TUN: Detecting Significant Points in Persistence Diagrams with Deep Learning

TL;DR

This paper introduces TUN, a deep learning model that automatically detects significant points in persistence diagrams, improving the interpretability and reliability of topological data analysis for practical applications.

Contribution

We propose TUN, a novel multi-modal neural network that combines advanced PD descriptors, self-attention, and point cloud encoding for automatic significance detection in persistence diagrams.

Findings

TUN outperforms classic methods in detecting significant points.

TUN effectively handles imbalanced data and provides reliable identification.

Experiments demonstrate TUN's applicability in real-world scenarios.

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.