README.md

---
title: TDA Explorer
emoji: "\U0001F52E"
colorFrom: indigo
colorTo: blue
sdk: gradio
sdk_version: 5.29.1
app_file: app.py
pinned: false
license: mit
short_description: Interactive Persistent Homology & Betti Numbers
tags:
  - topological-data-analysis
  - persistent-homology
  - mathematics
  - data-science
  - visualization
---

# TDA Explorer

**Interactive Topological Data Analysis** - Explore persistent homology, Betti numbers, and simplicial complexes on point cloud datasets.

## Features

- **8 preset datasets**: Circle, Figure-8, Concentric Circles, Clusters, Moons, Sphere (3D), Torus (3D), Random Noise
- **Persistent homology**: Compute H0 (components), H1 (loops), H2 (voids) using Ripser
- **Persistence diagrams & barcodes**: Visualize feature birth/death
- **Interactive filtration**: Drag the epsilon slider to watch the Vietoris-Rips complex form in real time
- **Betti numbers**: Live count of topological features at any scale
- **Custom data**: Upload your own CSV point cloud
- **Educational**: Learn TDA concepts with the built-in guide

## How to Use

1. Select a dataset and click **Generate & Analyze**
2. Explore the persistence diagram and barcode to understand the topology
3. Drag the **epsilon slider** to see how the simplicial complex evolves
4. Watch Betti numbers change as you adjust the filtration
5. Upload your own data (CSV with x,y or x,y,z columns)

## Built By

**Dr. Milan Amrutkumar Joshi** - Senior Faculty, AI & Data Science
Research interests: Persistent Homology, Topological Data Analysis, Machine Learning

- [Hugging Face](https://huggingface.co/mlnjsh)
- [Google Scholar](https://scholar.google.com/citations?user=_ML2_woAAAAJ)
- [GitHub](https://github.com/mlnjsh)