persistent homology

Discovering a new drug costs more than a billion dollars and takes ten years or
more. So researchers are always looking for new ways to use computers to find
more promising candidate drugs. We present a promising new system that applies
the two-parameter persistent homology to the
complex task of finding good drug candidates, by finding similarities in the 3D
shapes of the molecules.

In this talk, we will discuss a variety of applications of persistent homology. We will begin with a quick overview of some of the classic examples of applications such as sensor networks and natural imagery. Then, we will explore a number of additional applications such as brain arteries, hyperspectral imagery, dynamical systems, and biological aggregations. Throughout, we will discuss methods to combine topological features with machine learning.

A fundamental question in the study of high-dimensional data is as
follows: Given high-dimensional point cloud samples, how can we infer
the structures of the underlying data?
In manifold learning, we assume the data is supported by a
low-dimensional space with a manifold structure.
However, such an assumption may be too restrictive in practice when we are given point cloud samples not of a manifold but of a stratified space, which contain singularities and mixed dimensionality.