# Reconstructing Latent Orderings by Spectral Clustering

arXiv: https://arxiv.org/abs/1807.07122 · HTML: https://mlsanity.com/paper/1807.07122/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jul 2018.

## Built on by (most cited first, 4 of 4)

- [Localization in 1D non-parametric latent space models from pairwise affinities](https://mlsanity.com/paper/2108.03098/) (2021)
- [Matrix Reordering for Noisy Disordered Matrices: Optimality and Computationally Efficient Algorithms](https://mlsanity.com/paper/2201.06438/) (2022)
- [Estimating the history of a random recursive tree](https://mlsanity.com/paper/2403.09755/) (2024)
- [Active Seriation: Efficient Ordering Recovery with Statistical Guarantees](https://mlsanity.com/paper/2603.15336/) (2026)

## Abstract (arXiv)

Spectral clustering uses a graph Laplacian spectral embedding to enhance the cluster structure of some data sets. When the embedding is one dimensional, it can be used to sort the items (spectral ordering). A number of empirical results also suggests that a multidimensional Laplacian embedding enhances the latent ordering of the data, if any. This also extends to circular orderings, a case where unidimensional embeddings fail. We tackle the task of retrieving linear and circular orderings in a unifying framework, and show how a latent ordering on the data translates into a filamentary structure on the Laplacian embedding. We propose a method to recover it, illustrated with numerical experiments on synthetic data and real DNA sequencing data. The code and experiments are available at https://github.com/antrec/mdso.