The last decade saw an enormous boost in the field of computational topology: methods and
concepts from algebraic and differential topology, formerly confined to the realm of pure …

With the recent explosion in the amount, the variety, and the dimensionality of available
data, identifying, extracting, and exploiting their underlying structure has become a problem …

Time series analysis has proven to be a powerful method to characterize several
phenomena in biology, neuroscience and economics, and to understand some of their …

Segmentation algorithms are prone to make topological errors on fine-scale struc-tures, eg,
broken connections. We propose a novel method that learns to segment with correct …

The Wasserstein distance and its variations, eg, the sliced-Wasserstein (SW) distance, have
recently drawn attention from the machine learning community. The SW distance …

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 …

Attempts to incorporate topological information in supervised learning tasks have resulted in
the creation of several techniques for vectorizing persistent homology barcodes. In this …

We introduce giotto-tda, a Python library that integrates high-performance topological data
analysis with machine learning via a scikit-learn-compatible API and state-of-the-art C++ …

In this paper we study generative modeling via autoencoders while using the elegant
geometric properties of the optimal transport (OT) problem and the Wasserstein distances …

The reemergence of Deep Neural Networks (DNNs) has lead to high-performance
supervised learning algorithms for the Electro-Optical (EO) domain classification and …