# Low-Rank Isomap Algorithm

arXiv: https://arxiv.org/abs/2103.04060 · HTML: https://mlsanity.com/paper/2103.04060/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 37 references that are in the map.
- First posted on arXiv 6 Mar 2021.

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

- [TopoMap: A Feature-based Semantic Discriminator of the Topographical Regions in the Test Input Space](https://mlsanity.com/paper/2509.03242/) (2025)

## Abstract (arXiv)

The Isomap is a well-known nonlinear dimensionality reduction method that highly suffers from computational complexity. Its computational complexity mainly arises from two stages; a) embedding a full graph on the data in the ambient space, and b) a complete eigenvalue decomposition. Although the reduction of the computational complexity of the graphing stage has been investigated, yet the eigenvalue decomposition stage remains a bottleneck in the problem. In this paper, we propose the Low-Rank Isomap algorithm by introducing a projection operator on the embedded graph from the ambient space to a low-rank latent space to facilitate applying the partial eigenvalue decomposition. This approach leads to reducing the complexity of Isomap to a linear order while preserving the structural information during the dimensionality reduction process. The superiority of the Low-Rank Isomap algorithm compared to some state-of-art algorithms is experimentally verified on facial image clustering in terms of speed and accuracy.