TDA Comparison: Clustering vs. Persistent Homology vs. KeplerMapper

This repository contains a Python script (tda_comparison.py) that demonstrates and compares different data analysis techniques on a synthetically generated "noisy circle" dataset. The goal is to illustrate how Topological Data Analysis (TDA) methods can reveal underlying structural features that traditional methods might miss.

Techniques Explored:

1. K-Means Clustering: A standard partitioning clustering algorithm.
2. Persistent Homology (via giotto-tda): Computes a persistence diagram to quantify topological features like connected components (H0) and loops/holes (H1).
3. Mapper (via kmapper) : Constructs a graph-based (simplicial complex) representation of the data, providing a visual summary of its shape and connectivity.

Features:

• Generates a 2D noisy circle dataset.
• Applies K-Means clustering and visualizes the results.
• Computes and visualizes a persistence diagram.
• Constructs and visualizes a KeplerMapper graph (outputs an interactive HTML file).
• Provides clear Matplotlib visualizations and console output for interpretation.
• Well-commented and structured Python code.

How to Run:

1. Clone the repository:

   git clone <your-repo-url>
   cd <your-repo-name>

2. Install dependencies: Ensure you have Python 3 installed. Then, install the required libraries:

   pip install numpy matplotlib scikit-learn giotto-tda kmapper

   (You might want to use a virtual environment for this.)

3. Run the script:

   python tda_comparison.py

4. View Outputs:

   • Console output will provide summaries and insights.
   • Matplotlib plots will display K-Means results and the persistence diagram.
   • An HTML file (default: kepler_mapper_noisy_circle.html) will be generated for the interactive KeplerMapper graph. This file will attempt to open in your default web browser.

Expected Outcome:

The script aims to show:

• How K-Means might segment the circle based on local density.
• How the persistence diagram clearly identifies the single significant loop (H1 feature) of the circle.
• How the KeplerMapper graph visually represents this circular structure as a looped graph.

This comparison highlights the strengths of TDA in capturing global topological characteristics of data.

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