Topological Data Learning: A Deep Learning Model for Analyzing Complex Systems

Abstract

This paper introduces a novel deep learning model designed for analyzing complex systems by directly processing topological data. The core concept revolves around representing complex data as graphs and leveraging Graph Neural Networks (GNNs) for deep learning. Traditional deep learning methods often struggle with non-Euclidean data, presenting a significant limitation when dealing with systems where relationships are more important than coordinates. This research aims to bridge this gap by providing a framework capable of learning from topological features, ultimately leading to improved insights and predictive capabilities. The model utilizes persistent homology to extract topological features and then feeds them into a GNN for further processing. We demonstrate the potential of this approach through theoretical analysis and discuss its implications for various applications. This work contributes to the growing field of topological data analysis (TDA) by integrating it with the power of deep learning.