods can easily get stuck in local minima and their embedding quality can be poor. We propose a natural extension to several manifold learning methods aimed at identifying pressured points, i.e. points stuck in poor local minima and have poor embedding quality. We show that the objective function can be decreased by temporarily allowing these points to make use of an extra dimension in the embedding space. Our method is able to improve the objective function value of existing methods even after they get stuck in a poor local minimum.