TUN: Detecting Significant Points in Persistence Diagrams with Deep Learning

2025-12-16

AI Summary

This study addresses the automatic and robust identification of genuine topological signal points in persistence diagrams (PDs) to enhance the interpretability and practical applicability of topological data analysis. To this end, we propose TUN—the first multimodal neural network designed for semantic understanding of PDs—integrating enhanced geometric/topological descriptors, self-attention mechanisms, PointNet-style point cloud encoding, and a learnable multimodal feature fusion module for end-to-end salient point detection. To handle PDs’ inherent sparsity and extreme class imbalance, we introduce specialized preprocessing and weighted training strategies. Evaluated on multiple standard benchmarks, TUN significantly outperforms both classical heuristic and existing deep learning methods in detection accuracy and robustness. Our approach establishes a generalizable technical paradigm for automated PD interpretation, advancing the deployment of topological features in real-world applications.

Technology Category

• Machine Learning: Multimodal Learning
• Computer Vision: Multi-modal Vision
• Intelligent Robots: Multimodal Perception & Sensor Fusion

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Large pretrained models with web data
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

Persistence diagrams (PDs) provide a powerful tool for understanding the topology of the underlying shape of a point cloud. However, identifying which points in PDs encode genuine signals remains challenging. This challenge directly hinders the practical adoption of topological data analysis in many applications, where automated and reliable interpretation of persistence diagrams is essential for downstream decision-making. In this paper, we study automatic significance detection for one-dimensional persistence diagrams. Specifically, we propose Topology Understanding Net (TUN), a multi-modal network that combines enhanced PD descriptors with self-attention, a PointNet-style point cloud encoder, learned fusion, and per-point classification, alongside stable preprocessing and imbalance-aware training. It provides an automated and effective solution for identifying significant points in PDs, which are critical for downstream applications. Experiments show that TUN outperforms classic methods in detecting significant points in PDs, illustrating its effectiveness in real-world applications.

Problem

• Automated detection of significant points in persistence diagrams
• Enhancing topological data analysis for practical applications
• Improving reliability of persistence diagram interpretation for decision-making

Innovation

• Multi-modal network with self-attention and PointNet-style encoder
• Stable preprocessing and imbalance-aware training for robustness
• Automated per-point classification for persistence diagram significance detection