Topological structure of complex predictions

A demo site for a paper by Meng Liu, Tamal Dey, and David Gleich.

What is GTDA and Reeb net analysis?

Topological Data Analysis (TDA) applies ideas from topology to study real-world data. GTDA or Graph-based TDA, is a related concept we derived that utilizes graph structure instead of point cloud structure for TDA.

What does this have to do with complex predictive models?

We use GTDA and the Reeb network structure it produces in order to analyze the results of neural network-like methods. Given a set of data points and their relationships as a graph (or created via a nearest neighbor computation) and a predictive model that outputs the probability that each datapoint belongs to a class. (This can typically be extracted from the last layer of a deep learning model.) Then the Reeb network analyzes the interaction between the structure of the data and the structure of the predictions.

This makes it easy to flag problematic points.

Where are the demos?

In order to appreciate these demos, you may want to familiarize yourself with a quick overview of the idea in our manuscript. We are working on more self-contained introductions to the idea.

• Demostration on Swiss Roll using a Graph Convolution Network (GCN)
• Demo on Amazon product categories with GCN
• Demo on Imagenette
• Demo on BRCA1 gene variants
• Demo on Fashion MNIST