Network-based modeling of complex systems and data using the language of graphs has
become an essential topic across a range of different disciplines. Arguably, this graph-based …

In topological data analysis (TDA), one often studies the shape of data by constructing a
filtered topological space, whose structure is then examined using persistent homology …

" In this chapter, we introduce some of the very basics that are used throughout the book.
First, we give the definition of a topological space and related notions of open and closed …

A suitable feature representation that can both preserve the data intrinsic information and
reduce data complexity and dimensionality is key to the performance of machine learning …

Our intention, at the beginning, was to write a short paper resolving some technical issues in
the theory of topological persistence. Specifically, we wished to present a clean easy-to-use …

AMS :: Bulletin of the American Mathematical Society Skip to Main Content American
Mathematical Society American Mathematical Society MathSciNet Bookstore Publications …

This work introduces a number of algebraic topology approaches, including multi-
component persistent homology, multi-level persistent homology, and electrostatic …

We study how the topology of a data set M= Ma∪ Mb⊆ ℝ d, representing two classes a and
b in a binary classification problem, changes as it passes through the layers of a well-trained …

Data analysis techniques from network science have fundamentally improved our
understanding of neural systems and the complex behaviors that they support. Yet the …

Graph neural networks (GNNs) are a powerful architecture for tackling graph learning tasks,
yet have been shown to be oblivious to eminent substructures such as cycles. We present …