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 …

Many data sets can be viewed as a noisy sampling of an underlying space, and tools from
topological data analysis can characterize this structure for the purpose of knowledge …

The continued and dramatic rise in the size of data sets has meant that new methods are
required to model and analyze them. This timely account introduces topological data …

Persistence diagrams, the most common descriptors of Topological Data Analysis, encode
topological properties of data and have already proved pivotal in many different applications …

We explore the evolution of daily returns of four major US stock market indices during the
technology crash of 2000, and the financial crisis of 2007–2009. Our methodology is based …

Topological data analysis (TDA)(Edelsbrunner & Harer, 2010),(Carlsson, 2009) is a field
focused on understanding the shape and structure of data by computing topological …

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 …

In this paper we discuss the adaptation of the methods of homology from algebraic topology
to the problem of pattern recognition in point cloud data sets. The method is referred to as …

This paper focuses on a classification problem for volatile time series. One of the most
popular approaches for time series classification is dynamic time warping and feature-based …