This article surveys recent work of Carlsson and collaborators on applications of
computational algebraic topology to problems of feature detection and shape recognition in …

Abstract Information networks are becoming increasingly popular to capture complex
relationships across various disciplines, such as social networks, citation networks, and …

Although deep learning approaches have had tremendous success in image, video and
audio processing, computer vision, and speech recognition, their applications to three …

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

We study the homology of a filtered d-dimensional simplicial complex K as a single
algebraic entity and establish a correspondence that provides a simple description over …

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

The persistence diagram of a real-valued function on a topological space is a multiset of
points in the extended plane. We prove that under mild assumptions on the function, the …

Persistent homology is an algebraic tool for measuring topological features of shapes and
functions. It casts the multi-scale organization we frequently observe in nature into a …

Persistent homology captures the topology of a filtration-a one-parameter family of
increasing spaces-in terms of a complete discrete invariant. This invariant is a multiset of …

Extracting useful information from large data sets can be a daunting task. Topological
methods for analysing data sets provide a powerful technique for extracting such …