Topological data analysis (TDA) can broadly be described as a collection of data analysis
methods that find structure in data. These methods include clustering, manifold estimation …

Combining concepts from topology and algorithms, this book delivers what its title promises:
an introduction to the field of computational topology. Starting with motivating problems in …

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 persistence has proven to be a key concept for the study of real-valued
functions defined over topological spaces. Its validity relies on the fundamental property that …

Comparing points on 3D shapes is among the fundamental operations in shape analysis. To
facilitate this task, a great number of local point signatures or descriptors have been …

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 …

Manifold reconstruction has been extensively studied for the last decade or so, especially in
two and three dimensions. Recent advances in higher dimensions have led to new methods …

The nerve theorem is a basic result of algebraic topology that plays a central role in
computational and applied aspects of the subject. In topological data analysis, one often …

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

Topological data analysis and its main method, persistent homology, provide a toolkit for
computing topological information of high-dimensional and noisy data sets. Kernels for one …