README.md

metadata

title: TDA Explorer
emoji: 🔮
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
• Google Scholar
• GitHub