End-to-end topological learning using 1-parameter persistence is well-known. We show that
the framework can be enhanced using 2-parameter persistence by adopting a recently …

Hypergraphs have seen widespread applications in network and data science communities
in recent years. We present a survey of recent work to define topological objects from …

Persistent homology (PH) is one of the main methods used in Topological Data Analysis. An
active area of research in the field is the study of appropriate notions of PH representatives …

The barcode computation of a filtration can be computationally expensive. Therefore, it is
useful to have methods to update a barcode if the associated filtration undergoes small …

Microscopic examination of slides prepared from tissue samples is the primary tool for
detecting and classifying cancerous lesions, a process that is time-consuming and requires …

Topological data analysis (TDA) is an emerging branch of data science that utilizes
algebraic topology. Despite its wide range of applications, it has been challenging to apply …

The use of persistent homology in applications is justified by the validity of certain stability
results. At the core of such results is a notion of distance between the invariants that one …

DONUT1 [GLR22] is a database of papers about practical, real-world uses of topological
data analysis (TDA). Its original seed was planted in a group chat formed during the HIM …

Scientific background Topological data analysis (TDA) is a novel approach to gain insights
on complex data sets using tool from algebraic topology [3]. Since its advent around 25 …