Topometry

Abstract

1. Introduction

Empirically, TopoMetry often outperforms PCA-based pipelines and stand-alone layouts. Still, let the data decide—TopoMetry includes metrics and reports to support evidence-based choices.

For background, see our preprint: https://doi.org/10.1101/2022.03.14.484134

We approximate the Laplace–Beltrami operator (LBO) by learning well-weighted similarity graphs and their Laplacian/diffusion operators. The eigenfunctions of these operators form an orthonormal basis—the spectral scaffold—that captures the dataset’s intrinsic geometry across scales. This view connects to Diffusion Maps, Laplacian Eigenmaps, and related kernel eigenmaps, and enables downstream tasks such as clustering and graph-layout optimization with geometry preserved.

2. Objective

Systematically learn and evaluate the latent geometry of high-dimensional data, with a focus on scRNAseq analysis

This project demonstrates how Python, Machine Learning, scikit-learn can be applied to a real-world Data Science problem.

4. Technology Stack

5. System Requirements

General requirements for this technology stack — check the README for exact versions.

• Python 3.8 or later
• pip / virtualenv for dependencies
• VS Code, PyCharm or Jupyter Notebook
• Git (to clone the repository)

6. Installation & Setup

git clone https://github.com/davisidarta/topometry.git
cd topometry

sudo apt-get install cmake
pip install scikit-build setuptools

pip install topometry

Full setup instructions are in the project README.

7. Future Enhancements

Suggested extensions you can add to make this your own project.

• Turn the analysis into an interactive dashboard
• Automate data refresh with a scheduled job
• Add a predictive model on top of the analysis

8. Viva / Review Questions

Common questions examiners ask for projects in this domain.

1. What is the source of the dataset and how was missing data handled?
2. Which exploratory analysis steps revealed the most useful insight?
3. Why were these particular charts chosen to present the data?
4. Which statistical or ML technique supports the conclusions?
5. How could the analysis be automated or refreshed with new data?

9. Source Code & License

This project is developed by davisidarta and published on GitHub under the MIT License. Please follow the license terms and credit the original author when you use or modify this code.