Related papers: Dynamical Persistent Homology via Wasserstein Grad…
We introduce in this paper two time discretization schemes tailored for a range of Wasserstein gradient flows. These schemes are designed to preserve mass, positivity and to be uniquely solvable. In addition, they also ensure energy…
Signal processing and machine learning algorithms for data supported over graphs, require the knowledge of the graph topology. Unless this information is given by the physics of the problem (e.g., water supply networks, power grids), the…
Persistence diagrams, an important summary in topological data analysis, consist of a set of ordered pairs, each with positive multiplicity. Persistence diagrams are obtained via Mobius inversion and may be compared using a one-parameter…
Generative modeling typically concerns transporting a single source distribution to a target distribution via simple probability flows. However, in fields like computer graphics and single-cell genomics, samples themselves can be viewed as…
Unravelling the block structure of a network is critical for studying macroscopic features and community-level dynamics. The weighted stochastic block model (WSBM), a variation of the traditional stochastic block model, is designed for…
Techniques from computational topology, in particular persistent homology, are becoming increasingly relevant for data analysis. Their stable metrics permit the use of many distance-based data analysis methods, such as multidimensional…
The Hamiltonian formalism plays a central role in classical and quantum physics. Hamiltonians are the main tool for modelling the continuous time evolution of systems with conserved quantities, and they come equipped with many useful…
Persistent homology is a popular tool in Topological Data Analysis. It provides numerical characteristics of data sets which reflect global geometric properties. In order to be useful in practice, for example for feature generation in…
In this work, we develop a pipeline that associates Persistence Diagrams to digital data via the most appropriate filtration for the type of data considered. Using a grid search approach, this pipeline determines optimal representation…
Recently a new feature representation and data analysis methodology based on a topological tool called persistent homology (and its corresponding persistence diagram summary) has started to attract momentum. A series of methods have been…
Distances have a ubiquitous role in persistent homology, from the direct comparison of homological representations of data to the definition and optimization of invariants. In this article we introduce a family of parametrized pseudometrics…
Finding latent structures in data is drawing increasing attention in diverse fields such as image and signal processing, fluid dynamics, and machine learning. In this work we examine the problem of finding the main modes of gradient flows.…
Inspired by topological data analysis techniques, we introduce persistent homology observables and apply them in a geometric analysis of the dynamics of quantum field theories. As a prototype application, we consider data from a…
Graphs are playing a crucial role in different fields since they are powerful tools to unveil intrinsic relationships among signals. In many scenarios, an accurate graph structure representing signals is not available at all and that…
Graphs are a basic tool for the representation of modern data. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological…
Increased attention has been paid over the last four years to dynamic network embedding. Existing dynamic embedding methods, however, consider the problem as limited to the evolution of a topology over a sequence of global, discrete states.…
Recent studies have actively employed persistent homology (PH), a topological data analysis technique, to analyze the topological information in time series data. Many successful studies have utilized graph representations of time series…
We propose an approach to learning with graph-structured data in the problem domain of graph classification. In particular, we present a novel type of readout operation to aggregate node features into a graph-level representation. To this…
Persistent (co)homology is a central construction in topological data analysis, where it is used to quantify prominence of features in data to produce stable descriptors suitable for downstream analysis. Persistence is challenging to…
Variational inference (VI) can be cast as an optimization problem in which the variational parameters are tuned to closely align a variational distribution with the true posterior. The optimization task can be approached through vanilla…