We present a novel framework for characterizing signals in images using techniques from
computational algebraic topology. This technique is general enough for dealing with noisy …

In the last decade, there has been increasing interest in topological data analysis, a new
methodology for using geometric structures in data for inference and learning. A central …

Topological data analysis (TDA) applies methods of topology in data analysis and found
many applications in data science in the recent decade that go well beyond machine …

One of the primary areas of interest in applied algebraic topology is persistent homology,
and, more specifically, the persistence diagram. Persistence diagrams have also become …

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 …

The brain network is usually constructed by estimating the connectivity matrix and
thresholding it at an arbitrary level. The problem with this standard method is that we do not …

We consider the problem of statistical computations with persistence diagrams, a summary
representation of topological features in data. These diagrams encode persistent homology …

Topological statistics, in the form of persistence diagrams, are a class of shape descriptors
that capture global structural information in data. The mapping from data structures to …

Topological data analysis provides a multiscale description of the geometry and topology of
quantitative data. The persistence landscape is a topological summary that can be easily …

Natural data offer a hard challenge to data analysis. One set of tools is being developed by
several teams to face this difficult task: Persistent topology. After a brief introduction to this …