# Nonlinear Dimensionality Reduction via Path-Based Isometric Mapping

arXiv: https://arxiv.org/abs/1312.0803 · HTML: https://mlsanity.com/paper/1312.0803/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Dec 2013.

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

- [Density-based Isometric Mapping](https://mlsanity.com/paper/2403.02531/) (2024)

## Abstract (arXiv)

Nonlinear dimensionality reduction methods have demonstrated top-notch performance in many pattern recognition and image classification tasks. Despite their popularity, they suffer from highly expensive time and memory requirements, which render them inapplicable to large-scale datasets. To leverage such cases we propose a new method called "Path-Based Isomap". Similar to Isomap, we exploit geodesic paths to find the low-dimensional embedding. However, instead of preserving pairwise geodesic distances, the low-dimensional embedding is computed via a path-mapping algorithm. Due to the much fewer number of paths compared to number of data points, a significant improvement in time and memory complexity without any decline in performance is achieved. The method demonstrates state-of-the-art performance on well-known synthetic and real-world datasets, as well as in the presence of noise.