https://github.com/aidos-lab/curvature-filtrations
SCOTT: Synthesizing Curvature Operations and Topological Tools
https://github.com/aidos-lab/curvature-filtrations
curvature graph-generative-model neurips-2023 topological-data-analysis topological-machine-learning
Last synced: about 1 month ago
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SCOTT: Synthesizing Curvature Operations and Topological Tools
- Host: GitHub
- URL: https://github.com/aidos-lab/curvature-filtrations
- Owner: aidos-lab
- License: bsd-3-clause
- Created: 2023-10-24T13:46:41.000Z (almost 2 years ago)
- Default Branch: main
- Last Pushed: 2025-07-04T13:43:33.000Z (3 months ago)
- Last Synced: 2025-07-10T15:27:20.896Z (3 months ago)
- Topics: curvature, graph-generative-model, neurips-2023, topological-data-analysis, topological-machine-learning
- Language: Python
- Homepage: https://aidos.group/curvature-filtrations/
- Size: 1.05 MB
- Stars: 14
- Watchers: 2
- Forks: 3
- Open Issues: 4
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# SCOTT
## **S**ynthesizing **C**urvature **O**perations and **T**opological **T**ools
[](https://codeclimate.com/github/aidos-lab/curvature-filtrations/maintainability)   [](https://arxiv.org/abs/2301.12906)
`SCOTT` is a Python package for computing **curvature filtrations** for graphs and graph distributions. This repository accompanies our NeurIPS 2023 paper: [_Curvature Filtrations for Graph Generative Model Evaluation_](https://arxiv.org/abs/2301.12906).
Our method introduces a novel way to compare graph distributions, avoiding the limitations of Maximal Mean Discrepancy (MMD), which has known [drawbacks](https://arxiv.org/abs/2106.01098).
By combining **discrete curvature** on graphs with **persistent homology**, `SCOTT` provides expressive descriptors of graph sets that are:
- **Robust**
- **Stable**
- **Expressive**
- **Compatible with Statistical Testing**
The package is highly adaptable, offering several options for **user customization**, including different curvature computation methods and diverse metrics for comparing persistent homology outputs.
### **Cite Us**
If you find this package useful in your research, please consider citing:
```bibtex
@misc{southern2023curvature,
title={Curvature Filtrations for Graph Generative Model Evaluation},
author={Joshua Southern and Jeremy Wayland and Michael Bronstein and Bastian Rieck},
year={2023},
eprint={2301.12906},
archivePrefix={arXiv},
primaryClass={cs.LG}
}
```
# Installation
### Using `pip`
Install `curvature-filtrations` via pip:
```bash
$ pip install curvature-filtrations
```
### Building from Source
Our dependencies are managed with [`poetry`](https://python-poetry.org), which can be installed with `pip install poetry`. To install from source:
1. Clone the repository
```bash
$ git clone https://github.com/aidos-lab/curvature-filtrations.git
```
1. Navigate to the directory
```bash
$ cd curvature-filtrations
```
3. Install dependencies
```bash
$ poetry install
```
# Quick Start
The example.py script demonstrates how to compute the distance between two graph distributions.
To use SCOTT with your own data, replace the example graph distributions with your own. Distributions should be lists of `networkx` graphs or single `networkx` graphs.
### Run our Example Script
```bash
python scripts/example.py
```
# Tutorials
For a walkthrough of customization options and the intermediary functionalities supported by SCOTT objects, please see `/notebooks`. We offer the following two tutorials:
### 1. **Customizing how your comparison is executed:** `custom_compare.ipynb`
**_Read this section if:_** Your primary goal is to find the distance between your graph distributions, but you are looking for additional ways to customize the curvature and distance measures used.
Functionalities demonstrated in this tutorial include:
- Changing the method used for curvature calculations and associated hyperparameters
- Selecting and customizing the vectorization used to compare persistence diagrams
### 2. **Breakdown of intermediate functionalities:** `bagpipeline.ipynb`
**_Read this section if:_** You want to better understand the underlying workflow of this process and/or are interested in the output from intermediate steps in the process.
Functionalities demonstrated in this tutorial include:
- Calculating curvature for one graph or graph distribution
- Executing a curvature filtration to produce a persistence diagram
- Converting persistence diagrams into a topological descriptor (e.g. persistence landscape)
- Computing the distance between topological descriptors
Both tutorials are supported by `/notebooks/utils.py`.
# Core Components
### KILT
`KILT` stands for: *K*rvature-*I*nformed *L*inks and *T*opology is an object that can compute curvature filtrations for single graphs.
```python
import networkx as nx
from scott import KILT,Comparator
G = nx.erdos_reyni(14,0.4)
kilt = KILT(measure="forman_curvature")
D = kilt.fit_transform(G)
print(f"Forman Curvature Filtration:")
print(f"Curvature Filtration Values:{kilt.curvature}")
print(D)
```
### Comparator
`Comparator` handles comparisons between graphs or graph distributions!
```python
import networkx as nx
from scott import KILT,Comparator
graph_dist1 = [nx.erdos_reyni(10,0.4) for _ in range(40)]
graph_dist2 = [nx.erdos_reyni(20,0.6) for _ in range(50)]
compare = Compare(measure="forman_curvature")
dist = compare.fit_transform(graph_dist1,graph_dist2,metric="image")
print(f"Distance between distributions measured by Forman Filtration: {dist}")
```