Topo Descriptor Experiments

This repository contains the code for experiments presented in:

B. T. Fasy, M. Makarchuk, S. Mika, and D. L. Millman
"Too Many or Too Few? Sampling Bounds for Topological Descriptors."

These experiments study how different sampling strategies impact the use of topological descriptors, focusing on the challenges of oversampling, undersampling, and proposing an alternative method based on coarse stratification.

---

Project Overview

The central theme of this project is sampling for topological descriptors.
We explore two key issues:

• Oversampling: when geometric discretization produces too many descriptors.
• Undersampling: when fixed-size discretizations miss important strata.

Finally, we demonstrate the effectiveness of an alternative approach using coarse stratification on small plane graphs.

---

Setup Instructions

1. Clone the repository and navigate into the project directory:

   git clone <repo_url>
   cd topo-descriptor-experiments

2. Create and activate the conda environment:

   conda env create -n your_conda_environment_name -f environment.yml
   conda activate your_conda_environment_name

3. Preprocess the datasets (RANDPTS, MPEG7, EMNIST):

   python preprocessing.py

---

Running Main Experiments

1. Experiment 1: Too Many — Geometric-Based Discretization

Goal:
Investigate how the size of the smallest one-stratum changes as the number of vertices increases.

Run:

```bash
python exp_handler.py --epsilon 001 --experiment 1 --data 4
python exp_handler.py --epsilon 005 --experiment 1 --data 4
```

• epsilon controls the ε-net resolution (001 for 0.01 or 005 for 0.05).
• data 4 runs across all datasets (RANDPTS, MPEG7, EMNIST).
• You can also run individually:
  • --data 1 for RANDPTS
  • --data 2 for MPEG7
  • --data 3 for EMNIST

---

2. Experiment 2: Too Few — Constant Size Discretization

Goal:
Study how fixing the discretization size affects the number of captured strata as the number of vertices varies.

Run:

```bash
python exp_handler.py --epsilon 001 --experiment 2 --data 4
python exp_handler.py --epsilon 005 --experiment 2 --data 4
```

• Same dataset options as in Experiment 1.

---

3. Experiment 3: Alternative Approach — Small Graphs

Goal:
Demonstrate the use of coarse stratification for distinguishing small plane graphs.

Run:

```bash
python small_graph_exp.py --bbox 60 --number_of_vertices 4
python small_graph_exp.py --bbox 80 --number_of_vertices 5
python small_graph_exp.py --bbox 30 --number_of_vertices 6
```

• bbox controls the bounding box size.
• number_of_vertices sets how many vertices are in the graph.

---

Notes

• Results will be saved in different locations depending on the script — no unified /results folder is created.
• The environment.yml installs all necessary dependencies for graph processing and topological data analysis.
• Compatible with Python 3.9.13 only!