Topological Data Analysis (TDA) is a recent and fast growing field providing a set of new
topological and geometric tools to infer relevant features for possibly complex data. This …

Attempts to incorporate topological information in supervised learning tasks have resulted in
the creation of several techniques for vectorizing persistent homology barcodes. In this …

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

Examination of chest X-ray images is currently one of the most important methods for the
screening and diagnosis of thoracic diseases and, in some cases, for assessing response to …

In this paper we develop an alternative topological data analysis (TDA) approach for
studying graph representations of time series of dynamical systems. Specifically, we show …

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 …

Persistence diagrams are one of the main tools in the field of Topological Data Analysis
(TDA). They contain fruitful information about the shape of data. The use of machine learning …

We present a method called Significant Cosmic Holes in Universe (SCHU) for identifying
cosmic voids and loops of filaments in cosmological datasets and assigning their statistical …

Persistent homology (PH) is one of the most popular methods in Topological Data Analysis.
Even though PH has been used in many different types of applications, the reasons behind …

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 …