# Multiscale methods for signal selection in single-cell data

arXiv: https://arxiv.org/abs/2206.07760 · HTML: https://mlsanity.com/paper/2206.07760/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 74 references that are in the map.
- First posted on arXiv 15 Jun 2022.

## Builds on (most cited first, 12 of 12)

- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Topological Signal Processing over Simplicial Complexes](https://mlsanity.com/paper/1907.11577/) (2019)
- [Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyond](https://mlsanity.com/paper/2101.05510/) (2021)
- [What are higher-order networks?](https://mlsanity.com/paper/2104.11329/) (2021)
- [Random walks and diffusion on networks](https://mlsanity.com/paper/1612.03281/) (2016)
- [Persistent Laplacians: properties, algorithms and implications](https://mlsanity.com/paper/2012.02808/) (2020)
- [Random Walks, Markov Processes and the Multiscale Modular Organization of Complex Networks](https://mlsanity.com/paper/1502.04381/) (2015)
- [Graph-based data clustering via multiscale community detection](https://mlsanity.com/paper/1909.04491/) (2019)
- [Multimodal Data Visualization and Denoising with Integrated Diffusion](https://mlsanity.com/paper/2102.06757/) (2021)
- [Finding role communities in directed networks using Role-Based Similarity, Markov Stability and the Relaxed Minimum Spanning Tree](https://mlsanity.com/paper/1309.1795/) (2013)
- [The stability of a graph partition: A dynamics-based framework for community detection](https://mlsanity.com/paper/1308.1605/) (2013)
- [Flow-based network analysis of the Caenorhabditis elegans connectome](https://mlsanity.com/paper/1511.00673/) (2015)

## Built on by (most cited first, 2 of 2)

- [Analysing Multiscale Clusterings with Persistent Homology](https://mlsanity.com/paper/2305.04281/) (2023)
- [MCbiF: Measuring Topological Autocorrelation in Multiscale Clusterings via 2-Parameter Persistent Homology](https://mlsanity.com/paper/2510.14710/) (2025)

## Abstract (arXiv)

Analysis of single-cell transcriptomics often relies on clustering cells and then performing differential gene expression (DGE) to identify genes that vary between these clusters. These discrete analyses successfully determine cell types and markers; however, continuous variation within and between cell types may not be detected. We propose three topologically motivated mathematical methods for unsupervised feature selection that consider discrete and continuous transcriptional patterns on an equal footing across multiple scales simultaneously. Eigenscores (eigi) rank signals or genes based on their correspondence to low-frequency intrinsic patterning in the data using the spectral decomposition of the Laplacian graph. The multiscale Laplacian score (MLS) is an unsupervised method for locating relevant scales in data and selecting the genes that are coherently expressed at these respective scales. The persistent Rayleigh quotient (PRQ) takes data equipped with a filtration, allowing the separation of genes with different roles in a bifurcation process (e.g., pseudo-time). We demonstrate the utility of these techniques by applying them to published single-cell transcriptomics data sets. The methods validate previously identified genes and detect additional biologically meaningful genes with coherent expression patterns. By studying the interaction between gene signals and the geometry of the underlying space, the three methods give multidimensional rankings of the genes and visualisation of relationships between them.