Topological Data Analysis (TDA) is a recent and fast growing field providing a set of new
topological and geometric tools to infer relevant features for possibly complex data. This …

This tutorial provides a gentle introduction to kernel density estimation (KDE) and recent
advances regarding confidence bands and geometric/topological features. We begin with a …

We present an accelerated algorithm for hierarchical density based clustering. Our new
algorithm improves upon HDBSCAN*, which itself provided a significant qualitative …

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 …

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 …

Geometric and topological inference deals with the retrieval of information about a geometric
object using only a finite set of possibly noisy sample points. It has connections to manifold …

One of the most elusive challenges within the area of topological data analysis is
understanding the distribution of persistence diagrams arising from data. Despite much effort …

Both music and language are found in all known human societies, yet no studies have
compared similarities and differences between song, speech, and instrumental music on a …

Persistent homology (PH) provides topological descriptors for geometric data, such as
weighted graphs, which are interpretable, stable to perturbations, and invariant under, eg …