This work introduces a new dataset and framework for the exploration of topological data
analysis (TDA) techniques applied to time-series data. We examine the end-to-end TDA …

We propose PLLay, a novel topological layer for general deep learning models based on
persistence landscapes, in which we can efficiently exploit the underlying topological …

Persistent homology is a powerful mathematical tool that summarizes useful information
about the shape of data allowing one to detect persistent topological features while one …

Semi-supervised graph domain adaptation, as a branch of graph transfer learning, aims to
annotate unlabeled target graph nodes by utilizing transferable knowledge learned from a …

Experimental measurements of physical systems often have a limited number of
independent channels, causing essential dynamical variables to remain unobserved …

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 …

Persistent homology is a recently developed theory in the field of algebraic topology to study
shapes of datasets. It is an effective data analysis tool that is robust to noise and has been …

This paper introduces decorated merge trees (DMTs) as a novel invariant for persistent
spaces. DMTs combine both π 0 and H n information into a single data structure that …

Persistence diagrams offer a way to summarize topological and geometric properties latent
in datasets. While several methods have been developed that use persistence diagrams in …

Topological features such as persistence diagrams and their functional approximations like
persistence images (PIs) have been showing substantial promise for machine learning and …