Topological data analysis refers to approaches for systematically and reliably computing
abstract 'shapes' of complex data sets. There are various applications of topological data …

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 …

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

Electroencephalography (EEG) is a widely used cerebral activity measuring device for both
clinical and everyday life applications. In addition to denoising and potential classification, a …

It has long been observed that trimethylamine N-oxide (TMAO) and urea demonstrate
dramatically different properties in a protein folding process. Even with the enormous …

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 …

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 and persistent entropy have recently become useful tools for patter
recognition. In this paper, we find requirements under which persistent entropy is stable to …

In this paper, we systematically review weighted persistent homology (WPH) models and
their applications in biomolecular data analysis. Essentially, the weight value, which reflects …

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 …