🍩 Database of Original & Non-Theoretical Uses of Topology

(found 2 matches in 0.000755s)
  1. Persistent Homology Based Graph Convolution Network for Fine-Grained 3D Shape Segmentation (2021)

    Chi-Chong Wong, Chi-Man Vong
    Abstract Fine-grained 3D segmentation is an important task in 3D object understanding, especially in applications such as intelligent manufacturing or parts analysis for 3D objects. However, many challenges involved in such problem are yet to be solved, such as i) interpreting the complex structures located in different regions for 3D objects; ii) capturing fine-grained structures with sufficient topology correctness. Current deep learning and graph machine learning methods fail to tackle such challenges and thus provide inferior performance in fine-grained 3D analysis. In this work, methods in topological data analysis are incorporated with geometric deep learning model for the task of fine-grained segmentation for 3D objects. We propose a novel neural network model called Persistent Homology based Graph Convolution Network (PHGCN), which i) integrates persistent homology into graph convolution network to capture multi-scale structural information that can accurately represent complex structures for 3D objects; ii) applies a novel Persistence Diagram Loss (ℒPD) that provides sufficient topology correctness for segmentation over the fine-grained structures. Extensive experiments on fine-grained 3D segmentation validate the effectiveness of the proposed PHGCN model and show significant improvements over current state-of-the-art methods.
  2. Topological Data Analysis for Arrhythmia Detection Through Modular Neural Networks (2020)

    Meryll Dindin, Yuhei Umeda, Frederic Chazal
    Abstract This paper presents an innovative and generic deep learning approach to monitor heart conditions from ECG signals. We focus our attention on both the detection and classification of abnormal heartbeats, known as arrhythmia. We strongly insist on generalization throughout the construction of a shallow deep-learning model that turns out to be effective for new unseen patient. The novelty of our approach relies on the use of topological data analysis to deal with individual differences. We show that our structure reaches the performances of the state-of-the-art methods for both arrhythmia detection and classification.