Network-based modeling of complex systems and data using the language of graphs has
become an essential topic across a range of different disciplines. Arguably, this graph-based …

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 …

We propose a novel approach for preserving topological structures of the input space in
latent representations of autoencoders. Using persistent homology, a technique from …

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 …

Biology has entered the age of Big Data. The technical revolution has transformed the field,
and extracting meaningful information from large biological data sets is now a central …

Persistent homology is a widely used tool in Topological Data Analysis that encodes
multiscale topological information as a multi-set of points in the plane called a persistence …

We present a short tutorial and introduction to using the R package TDA, which provides
some tools for Topological Data Analysis. In particular, it includes implementations of …

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 …

The learnability of different neural architectures can be characterized directly by computable
measures of data complexity. In this paper, we reframe the problem of architecture selection …

We propose PLLay, a novel topological layer for general deep learning models based on
persistence landscapes, in which we can efficiently exploit the underlying topological …