Persistent homology (PH) is a method used in topological data analysis (TDA) to study
qualitative features of data that persist across multiple scales. It is robust to perturbations of …

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 …

Topological deep learning (TDL) is an emerging area that combines the principles of
Topological data analysis (TDA) with deep learning techniques. TDA provides insight into …

Regularization plays a crucial role in supervised learning. Most existing methods enforce a
global regularization in a structure agnostic manner. In this paper, we initiate a new direction …

Epilepsy is a neurological disorder that can negatively affect the visual, audial and motor
functions of the human brain. Statistical analysis of neurophysiological recordings, such as …

A crucial step in the analysis of persistent homology is the transformation of data into an
appropriate topological object (which, in our case, is a simplicial complex). Software …

The persistence diagram is an increasingly useful tool from Topological Data Analysis, but
its use alongside typical machine learning techniques requires mathematical finesse. The …

As the field of Topological Data Analysis continues to show success in theory and in
applications, there has been increasing interest in using tools from this field with methods for …

Nearest neighbor-based methods are commonly used for classification tasks and as
subroutines of other data-analysis methods. An attacker with the capability of inserting their …

In this chapter, we present an overview of recent techniques from the emerging area of
topological data analysis (TDA), with a focus on machine-learning applications. TDA …